OLYMPIADS VIII
RATIONAL NUMBERS
IMPORTANT FACTS AND FORMULAE
1) Fractions: Number of the form a/b, where a and b are whole numbers and b≠ 0, are called fraction, e.g., 2/3, 7/9, 11/9, etc.
2) Rational Numbers: Numbers of the form p/q, where p and q are integers and q≠ 0, are called rational number, e.g., 0, -3, 5/6, -7/8, 23/30 etc.,
Clearly, all fraction are rational numbers but all rational numbers are not fractions .
3) if N= set of natural numbers .
W= set of phone numbers .
I= set of integers.
Q= set of rational numbers.
Then N ⊂ W ⊂ I ⊂ Q, where '⊂' denotes ' is a subset of '
Thus, all natural numbers , whole numbers and integers are rational numbers.
4) Equivalent Rational Numbers: A rational number obtained by multiplying or dividing the numerator and denominator of a given rational number by the same nonzero integer is said to be equivalent to the given rational number.
Thus, p/q, (p/m)/(q/m) and pm/qm (where m is a nonzero integer) are equivalent rational numbers.
5) Standard Form of a Rational Number: A rational number a/b is said to be in standard form if
i) a and b are integers having no common divisors/factor other than 1, and
ii) b is a positive.
6) Comparison of Rational Numbers : Let a/b and c/d be two rational numbers.
Then,
i) a/b = c/d if ad = bc,
ii) a/b > c/d if ad > bc.
iii) a/b < c/d if ad< bc.
7) Every rational number can be represented by the unique point on the number line.
Positive rational numbers lie on the right side of 0 on the number line while negative rational numbers lie on the left side of 0.
Thus, -2/3 lies on the left side of 0, while 5/6 lies on the right side of 0 on the number line.
Remember
-5/-6 is written as 5/6 and so lies on the right side of 0 on the number line .
8) Addition Of Rational Numbers
Property. Satisfied or not satisfied
a) Closure property satisfied
The sum of two rational numbers is a rational number
b) commutative (Ordering) property. Satisfied a/b + c/d = c/d + a/b
c) Associative (Grouping property) property satisfied (a/b + c/d)+ e/f = a/b + (c/d + e/f)
d) additive identity 0 is the additive identity a/b + 0 = 0 + a/b = a/b
e) Existence of additive inverse additive additive inverse of a/b is - a/b.
a/b + (-a/b)= (-A/b) + a/b = 0
Note
i) Additive inverse of 0 is 0.
ii) - (-a/b)= a/b.
9) Subtraction of Rational Numbers
Property satisfied or Not satisfied
a) closure property satisfied
the difference of two rational numbers is a rational number.
b) commutative property not satisfied a/b - c/d ≠ c/d - a/b
c) Associative property. notes satisfied a/b - (c/d - e/f)≠ (a/b - c/d) - e/f
10) Multiplication of Rational Numbers
property satisfied or not satisfied
a) Closure property satisfied
the product of two rational numbers is rational numbers
b) commutative property satisfied a/b x c/d = c/d x a/b
c) associative property satisfied (a/b x c/d) x e/f = a/b x (c/d x e/f).
d) multiplicative identity 1 is the multiplicative identity. a/b x 1 = 1 x a/b = a/b
e) Existence of multiplicative inverse (or reciprocal) Multiplicative inverse a/b is b/a
a/b x b/a = b/a x a/b = 1
f) Distributive law of multiplication over addition. a/b x (c/d + e/f)= (a/b x c/d)+ (a/b x e/f)
Note:
i) 0 has no reciprocal.
ii) 1 and -1 are their own reciprocal.
iii) a/b x 0 = 0 x a/b = 0
iv) The reciprocal of reciprocal of a number is the number itself.
11) Division of Rational Numbers
property satisfied or not satisfied
a) closure property. satisfied only by non zero rational numbers.
The quotient of two non-zero rational numbers is a rational number.
b) Commutative property not satisfied a/b ÷ c/d ≠ c/d ÷ a/b
c) Associative property not satisfied (a/c ÷ c/d) ÷ e/f ≠ a/b ÷(c/d ÷ e/f).
Note
i) a/b ÷ 1 = a/b and a/b ÷ a/b = 1
ii) a/b ÷ c/d = a/d x d/c.
iii) Division by zero is not defined.
iv) a/b ÷ (-1)= -a/b ; -a/b ÷ 1 = -a/b; -a/b÷ (-1)= a/b.
v) For three rational numbers a, b and c,
a÷ (b + c) ≠ a ÷ b + a ÷ c;
a ÷ (b - c)≠ a ÷ b - a ÷ c
12) Absolute Value Of A Rational Number
If a is any rational number then
a if a > 0
|a|= - a if a < 0,
0 if a= 0
Note:
i) The absolute value of both a and - a is a
ii) if a and b are rational numbers then |a + b| ≤ |a| + |b| and |a x b|= |a| x |b|.
13) Between any two given rational numbers , there exist infinitely many rational numbers.
14) if x and y are two rational numbers then (x + y)/2 is a rational number between x and y, i.e., x < (x+ y)/2 < y.
Thus the idea of mean is used to find a rational number between two given rational numbers.
15) Decimal Representation of Rational Numbers
Rational numbers when expressed in decimal have either terminating or non terminating repeating (or recurring 0) forms.
A rational number can be expressed as a terminating decimal if the denominator has only 2 or 5 as factors.
Thus, 13/80 has a terminating decimal representation since 80 = 2⁴ x 5, but 13/24 has a non terminating repeating decimal representation as 24 = 2³ x 3.
16) Irrational Numbers :
Numbers which when expressed in decimals would be in nonterminating and non repeating from are called irrational numbers. These include:
a) square roots of numbers which are not perfect square, e.g., √2, √3, √5, √7, √11, √19, etc.
b) cube roots of numbers which are not perfect cubes, e.g., ³√2, ³√7, ³√13, etc.
c) π
iv) nonterminating and non repeating decimal numbers like 0.101001000100001000001....., 0.4141141114..... etc.,
EXERCISE - 1(A)
a) A Rational number of the form p/q is said to be a rational number if
a) p and q are whole numbers and q ≠ 0
b) p is a whole number and Q is a natural number.
c) p and q are integers and q ≠ 0
d) p and q are integers and p≠ 0, q≠ 0
2) Which of the following rational numbers is in the standard form?
a) -78/143 b) -29/37 c) 61-71 d) -97873
3) Between which of the following pairs of the number does the rational number -15/4 lies on the number line ?
a) 0 and -1 b) - 1 and- 2 c) - 2 and- 3 d) - 3 and - 4
4) The additive inverse of - 6/13 is
a) 6/13 b) 13/6 c) -13/6 d) 3/16
5) The multiplicative inverse of -6/13 is
a) 6/13 b) 13/6 c)!- 13/6 d) 3/16
6) The multiplicative inverse of -11/4 is
a) 4/11 b) -4/11 c) 11/4 d) -11/4
7) The reciprocal of x⁻¹ is
a) - x b) 1/x c) -1/x d) x
8) The multiplicative inverse of (x +1) + 1/(x -1) is
a) (x +1)/x² b) 1/(x -1) + (x -1) c) (x-1)/x² d) (x -1) - 1/(x +1)
9) The sum of the additive inverse and multiplicative inverse of 5 is
a) 24/5 b) - 24/5 c) 26/5 d) - 26/5
10) The product of additive inverse and multiplicative inverse of -1/4 is
a) 1 b) - 1 c) 0 d) -1/16
11) The reciprocal of a negative number
a) is a positive rational number
b) is a negative rational number
c) can be either a positive or a negative rational number
d) does not exist.
12) which of the following does not yield -1 as the final answer ?
a) (-a)÷ a b) a ÷ (-a) c)!(-1/a) ÷ a d) a x (1/a)
13) Which rational numbers are equal to the reciprocals?
a) 0, 1 b) -1, 0 c) -1,1 c) -1, 0, 1
14) Among the numbers √5 +√5, √5- √5, √5 x √5, √5÷√5, how many are rational ?
a) 1 b) 2 c) 3 d) 4
15) -1/9 + 3/5 = 3/5 +(-1/9) is an example to show that
a) rational numbers are closed under addition.
b) addition of rational numbers is Commutative
c) rational numbers are Distributive over addition.
d) addition of rational numbers is associative.
16) Which of the following sets of numbers is closed under subtraction ?
a) fractions b) negative numbers c) natural numbers d) rational numbers
17) Which of the following statements is not true ?
a) rational numbers are closed under addition.
b) rational numbers are closed under subtraction.
c) rational numbers are closed under multiplication.
d) rational numbers are close under division.
18) Which of the following expressions shows that rational numbers are associative under multiplication ?
a) 3/4 x (-5/6 x 7/8)= (3/4 x -5/6) x 7/8
b) 3/4 x (-5/6 x 7/8)= 3/4 x (7/8 x -5/6)
c) 3/4 x (-5/6 x 7/8)= (7/8 x 3/4) x -5/6
d) (3/4 x -5/6) x 7/8!= (-5/6 x 3/4) x 7/8.
19) -1/5 x [3/4 + (-6/7)]=?
a) [-1/5 x 3/4]+ [-1/5 x (-6/7)]
b) (1/5 x 3/4) - (-6/7)
c) 3/4 + (-1/5) x (-6/7)
d) [3/4 + (-6/7)] - 1/5
20) Which of the following statement is true ?
a) Every point on the number line represents a rational number.
b) the product of a rational number and its reciprocal is 0.
c) (13 x 15)⁻¹ = 13⁻¹ x 15
d) Rational numbers are not always closed under division.
21) Which of the following statements is not true?
a) (-7/8)+ (-8/11)= (-8/11)+ (-7/8)
b) 5/7+ [9/11+ (-3/4)]= (5/7+ 9/11)+ (-3/4)
c) 7/7 - (-5/6)= (-5/6) - 7/8
d) -7/-8 + 0 = 7/8
22) Which of the following relations hold true for three rational numbers x, y, z ?
a) x ÷ (y + z)= x÷ y + x ÷ z
b) x ÷ (y - z)= x÷ y - x ÷ z
c) (x ÷ y) x zn= x÷ (y x z)
d) x x (y ÷ z)= y +∆x ( x ÷ z).
23) Which of the following properties of rational numbers is exhibit below ?
9/5 x [ -7/3 + (-11/6)]= 9/5 x (-7/3) + 9/5 x (-11/6)
a) associative of addition
b) Associative of multiplication
c) Distributive of multiplication over addition
d) distributive of addition over multiplication
24) Which of the following is a rational number equivalent to -7/-3 ?
a) -35/15 b) 35/-15 c) 35/15 d) -35/30
25) if y be the reciprocal of rational number x then the reciprocal of y will be
a) x b) y c) x/y d) y/x
26) if y be the reciprocal of x then the reciprocal of y² in terms of x will be
a) 1/x b) x² c) 1/x² d) -1/x
27) If a is a rational number such that a< 0 then |a|= ?
a) a b) - a c) -(-a) d) 1/a
28) By what rational number should -5/24 be multiplied to get 10 ?
a) 12 b) -12 c) 48 d) -48
29) Which of the following holds true for two rational numbers a and b?
a) (a +b)⁻¹ = a⁻¹ + b⁻¹
b) (a - b)⁻¹ = a⁻¹ - b⁻¹
c) (a x b)⁻¹ = a⁻¹ x b⁻¹ d) none
30) What should be added to -3/4 to get 7/6 ?
a) 11/24 b) 9/24 c) 10/25 d) 23/12
31) What should be subtracted from -7/11 to get -2 ?
a) 15/11 b) -29/11 c) 29/11 d) -15/11
32) What should be subtracted from -7/8 so as to get 5/12 ?
a) 31/24 b) 8/5 c) - 31/24 d) -6/8
33) What should be subtracted from -3/4 to get 5/6 ?
a) - 19/12 b) -11/12 c) 1/12 d) -1/12
34) The sum of two rational numbers is - 3. If one of the number is -7/5 then the other number is
a) -8/5 b) 8/5 c) - 6/5 c) 6/5
35) The product of two numbers is -16/35. If one of the number is - 15/14 the other is
a) - 2/5 b) - 8/3 c) 8/15 d) 32/75
36) Which of the following is equivalent to (-3/10 + 7/15 + 3/-20 + -9/10 + 13/15 + 13/-20)?
a) 2/3 b) -2/3 c) 5/6 d) -5/6
37) if we divide the sum of -13/5 and 12/7 by the product of -31/7 and -1/2, we get
a) 2/5 b) -2/5 c) -3/5 d) 1/5
38) If x = -4/11 then which of the following rational numbers lies between x and |x| ?
a) -2/11 b) 5/8 c) -11/15 d) 7/3
39) Which of the following statements is true ?
a) 8/11÷[(-3/7)÷1/4]=[8/11÷(-3/7)]÷1/4.
b) (9/10 - 17/20)÷ 14/5= (9/19 ÷ 14/5) - (17/20÷ 14/5)
c) (-6/7)÷ 0= 0 d) -21/34 ÷ 34/-21= 1
40) Between any two given rational numbers , we can find
a) one and only one rational number
b) only 2 rational numbers
c) only 10 rational numbers
d) infinitely many rational numbers.
41) Which of the following is a rational number between x and y ?
a) (x +y)/2 b) (x -y)/2 c) xy/2 d) (x ÷y)/2
42) A rational number between 1/5 and 1/2 is
a) 1/10 b) 1/20 c) 7/10 d) 7/20
43) The rational number which lies exactly the middle of 1/3 and 1/4 is
a) 5/12 b) 7/24 c) 8/258 d) 13/48
44) Which of the following is a rational number between 1/4 and 1/3 ?
a) 7/24 b) 8/15 c) 13/48 d) both a and c
45) Identify a rational number between 1/3 and 4/5.
a) 1/4 b) 9/10 c) 17/30 d) 17/10
46) The sum of a rational number and its reciprocal is 10/3. The number is
a) 3 b) 1/3 c) - 3 d) both a and b
47) Which of the following is not true for rational number a and b ?
a) |a| = a and|-a|= a b) |a + b| ≤ |a| + |b| c) |a x b| = |a| x |b| d) |a - b| ≥ |a| - |b|
48) The arrangement of rational numbers -7/10 , 5/-8, 2/-3 in ascending order is
a) 2/-3, 5/-8, -7/10 b) -7/10, 2/-3, 5/-8 c) 5/-8, -7/10, 2/-3 d) -7/10, 5/-8, 2/-3
49) Which number is in the middle of -1/6, 4/9, 6/-7, 2/5 and -3/4 are arranged in descending order ?
a) 2/5 b) 6/-7 c) -1/6 d) 4/9
50) (-1/2- 2/3+4/5-1/3+1/5+3/4)/(1/2+2/3-4/3+1/3-1/5-4/5) is simplified to
a) -3/10 b) -10/3 c) -2 d) 1
51) If P= (-3/4)³, Q= (-2/5)², R= (0.3)², S= (-1.2)² then
a) P>Q>R>S b) S> P>Q>R c) S>R>P>Q d) S>Q>R>P
52) identify the one that is/are greater than n, if n= 7/9.
i) 1/n ii) (n+1)/n iii) (n +1)/(n -1)
a) i) only b) i) and ii) only c) ii) and iii) only d) i) and iii) only
54) which of the following statements is true?
a) 7/9<9/11<11/13 b) 7/9<9/11> 11/13 c) 9/11<11/13<7/9 d) 9/11<7/9<11/13
55) State which of the following numbers are rational
i) √3 x √48 ii) 22/7 iii) 3√2 iv) π
a) i) and ii) only b) ii) and iv) only c) i) and iii) only d) iii) and iv) only
56) when (1/2-1/4+1/5-1/6) is divided by (2/5-5/9+3/5-7/18), the result is
a) 37/8 b) 19/6 c) 33/10 d) 51/10
57) Which of the following can be used the compute (54 x 9/2)?
a) (50 x 4)+(4 x 9/2) b) (54 x 40)+(54 x 1/2) c) (50 x 9/2)+(4 x 4) d) (54 x 1/2)+(50 x 4) + (4 x 4)
58) 3 rational numbers lying between -3/4 and 1/2 are
a) -5/4,0,1/4 b) -1/4,0,1/4 c) -1/4,1/4,3/4 d) -1/2,0,3/4
59) Let a= (4÷3)÷(3÷4, b= 4÷(3÷3)÷4, c= 4÷3÷(3÷4).
The maximum value among the three is
a) a b) b c) c d) all are equal
60) What fraction should be added to the sum of 23/4, 24/5 and 59/8 to make the result a whole number?
a) 1/40 b) 1/20 c) 3/40 d) 4/40
61) if x is a positive number then which of the following has the greatest value?
a) x/x b) x/(x +1) c) (x +1)/x d) (x +2)/(x +3)
62) If we multiply a fraction by itself and divide the products by reciprocal, the fraction thus obtained is 222/27. The original fraction is
a) 8/27 b) 4/3 c) 8/3 d) none
63) Simplify: [2/3 x (-5/4)]+[(-10/3) x 5/2] - [(-16/3) x (-55/32)]/[3/2 x {(-9/14) x (-1/7}
64) Which of the following statement is/are true ?
i) -5/0 is a negative rational number.
ii) the reciprocal of 1/a, if a= 0, is 1/0.
iii) 1 ÷ (-1/4)= -4.
iv) For rational number x, y and z, we have x + (y . z)= (x + y). (x + z).
a) both i) and ii) b) only iii) c) i), ii), iv) d) ii, iii, iv
65) Mr Gopal gives 1/2 of his property to his wife and 1/2 of the rest to is son. The remainder is divided equally between his two daughters. The share of each daughter is
a) 1/4 b) 1/6 c) 1/8 d) 2/3
66) find the sum: 1/2 +1/6 +1/12+ 1/20 + 1/30+ 1/42+ 1/56 + 1/72+ 1/90 + 1/110 + 1/132
a) 7/8 b) 11/12 c) 15/16 d) 17/18
67) The sum of the first 47 terms of the series
1/2+1/3-1/4-1/2-1/3+1/4+1/2+1/3-1/4 -..... is
a) -1/2 b) -1/4 c) 1/4 d) none
68) By how much does 6/(7/8) exceed (6/7)/8 ?
a) 49/8 b) 27/4 c) 31/4 d) 47/6
69) Aruna earns twice as much in the month of June as in the each of the other months of the year. What part of the entire annual earnings was earned in June ?
a) 1/6 b) 1/7 c) 2/11 d) 2/13
70) A waiter's salary consists of his salary and tips. During one week. his tips were 5/4 of his salary. What part of his income came from tips ?
a) 4/9 b) 5/4 c) 5/8 d) 5/9
71) a man read 3/8 th of a book on one day and 4/5th of the remainder on another day. If there were 30 pages unread, how many pages did the book contain ?
a) 240 b) 300 c) 405 d) 600
72) A school organized a picnic and 1/5 of the girls and 1/8 of the boys participated in the same. What fraction of the total number of student joined the picnic .
a) 2/13 b) 13/40 c) 1/40 d) data inadequate
73) Four children A, B, C and D divide a bag of sweets. A takes 1/3 of them, B 2/5 th of the remainder and the rest is equally shared between C and D. What fraction of the sweets did C or D get ?
a) 1/4 b) 1/5 c) 1/6 d) 1/17
74) Match the Following:
a) if 18/45 and x/5 are equivalent then x= i) -1
b) Sum of a rational number and its additive inverse. ii) 1
c) {(-65/14) ÷(13/-7)} x (-2/5) iii) 2
d) Product of a Rational number and its reciprocal. iv) 0
75) If 1/8 of a pencil is yellow, 1/2 of the remaining is green and the remaining is 7/2 cm is black then the length of the pencil is
a) 6cm b) 7cm c) 8cm d) 10cm
76) Rohan had a bag of sweets. On the first day, he distributed one third of the sweets. On the second day, he gave away one quarter of the remaining sweets . if he gave away 8 sweets on the second day, how many sweets were there in the bag to begin with ?
a) 32 b) 48 c) 60 d) 96
77) oyne fruit salad recipe required 1/2 cup of sugar. Another recipe for the same fruit salad requires 2 tablespoon of sugar. If 1 tablespoon is equivalent to 1/16 Cup, how much more sugar does the first recipe require ?
a) 3/8 cup b) 5/8 cup c) 4/5 cup d) 6/5 cup
78) Eight people plan to share equally the cost of a rental car. If one person withdraws from the arrangement and the other share equally the entire rent of the car then the share of each of the remaining persons increased by
a) 1/8 b) 1/7 1/9 d) 7/8
79) In an examination, a student was asked to find 3/14 of a number. By mistake, he found 3/4 of it. if his answer was 150 more than the correct answer then the given number is
a) 180 b) 240 c) 280 d) 290
80) A student was asked to divide a number by 17/8. Instead , he actually multiplied it by 17/8 and hence got 225 more than the expected answer. What was the expected answer ?
a) 64 b) 126 c) 136 d) none
81) Which of the following options does not depict the distributive law?
a) a(b + c)= ab + ac b) a(b - c)= ab - ac c) a(b ÷ c)= ab ÷ ac d) both b and c
82) Which of the following does not have a terminating decimal representations ?
a) 11/64 b) 13/625 c) 67/200 d) 25/192
EXERCISE - 1(B)
1)The multiplicative inverse of a rational number is also termed as its____.
2) The multiplicative inverse of 4/3 is____
3) the reciprocaller - 1 is _____
4) The reciprocal of 0 is _____.
5) Rational number can be____ and___ in any order.
6) The multiplicative inverse of a negative rational number is a____ rational number.
7) The additive inverse of a negative rational number is a ____rational number.
8) -5/6 + 1/= 1/7 + (-5/6) depicts ____property of addition of rational numbers.
9) The numbers ____and___ are their own reciprocals .
10) _____has no reciprocal.
11) The negative of a negative rational number is always a ____rational number.
12) Two rational numbers whose absolute value is 1/3 are ___ and____.
13) The reciprocal of |-6/7| is ____.
14) When a rational number is multiplied by its multiplicative inverse, we get ___ as product.
15) -5/7 is____ then -3.
16) Among -5/11, 5/13 and -5/7, the greatest rational number is ____.
17) The idea of____ helps us to find a rational number between two given rational numbers .
18) -6/7 ÷ 6/7= ___
19) ____÷ (-1)= 5/17
20) 7/15 ÷ ____= 1.
21) ____ ÷ 1 = -8/15.
22) (-11/17)÷ ___= 1
23) 17/8 ÷ ____= -10 .
24) -13/9 x _____= -2/3
25) (-1) + _____= -3/7
26) -2/3 - ____= 1/15.
TRUE OR FALSE
1) Every fraction is a rational number.
2) The negative of 0 does not exist.
3) Every whole number is a rational number with denominator 1.
4) Every rational number can be represented on the number line.
5) The reciprocal of reciprocal of a number is the number itself.
6) Every rational number has a reciprocal.
7) There exists only one rational number which which is equal to its reciprocal.
8) -4/5 is smaller than -1.
9) Subtraction of rational numbers is commutative.
10) For every rational number a/b, we have a/b = (a + m)/(b + m), where m is any non zero integer.
11) If x and y are negative rational numbers then so is x + y.
12) - 1 is not the reciprocal of any rational number.
13) The multiplicative inverse of -5/6 is 6/5.
14) The additive inverse of 1/3 is -3.
15) 1 is the only number which is its own reciprocal.
16) 0 is the smallest rational number.
17) We have a definite number of rational numbers between two rational numbers.
18) 7/0 is a rational number.
19) The additive inverse of -9/-10 is -9/10.
20) 0 x 3/4 = 3/4 x 0 implies that 0 is the multiplicative identity for rational numbers.
21) The rational numbers 1/3 and -5/3 are on the opposite sides of 0 on the number line.
22) The rational number -3/-8 can be depicted on either side of zero on the number line.
23) If x/y is the additive inverse of a/b then x/y - a/b = 0.
24) If x+ y = 0 then -y is known as the negative of x, where x and y are rational numbers.
25) For every rational numbers a, b and c, a + (b x c)= (a + b) x (a + c).
26) There are countless rational numbers between 2/3 and 5/6.
27) For rational numbers a/b and c/d, if a/b < c/d then -a/b < - c/d.
28) If a/b and c/d are two rational numbers such that c/d ≠ 0 then a/b + c/d = b/a x c/d.
29) If a, b and c are three rational numbers then (a - b) - c = a - (b - c).
30) Equivalent rational numbers correspond to the same point on the number line.
31) a/b - c/d = a/b + (additive inverse of c/d).
32)!a/b ÷ c/d = a/b x (multiplicative inverse of c/d).
33) if x < y then|x |<|y|.
34) For every rational number a, |a⁻¹|= |a|⁻¹.
35) Absolute Value of a rational number is its numerical value regardless of its sign.
36) Two equidistant rational numbers on opposite sides of zero on the number line have the same absolute value.
EXPONENTS
EXERCISE - 2(A)
A) 1⁵ B) 5⁰ C) 0⁵ D) 5¹
a) A and B b) B and C c) A and C d) A and D
2) (6⁰ - 2⁰)(6⁰+2⁰)= ?
a) 0 b) 1 c) -1 d) 2
3) The multiplicative inverse of 10⁻¹⁰⁰ is
a) 10 b) 100 c) 10¹⁰⁰ d) 1/10¹⁰⁰
4) The multiplicative inverse of (-4/9)⁻⁹⁹
a) (-4/9)⁹⁹ b) (4/9)⁹⁹ c) (9/-4)⁹⁹ d) (9/4)⁹⁹
5) If 5ˣ = 3125 then the value of 5ˣ⁻³ is
a) 25 b) 125 c) 625 d) 1625
6) The value of (256)⁵⁾⁴ is
a) 512 b) 984 c) 1024 d) 1032
7) The value of 27⁻²⁾³ lie between
a) 0 and 1 b) 1 and 2 c) 2 and 3 d) 3 and 4
8) The value of (32/243)⁻⁴⁾⁵ is
a) 4/9 b) 9/4 c) 16/81 d) 81/16
9) The value of (-1/216)⁻²⁾³ is
a) 36 b) -36 c) 1/36 d) -1/36
10) 120m²n⁻³/60m⁵n⁻² (m ≠0, n≠ 0) when expressed in simplest form becomes
a) 2m³/n b) 1/2m³n c) 2/m³n d) 2n/m³
11) The value of [2 - 3(2- 3)⁻¹]⁻¹ is
a) 5 b) -5 c) 1/5 d) -1/5
12) Evaluate: 5¹⁾⁴ x (125)⁰·²⁵
a) √5 b) 5 c) 5√5 d) 25
13) (256)⁰·¹⁶ x (256)⁰·⁰⁹ =?
a) 4 b) 16 c) 64 d) 256
14) The value of (8⁻¹ - 9⁻¹)⁻¹ ÷ (4⁻¹ - 9⁻¹)⁻¹ is
a) 5 b) 10 c) 14 d) 25
15) If p= (2⁻² - 2⁻³), q= (2⁻³ - 2⁻⁴) and r= (2⁻⁴ - 2⁻²) then the value of 3pqr equal
a) 9/1024 b) -9/2048 c) -63/2048 d) -63/1024
16) (64)⁻¹⁾² - (-32)⁻⁴⁾⁵ =?
a) 1/8 b) 3/8 c) 1/16 d) 3/16
17) (16)⁰·¹⁶ x (16)⁰·⁰⁴ x (2)⁰·² is
a) 1 b) 2 c) 4 d) 16
18) If m,n are positive integers (n > 1) such that mⁿ = 121 then the value of (m -1)ⁿ⁺¹ is
a) 1 b) 11 c) 1000 d) 12321
19) When simplified, (x⁻¹ + y ⁻¹) is equal to
a) (x+y)/xy b) xy c) 1/xy d) xy/(x + y)
20) Which of the following is the same as (-5/7)⁻⁷ ?
a) (5/6)⁻⁷ b) -(5/7)⁻⁷ c) (7/5)⁷ d) (-7/5)⁷
21) The value of 5³ ÷ 5⁻⁴ is
a) 5⁻¹ b) 5⁷ c) 5 d) 5⁻⁷
22) The value of (7⁻¹ - 8⁻¹)⁻¹ - (3⁻¹ - 4⁻¹)⁻¹ is
a) 12 b) 44 c) 56 d) 68
23) Which of the following is not true?
a) 343 x 7ⁿ⁻²= 7ⁿ
b) (2ⁿ)/4 = 2ⁿ⁻²
c) 25(5ⁿ⁻²)= 5ⁿ
d) 4ⁿ⁻¹ = 4ⁿ/4
24) Which of the following is not true to y⁶
a) (√y⁶)² b) ³√y¹⁸ c) (y¹⁾³)¹² d) (y²⁾³)⁹
25) If 3ˣ⁺ʸ = 81 and 81ˣ⁻ ʸ = 3⁸ then the values of x and y are
a) -1.-3 b) -1,3 c) 1,3 d) 3,1
26) When simplified and expressed with negative exponens, the expression (x + y)⁻¹.(x⁻¹ + y⁻¹) is equal
a) x⁻² + 2x⁻¹y⁻¹+ y⁻² b) x⁻¹ y⁻¹ c) x⁻²+ 2⁻¹ x⁻¹ y⁻¹ + y⁻² d) x⁻² + y⁻²
27) By what number should we multiply (-8)⁻¹ so that the product may be equal to (10)⁻¹ ?
a) 4/5 b) 5/4 c) -4/5 d) -5/4
28) If x= 1/{(3/2)⁻² x (2/3)⁻⁴} then the value of x⁻³ is
a) (2/3)¹⁰ b) (2/3)⁻⁶ c) (3/2)⁻¹² d) (3/2)⁸
29) Each of the numbers 1,2,3 and 4 is substituted, in some order for a,b,c and d. The greatest possible value of aᵇ + cᵈ is
a) 14 b) 19 c) 66 d) 83
30) If {(p⁻¹q²)/(p³q⁻²)} ÷ {(p⁶q⁻³)/(p⁻²q³)}= pᵃqᵇ then the value of a+ b, where p and q are different positive primes, is
a) -2 b) -1 c) 0 d) 1
31) If √2ⁿ = 64 then the value of n is
a) 2 b) 4 c) 6 d) 12
32) Out of the following, which one is the greatest?
a) (0.008)¹⁾³ b) 0.01¹⁾² c) 0.2² c) 1/100
33) (343 x 49)/(2 6 x 16 x 81)=?
a) 7⁵/6⁷ b) 7⁵/6⁸ c) 7⁶/6⁷ d) 7⁴/6⁸
34) (1000)¹²÷ +10)³⁰=?
a) 1000² b) 10 c) 100 d) 100²
35) 8⁷ x 2⁶ ÷ 8²·⁴ = 8^?
a) 6.6 b) 8.6 c) 9.6 d) 10.6
36) (0.04)² ÷ (0.008) x (0.2)⁶= (0.2)^?
a) 5 b) 6 c) 8 d) 7
37) (25)⁷·⁵ x (5)²·⁵ ÷ (125)¹·⁵ = 5^?
a) 8.5 b) 13 c) 16 d) 17.5
38) If 2⁰·² x 64 x 8¹·³ x 4⁰·² = 8ˣ then the value of x is
a) 2.5 b) 2.7 c) 3.5 d) 3.7
39) If 2ˣ⁺¹ = 8ˣ then x has the value
a) -1/3 b) 1/2 c) 1 d) 3
40) Which of the following is equal to (3)⁻³ - √81/√25 + (√64)⁻²⁾³/(16)⁻¹⁾⁴ ?
a) -1/541/54-341/270341/270
41) Match the Following
Column - I. Column II
a) If 2³⁴÷ 2¹⁶= 2ᵏ then k is i) 32
b) [(-8/13)⁻¹ ÷(16/5)⁻¹]÷ (-5/2)⁻¹=. ii) 9
c) If {25(a⁴)²}/{(5a)³ a⁵ 2⁵}= 1/(5n) then n is iii) 18
d) If +2/7)⁻⁶(14/9)⁻⁶ = (4/m)⁻⁶ then m is. iv) 13
Choose the correct combination:
a) a- iv, b- iii, c- i, d- ii
b) a- ii, b- i, c- iv, d- iii
c) a- iii, b- ii, c- iv, d- i
d) a- iii, b- iv, c- i, d- ii
42) If 3³·⁵ x 21² x 42²·⁵ ÷ 2²·⁵ x 7³·⁵ = 21ˣ then x is
a) 6.5 b) 8 c) 10 d) 12.5
43) What is the value of x if pˣ/pʸ = p¹⁰ and (pʸ)³ = pˣ for p> 1 ?
a) 5 b) 14 c) 20 d) 25
44) Find the value of 2³⁰ + 20³⁰ + 2³⁰+ 2³⁰.
a) 2³² b) 2³⁶ c) 8³⁰ d) 8¹²⁰
45) If 4ˣ + 4ˣ + 4ˣ + 4ˣ + 4ˣ + 4ˣ + 4ˣ + 4ˣ = 1/512 then what is the value of -3/x ?
a) -0.75 b) -4.25 c) 0.50 d) 0.75
46) Given that 9ⁿ + 9ⁿ + 9ⁿ = 3²⁰¹³, what is the value of n ?
a) 1005 b) 1006 c) 2011 d) 6019
47) If 3ˣ⁻¹ + 3ˣ⁺¹ =90 then x is
a) 0 b) 1 c) 2 d) 3
48) If 2ⁿ⁻¹ + 2ⁿ⁺¹ = 320 then n is
a) 5 b) 6 c) 7 d) 8
49) Income of a company doubles after every 1 year. If the initial income was Rs2 lakhs, what would be the income after n years (in lakh of rupees)?
a) 2ⁿ⁻¹ b) 2ⁿ c) 2ⁿ⁺¹ d) 2 + 2ⁿ
50) Breeding of a certain Species of insects occurs at such a rate that everyday the total number of such insects in a closed glass jar is double the number on the previous day. There was just one insect in the jar on 1st of a certain month and the jar was full to the brim with these insects in 28th of the same month. On which day of the month was the jar quarter full?
a) 7th b) 14th c) 26th d) none
51) the microbes in a petri dish double every minute and the petri dish becomes full in 1 hour. In how much time was the dish 1/32 full ?
a) 12 minutes b) 32 minutes c) 45 minutes d) 55 minutes
52) If (x/y)ⁿ⁻¹ = (y/x)ⁿ⁻³ then the value of n is
a) 1/2 b) 1 c) 2 d) 7/2
53) If 2²ⁿ⁻¹ = 1/8ⁿ⁻³ then the value of n is
a) -2 b) 0 c) 2 d) 3
54) If (25)ˣ = (125)ʸ then x: y equal to
a) 1:1 b) 1:3 c) 2:3 d) 3:2
55) If 3ˣ = √3/9 then the value of x is
a) -3/2 b) -2 c) 2/3 d) 3
56) If (9/4)ˣ(8/27)ˣ⁻¹= 2/3 then the value of x is
a) 1 b) 2 c) 3 d) 4
57) If 5²ˣ⁺¹ ÷ 25= 125 then the value of x is
a) 1 b) 2 c) 4 d) 5
58) The cells of a bacteria double in every 30 minutes. Beginning with a single cell, how many cells will be there after 8 hours ?
a) 2⁴ b) 2⁸ c) 2¹⁶ d) 2¹⁷
59) The solution of 3³ˣ⁺⁵ x 2³ˣ⁺³ = 9 is
a) -1 b) 0 c) 1 d) 2
60) If ((25)²ˣ⁺¹x (125)⁵)/(625)²= (3125)³ˣ then the value of x is
a) 0 b) 9/11 c) 1 d) 11/9
61) What number will replace the question mark in the following equation ?
(√8 x √8)¹⁾² + 9¹⁾² = (?)³ + √8 - 340
a) 7 b) 9 c) 18 d) ³√337
62) The simplified value of (2x 3ⁿ⁺¹+ 7 x 3ⁿ⁻¹)/(3ⁿ⁺² - w(1/3)¹⁻ ⁿ is
a) -1 b) 0 c) 1 d) 3
63) If m= (2⁻² - 2⁻³), n= (2⁻³ - 2⁻⁴) and p= (2⁻⁴ - 2⁻²) then the value of m³ + n³ + p³ is
a) -3/1024 b) -9/2048 c) 3/1024 d) 9/2048
64) The value of (125/64)²⁾³ ÷ 1/(625/256)⁻¹⁾⁴ + [{√36/³√64}⁰]¹⁾² is
a) 4/9 b) 6/5 c) 9/8 d) 9/4
65) If 2⁹⁹⁸ - 2⁹⁹⁷ - 2⁹⁹⁶ + 2⁹⁹⁵ = m . 2⁹⁹⁵ then the value of m is
a) 1 b) 2 c) 3 d) 4
66) The value of {(p + 1/p)ᵐ(p - 1/q)ᵐ}/{(q + 1/p)ᵐ(q - 1/p)ᵐ} is
a) p/q b) (p/q)ᵐ c) (p/q)²ᵐ d) (q/p²ᵐ
67) The value of [⁶√2{(625)³⁾⁵x (1024)⁻⁶⁾⁵÷ (25)³⁾⁵}¹⁾²/{(³√128)⁻⁵⁾². (125)¹⁾⁵} is
a) -1 b) 1 c) -1/2 d) 1/2
68) For what value of x is the given statement false ?
a) 3x² < (3x)².
a) -3 b) 0 c) 1/3 d) 1
69) Number of prime factors in (216)³⁾⁵ . (2500)²⁾⁵. (300)¹⁾⁵ is
a) 6 b) 7 c) 8 d) none
70) (xᵃ/xᵇ)ᵃ⁺ᵇ. (xᵇ/xᶜ)ᵇ⁺ᶜ . (xᶜ/xᵃ)ᶜ⁺ᵃ =?
a) 0 b) xᵃᵇᶜ c) xᵃ⁺ᵇ⁺ᶜ d) 1
71) (xᵇ/xᶜ)ᵇ⁺ᶜ⁻ᵃ . (xᶜ/xᵃ)ᶜ⁺ᵃ⁻ᵇ . (xᵃ/xᵇ)ᵃ⁺ᵇ⁻ᶜ =?
a) xᵃᵇᶜ b) 1 c) xᵃᵇ⁺ᵇᶜ⁺ᶜᵃ d) x ᵃ⁺ᵇ⁺ᶜ
72) (xᵃ/xᵇ)¹⁾ᵃᵇ.(xᵇ/xᶜ)¹⁾ᵇᶜ . (xᶜ/xᵃ)¹⁾ᶜᵃ =?
a) 1 b) x¹⁾ᵃᵇᶜ c) x¹/⁽ᵃᵇ⁺ᵇᶜ⁺ᶜᵃ⁾ d) none
73) If aˣ = b, bʸ = c and cᶻ= a then the value of xyz is
a) 0 b) 1 c) 1/abc d) abc
74) The expression (x⁻²ᵖ y³ᑫ)⁶ ÷ (x³ y⁻¹)⁻⁴ᵖ after simplification becomes
a) dependent on both x and y b) independent both x and y c) dependent on x alone d) dependent on y alone
75) The standard form for 0.000085 is
a) 85x10⁵ b) 85x 10⁻⁶ c) 8.5 x 10⁻⁵ d) 8.5 x 10⁻⁴
76) The standard form for 789000000 is
a) 7.89 x 10⁸ b) 0.789 x 10⁹ c) 7.89 x 10⁻⁸ d) 0.789 x 10⁻⁹
77) Human body has 1 trillion cells. This figure when expressed in standard form is equal to
a) 10⁸ b) 10⁹ c) 10¹⁰ d) 10¹²
78) The population of a country is 3.2 x10⁶, if there are 8 x 10⁵ children then the number of adults is
a) 3 x 10³ b) 2.4 x10⁵ c) 2.4 x 10⁶ d) 8 x 10³
79) Mars is 33900000 miles away from the Earth. How is this distance written in scientific notation ?
a) 339 x 10⁵ miles b) 3.39 x 10⁷ miles c) 33.9 x 10⁶ miles d) 339 lakh miles
80) There are 86400 seconds in a day. How many days long is a second? Express your answer in scientific notation up to 3 decimal places.
a) 1.157 x 10⁻⁵ b) 1.157 x 10⁻⁶ c) 1.234 x 10⁻⁵ d) 1.432 x 10⁻⁴
81) (10 + 10³) equal to
a)!1 x 10⁴ b) 1.1 x 10² c) 1.01 x 10³ d) none
82) The value of (8⁻²⁵ - 8⁻²⁶) is
a) 7 x 8⁻²⁵ b) 7x 8⁻²⁶ c) 8 x 8⁻²⁶ d) none
83) Which is greater 2¹² or 3⁸ ?
a) 2¹² b) 3⁸ c) both are equal d) cannot be compared
84) Which of the following is the greatest?
a) 2¹⁾² b) 3¹⁾³ c) 4¹⁾⁴ d) 6¹⁾⁶
85) Which of the following is the greatest?
a) 18⁶ b) 21¹² c) 45⁶ d) 54⁴
86) The ones digit in 5¹⁰⁰ is
a) 0 b) 5 c) cannot be determined d) none
87) The ones digit in 81¹⁰ is
a) 0 b) 1 c) 9 d) none
88) The ones digit in 17²¹ is
a) 7 b) 9 c) 3 d) 1
89) The ones digit in 29¹⁰ is
a) 1 b) 9 c) 7 d) 6
90) The ones digit in 3¹⁷ is
a) 3 b) 9 c) 7 d) 1
EXERCISE - 2(B)
1) In aᵇ, a is called the ____and b is called the____.
2) The value of (-3⁻⁴) is____
3) a⁷ x a⁻¹⁴= ____
4) (2⁰+ 3⁰)= ____
5) The expression for 5⁴ with a negative exponent is____
6) The multiplicative inverse of 10¹⁰ is _____
7) (-2)⁴ ÷ ⁴2 is equals to_____
8) The value of (-8)⁵÷ 8⁵ is ____
9) 3³ x 3⁻³=____
10) The expression for 8⁻³ as a power with the base 2 is _____
11) 1/343 Expressed as a power with base 7 is____
12) On dividing 9⁵ by _____, we get 9.
13) The one digit is 10¹⁰⁰ is____
14) (a/b)ⁿ ÷ (c/b)ⁿ when simplified is equals to____
15) If p= 10, q= 1 then the value of (p + 1)ᑫ⁻¹ is equal to___
16) The value of (1/2)⁻²+ (1/3)⁻² +(1/4)⁻² is____
17) On multiplying____ by 3⁻⁵, we get 3⁵.
18) On multiplying (7/3)⁴ by ____, we get 7⁴.
19) The value of x for which (3/7)⁴ x (3/7)⁻⁷= (3/7)²ˣ⁻¹ is ____
20) If 3. 3ⁿ= 3 then the value of n is ____.
21) Very small numbers can be expressed in standard form by using___ exponents.
22) Very large numbers can be expressed in standard form by using___ exponents.
23) To add the numbers given in standard form, we first convert them into ___ form or into numbers with___ exponents .
24) The standard form of 56780000 is____
25) The standard form of 78600000000 is
26) 1 nanometer = 1/1000000000 metres, which when expressed in standard form is ___ metres.
27) The standard form of 0.000000009 is ____
28) 7.85 x 10⁻⁴ in usual form is____
29) The usual form of 8.0101 x 10⁶ is____
30) The usual form of 6.0606 x 10⁻⁵ is____
TRUE OR FALSE
1) a⁰ - b⁰= 0.
2) aᵖ x bᑫ = (ab)ᵖᑫ.
3) (10)⁻¹⁰⁰ = (100)⁻¹⁰.
4) (-1)⁻¹= -1.
5) (2⁰ + 3⁰ - 4⁰)=1.
6) The reciprocal of (4/5)⁻² is (5/4)².
7) 1⁰ is equivalent to 0¹.
8) Both 7² and 2⁷ are two digit numbers.
9) 10⁵ x 10⁵= 10¹⁰.
10) (3³ + 3⁵) is the same as (³ x 3⁵).
11) 2¹⁰⁰ is the same as (100)².
12) 2ᵐ x 2ⁿ= 2ᵐⁿ.
13) n⁻¹⁾³ x n¹⁾³= 1.
14) The standard form of 8800000 is 88 x 10⁵.
15) The standard form of 0.00005 is 5 x 10⁻⁵.
16) (-6)⁻² x (-6)⁻³= (-6)⁻⁶.
17) aᵐ x bᵐ = (a + b)ᵐ.
18) (16)² > 2¹⁶.
19)5¹⁾⁴ x 5⁰·⁷⁵= 5.
20) [(2)⁻²]⁻³ is the same as 2⁶.
21) The one digit of (106)¹⁰⁶ is 6.
22) (81/256)² is equivalent to (3/4)⁸.
23) (-A)⁻ᵐ= 1/aᵐ.
24) The exponential form for (-2)⁴ x (7/2)⁴ is 7⁴.
25) (aᵖ/bᑫ)= (a/b)ᵖ⁻ᑫ .
26) 5. (2ⁿ⁺¹)+ 10(2ⁿ⁻¹) is the same as 15(2)ⁿ
SQUARES and SQUARE ROOTS
EXERCISE - 3
1) Which of the following will have a 9 at the units place ?
a) 31² b) 57² c) 91² d) 99²
2) Each of the following numbers has 6 ar the units place except
a) 34¹ b) 46² c) 68² d) 114¹
3) Which of the following is not a perfect square ?
a) 361 b) 1128 c) 1156 d) 1681
4) Which of the following is not a perfect square ?
a) 8281 b) 6889 c) 9925 d) 9881
5) If a 4 digit perfect square number is such that the number formed by the first two digits and the number formed by the last two digits are also perfect squares then the four digit number is
a) 1664 b) 1681 c) 3616 d) 6416
6) 32² will have the same digit at the units place as
a) 44² b) 68² c) 76² d) 97²
7) The digit in the units place in the square root of 15876 is
a) 2 b) 4 c) 6 d) 8
8) Which of the following is not a perfect square?
a) 22500 b) 6760000 c) 19600000 d) 121000000
9) A perfect square can have only one of the following digits at units place. Which is it ?
a) 2 b) 3 c) 1 d) 7
10) The value of √{176 + √2401} is
a) 14 b) 15 c) 18 d) 24
11) The value of √{248+ √(52 +√144)} is
a)14 b) 16 c) 18 d) 19
12) The value of √[41 +√{21+ √(19 - √9)}] is
a) 3 b) 5 c) 6 d) 6.4
13) √(225/729) - √(25/144) ÷ √(16/81)=?
a) 1/48 b) 5/48 c) 5/16 d) none
14) If 4050/√x = 450 then x =
a) 9 b) 49 c) 81 d) 100
15) if 52/x =√(169/289) then the value of x is
a) 52 b) 58 c) 62 d) 68
16) which number should replace both the question marks in the following equation?
?/1776= 111/?
a) 343 b) 444 c) 543 d) 644
17) What should come in place of both the question marks in the following equation?
?/√128= √162/?
a) 12 b) 14 c) 144 d) 196
18) the square root of (272² - 128²) is
a) 144 b) 200 c) 240 d) 256
19) if 1537# is a perfect square then the digit which replaces # is
a) 2 b) 4 c) 5 d) 6
20) The number of perfect square numbers between 50 and 1000 is
a) 21 b) 22 c) 23 d) 24
21) What percentage of the numbers from one to hundred have squares that end in the digit 9?
a) 5 b) 10 c) 11 d) 20
22) If √2ⁿ = 64 then n equal to
a) 6 b) 8 c) 10 d) 12
23) The square root of a perfect square number having 71 digits will have how many digits ?
a) 35 digits b) 36 digits c) either a or b d) cannot be ascertained
24) which of the following number, some of whose digits have been replaced by #, could possibly by the perfect square of a 3 digit odd number ?
a) 65 ###1 b) 10 ###4 c) 9##1 d) 9###### 5
25) A gardener wants to plant 17956 trees and arranges them in such a way that there are as many rows as there are trees in a row. What is the number of trees in a row ?
a) 136 b) 134 c) 144 d) 154
26) The number of trees in each row of a garden is equal to the total number of rows in the garden. After 111 trees have been uprooted in a storm, there remain 10914 trees in the garden. The number of rows of trees in the garden is
a) 100 b) 105 c) 115 d) 125
27) 1250 oranges were distributed among a group of boys of a class. Each boy got twice as many oranges as the number of boys in that class. The number of boys in the class was
a) 25 b) 45 c) 50 d) 100
28) A group of students decided to collect as many paise from each member of the group as is the number of members. If the total collection amounts to Rs59.29, the number of members in the group is:
a) 57 b) 67 c) 77 d) 87
29) Between which two ways consecutive whole numbers does √1000 lie ?
a) 29 and 30 b) 30 and 31 c) 31 and 32 d) 32 and 33
30) Which of the following is correct ?
a) √30.25= 6.5 b) √59.29= 7.7 c) √19.36 = 4.6 d) √10.89= 3.9
31) How many natural number are there between n² and (n +1)²?
a) n+1 b) 2n c) 2n+1 d) 2n -1
32) How many natural numbers lie between 15² and 16²?
a) 28 b) 30 c) 31 d) 32
33) √(48.4/0.289)= ?
a) 22/17 b) 195/17 c) 210/17 d) 129-7/17
34) The value of √0.4 is
a) 0.02 b) 0.2 c) 0.51 d) 0.63
35) If √(1+ x/169)= 14/13 then x is equals to
a) 1 b) 13 c) 27 d) none
36) If √0.00000676= 0.0026 then the square root of 6760000 is
a) 26 b) 260 c) 2600 d) 26000
37) If √15625= 125 then the value of √15625 + √156.25 + √1.5625 is
a) 1.3875 b) 13.875 c) 138.75 d) 156.25
38) Given that √4096 = 64 the value of √4096+ √40.96+ √0.004096 is
a) 70.4 b) 70.464 c) 71.104 d) 71.4
39) The smallest number by which 5808 should be multiplied so that the product becomes a perfect square is
a) 2 b) 3 c) 7 d) 11
40) The least number that should be subtracted from 1385 to make it a perfect square is
a) 11 b) 16 c) 21 d) 26
41) The least number that should be added to 6200 to make it a perfect square is
a) 21 b) 31 c) 41 d) 61
42) The decimal number which when multiplied by itself gives 70.56 is
a) 7.6 b) 8.4 c) 7.4 d) 8.6
43) A General wishes to draw up his 7500 soldiers in the form of a square. After arranging, he found that some of them are left out. How many soldiers are left out?
a) 36 b) 64 c) 96 d) 104
44) Given that √13= 3.605 and √130 = 11.40, the value of √1.3+ √1300 + √0.013 is
a) 36.164 b) 36.394 c) 37.164 d) 37.304
45) The square root of square root of 56+569/1225 is
a) 7+13/25 b) 7+ 17/35 c) 7+18/35 d) 7+ 7/25
46) The square root of 21+ 2797/3364 is
a) 4+ 27.52 b) 4+ 29/57 c) 4+ 33/58 d) 4+ 39/58
47) If M is a square number, what is the next immediate square number?
a) M + 5 b) M²+ 2M c) M + 2 √M -1 d) M + 2 √M +1
48) Which is the smallest natural number when added to the difference of the square of 17 and 13 to give a perfect square ?
a) 1 b) 5 c) 11 d) 24
49) a= 3, b= 9 and c = 10, then the value of the expression given by √(13+ a) + √(112+ b) + √(c -1) is
a) 12 b) 16 c) 18 d) 20
50) if √(2+ √y) = 3 then y =?
a) 1 b) √7 c) 7 d) 49
51) 1 + 3 + 5+....51=?
a) 576 b) 625 c) 651 d) 676
52) The sum of all odd numbers up to 100 is
a) 2401 b) 2450 c) 2500 d) 2601
53) Every month, a boy receives Rs 1 on the first day, Rs3 on the 2nd day, Rs5 on the 3rd day, Rs7 on the 4th day, .....and so on from his mother as pocket money. How much money does he get in all in the month of as pocket money. How much money doerhe get in all in the month of October?
a) Rs496 b) Rs841 c) Rs900 d) Rs961
54) The area of a square plot is 101+ 1/400 m². The length of each side of the plot is
a) 10+ 1/20 b) 10+ 11/20 c) 11+ 1/20 d) 11+ 11/20
55) Which of the following statement is true ?
a) If n is a perfect square then 2n is also a perfect square.
b) A perfect square number maybe positive or negative.
c) A perfect square number cannot end in 2, 3, 7 or 9.
d) The number of zeros at the end of a perfect square is always even.
56) Observe the pattern below :
• • • •
• • • • • • •
• • • • • • • • •
• • • • • • • • • •
If the above pattern continues, how many dots will be there in the 10th pattern?
a) 81 b) 90 c) 100 d) 110
57) The perimeters of two squares are 40 and 96 m respectively. The perimeter of another square having an area equal to the sum of the areas of the first two squares is:
a) 104m b) 112m c) 128m d) 136m
58) if one number of a Pythagorean triplet is 2p then the other two members are
a) p, p²+1 b) p²+1, p²-1 c) p², p²-1 d) p², p+1
58) the least number of 4 digits that is a perfect square is
a) 1016 b) 1024 c) 1036 d) 1064
60) The greatest number of 4 digit that is a perfect square is
a) 9891 b) 9864 c) 9961 d) 9981
61) The least perfect square number divisible by 3, 4, 5, 6 and 8 is
a) 900 b) 1200 c) 2500 d) 3600
62) If √(0.04 x 0.4 x a(= 0.004 x 0.4 x √b then a/b is equals to
a) 16x 10⁻² b) 16x 10⁻³ c) 16x 10⁻⁴ d) 16x 10⁻⁵
63) The square of which of the following numbers will contain the first 9 natural numbers ?
a) | | | | | | | b) | | | | | | | | c) | | | | | | | | | d) | | | | | | | | | |
64) The value of √[{(0.05)² +(0.31)²+ (0.089)²}/{(0.005)²+ 9.031)²+ (0.0089)²}] is
a) 0.1 b) 10 c) 10² d) 10³
65) If three numbers in the ratio 2:3:5 and the sum of their square is 608 then the sum of the three number is
a) 30 b) 36 c) 40 d) 48
66) A perfect square number always leaves a reminder of 0 or 1 when divided by m or p. Then, m and p can take the values
a) 2,3 b) 3,4 c) 4,5 d) 5,7
EXERCISE - 3(B)
1) There are _____perfect squares between 1 and 100.
2) The square of 9.1 is _____
3) The next two numbers in the number-pattern 121, 144, 169, 196.___ are ___ and ____.
4) The square of 600 will have____ zeroes.
5) 1m²= ___cm².
6) 1cm²= ____mm².
7) The sum of the first 7 odd natural numbers is ____
8) The sides of a right triangle whose hypotenuse 17cm are___ and ___
9) The least number by which 250 maybe multiplied to make it a perfect square is___
10) The greatest number of 3 digits which is 12 a perfect square is____
11) If 12, x, 37 make a Pythagoras triplet then x is___
12) There are ____ natural numbers between 25² and 26².
13) The square root of a 4 digit or a 3 digit perfect square number is always a ___digit number.
14) There are___ numbers between 1 and 100 whose squares end in the digit 5.
15) There are____ numbers from 1 to 50 whose squares end in the digit 4.
16) Sum of first ____consecutive odd natural numbers is 100.
17) the 20th number in the series 1, 3, 6, 10___ is____
18) if the pattern 4, 9, 16, 25 is continued, the 25th term would be ___
19) The square root of 0.000441 is ____
20) There are____ perfect squares between 500 and 600.
21) The value of √0.01 + √0.81 + √1.21+ √0.0009 is____
22) The value of √2 is about ____
23) If √3ⁿ= 729 then the value of n is ____
24) The smallest number of 3 digits which is a perfect square is___
TRUE OR FALSE
1) The number of digits in a perfect square number is always even.
2) The square root of 0.9 is 0.3.
3) The square root of 0.064 is 0.08.
4) All numbers ending in even number of zeros are perfect squares.
5) (441x 196) is a perfect square.
6) The square of a prime number can be prime.
7) The square root of a number having 81 digits will have 41 digits.
8) If a and b are perfect squares then a+ b is a perfect square.
9) There are 199 natural between (99)² and (100)².
10) All the numbers of a Pythagoras triplet are odd.
11) The product of two perfect squares is a perfect square.
12) - 25 is a perfect square.
13) If √7ⁿ= 2401 then n is equals to 8.
14) If √58564 = 242 then √585640= 2420.
15) If the units digit of a number n is 4 then the units digit of √n is 2 or 4.
16) The square of an improper fraction is greater than the fraction.
CUBES AND CUBE ROOTS
1) ³√148877 =?
a) 43 b) 49 c) 53 d) 59
2) ³√681472 =?
a) 76 b) 88 c) 96 d) 98
3) 1728 ÷ ³√262144 x ? - 288= 4491.
a) 148 b) 156 c) 173 d) 177
4) 99 x 21 - ³√?= 1968.
a) 111 b) 1367 c) 136731 d) 1366731
5) ³√0.000216= ?
a) 0.6 b) 0.06 c) 0.006 d) none
6) ³√(512/125)= ?
a) 7/5 b) 8/5 c) 9/5 d) 12/5
7) The value of √0.01 x ³√0.008 - 0.02 is
a) 0 b) 1 c) 2 d) 3
8) Which of the following is not a perfect cube ?
a) 9261 b) 196 c) 6859 d) 13826
9) If a is the cube root of b then b is equal to
a) a³ b) √a c) a/3 d) ³√a
10) A perfect cube can never end with
a) 3 b) 7 c) 9 d) none
11) choose the correct statement
a) √(a+ b)= √a + √b
b) ³√(a - b)= ³√a - ³√b
c) √(ax b)= √a x √b
d) ³√a/b = 3√a - ³√b
12) ³√√0.000064= ?
a) 0.02 b) 0.2 c) 2 d) none
13) The smallest positive integer n for which 864n is a perfect cube is
a) 1 b) 2 c) 3 d) 4
14) The value of ³√{(0.2 x 0.2 x 0.2+ 0.04 x 0.04 x 0.04)}/{(0.4x 0.4x 0.4 + 0.08x 0.08x 0.08)} is
a) 0.125 b) 0.25 c) 0.5 d) 0.75
15) The largest four digit number which is a perfect cube is
a) 8000 b) 9261 c) 9878 d) 9999
16) By what least number must 21600 be multiplied so as to make it a perfect cube.
a) 6 b) 10 c) 20 d) 30
17) What is the smallest number by which 3600 may be divided to make it a perfect cube.
a) 9 b) 50 c) 300 d) 450
18) Which smallest number must be added to 710 so that the sum is a perfect cube ?
a) 11 b) 19 c) 21 d) 29
19) Choose the incorrect statement.
a) if m³ has 3 at the units place then m has 7 at the units place.
b) if p has 6 at the units place then both p² and p³ have 6 at the units place.
c) if x has 1, 4, 5, 6 or 9 at the unit place then x³ as the same digit at the unit's place.
d) if q is a whole number then both q² and q³ cannot have 2 at the units place.
20) ³√-3584/189= ?
a) 8/3 b) 14/9 c) -8/3 d) -14/9
21) (13/10)³=?
a) 1027/1000 b) 2027/1000 c) 2197/1000 d) none
22) If √x =³√9 then what is x² equal to?
a) ³√81 b) 3 c) 9³√9 d) ³√9
23) The cube of a number is 8 times the cube of another number. If the sum of the cubes of the numbers is 243 then what is the difference between the two numbers.
a) 3 b) 4 c) 6 d) none
24) a and b are integers greater than 1, 5a is the square of a number and 75ab is the cube of a number. The smallest value of a + b is
a) 14 b) 18 c) 20 d) 30
25) The value of ³√{(343x 125)/0.064} is
a) 8.75 b) 87.5 c) 807.5 d) 875
26) if m, n , p and q are consecutive natural numbers and m³= n³+ p³+ q³, what is the least value of m
a) 3 b) 6 c) 9 d) 12
27) The difference of the cube and the square of a natural number is 48. The number is
a) 4 b) 5 c) 6 d) 8
28) Three numbers are in the ratio 1:2: 3. The sum of their cubes is 246924. The largest number is
a) 38 b) 51 c) 57 d) 61
29) The value of √(9/4) x √(4/3)²+ 1 ÷ ³√(27/8) is
a) 4/3 b) 10/3 c) 25/6 d) 11/2
30) By what least number must 25920 be divided to obtain a number which is a perfect cube ?
a) 5 b) 15 c) 25 d) 35
31) The value of the expression ³√0.729 ÷ √0.0009 x √0.25 - ³√3.375 is
a) 0.135 b) 1.35 c) 13.5 d) 135
32) The value of ³√{-p⁶ x q³ x r²¹)/r⁹ x p¹²} is
a) -qr⁴/p½ b) -pq⁴/r² c) qr⁴/p² d) -qr³/p²
33) if m³ has 9 has the units digit then the units digit of m is
a) 3 b) 7 c) 9 d) none
34) The smallest number that should be added to 6855 to make it a perfect cube is
a) 3 b) 4 c) 5 d) 7
35) If M= ³√³√p¹⁸ then M equals
a) p b) p² c) p³ d) p⁶
36) If in the five digit number 1y6x3, x is the the greatest single digit perfect cube and twice of its exceeds y by 7 then the sum of the number and its cube root is
a) 11862 b) 18700 c) 19710 d) 25320
37) If ³√{3(³√x - 1/³√x)}= 2 then the value of (x - 1/x) is
a) 328/15 b) 520/27 c) 728/9 d) 728/27
38) If ³√{3(³√x - 1/³√x)}= 2 then the value of (³√x - 1/³√x) is
a) -10/3 b) 10/3 c) 1/5 d) none
EXERCISE - B
1) There are____ natural numbers between (10)³ and (11)³.
2) The cube of 2000 will have ____zeroes.
3) There are ____perfect cubes between 1 and 1000.
4) The least number by which 81 should be multiplied to make it a perfect cube is___
5) The square of a negative integer is ___and its cube is____.
6) 1m³= ___cm³ and 1 cm³= mm³.
7) The cube root of 1.331 is ____
8) If the units digit of n³ is 3 then n has____ as the units digit.
9) if a perfect cube number ends in n zeros then n is a multiple of____
10) The square root of 15625 is ___ more than its cube root.
TRUE OR FALSE
1) There are five perfect cubes between 1 and 200.
2) There is no perfect square or perfect cube between 70 and 80
3) 363 x 99 is a perfect cube.
4) There is no cube root of a negative integer.
5) No perfect cube can end with exactly two zeros.
6) No perfect cube can end with even number of zeros.
6) A perfect cube cannot end with 3, 7 or 9.
7) The cube root of -1.728 is - 0.12.
8) For an integer m, m³ is always greater than m².
9) For a whole number p, p³ is always greater than p².
10) if a and b are integers such that a²> b² then a³> b³.
11) The order of the digit of (13)³ is reversed in (31)³.
12) The units digit of the cube of a number ending in 3 is 9.
13) if a² ends in 4 then a³ ends in 8.
14) If a² ends in 6 than a³ ends in 4.
15) If the square of a number is positive than the cube of that number is also positive.
16) The cube of a natural number which is a multiple of 3 is a multiple of 27.
17) The cube of a natural number which is a multiple of 3 is a multiple of 27.
18) If a number n has 5 at the units place then both n² and n³ have 5 at the units place.
19) If p² ends in 9 then p³ ends in 7.
20) Let m and n be natural numbers. If m divides n then m³ divides n³
21) The 6th power of every natural number is both a perfect square and a perfect cube.
PLAYING WITH NUMBERS
1) In a digital display as shown below, which digit can display all the digits from 0 to 9 ?
a) 0 b) 6 c) 8 d) 9
2) if a is even when which of the following must be odd?
a) a-2 b) a/3 c) 3a - 2 c) 3(a + 1)
3) The generalized form of a 3 digit number pqr is
a) p+ q+ r b) 100p+ 10q+ r c) 1000p+ 100q+ 10r d) 100r+ 10q + r
4) The usual form of 100x + y + 10z is
a) xyz b) zxy c) yxz d) xzy
5) The difference between the place value and face value of 6 in the numeral 856973 is
a) 973 b) 6973 c) 5994 d) none
6) P and Q are two positive integers such that P x Q= 64. Which of the following cannot be value of P + Q
a) 16 b) 20 c) 35 d) 65
7) A and B are two natural numbers such that A + B =15. The greatest possible value of A x B is
a) 50 b) 54 c) 56 d) 63
8) If x+ y+ z = 9 and both y and z are positive integers greater than zero then the maximum value of x can take is
a) 3 b) 7 c) 8 d) data insufficient
9) 3 -3+3-3+.....101 term=
a) 0 b) -3 c) 3 d) none
10) if (n -1) is an odd number, what are the two numbers nearest to it ?
a) n, n-2 b) n, n -3 c) n-3, n+1 d) n-3, n+5
11) Which would be the proper order of the following( in ascending order)?
i) trillion ii) thousand iii) billion iv) hundred v) million
a) 1,2,3,4,5 b) 1,5,32, 4 c) 4,2, 3,5,1 d) 4,2,5,3,1
12) Choose the incorrect relation.
a) 1 million= 10 lakh b) 100 million =10 crores c) 100 crores= 1 billion d) all are correct
13) if n is a negative then which of the following is the least.
a) 0 b) - n c) n² d) 2n
14) If 0< x <1, which of the following is the greatest
a) x b) x² c) 1/x d) 1/x²
15) What is the product of all the numbers on the dial of telephone ?
a) 362880 b) 181440 c) 40320 d) none
16) Which of the following numbers is not a prime ?
a) 107 b) 127 c) 133 d) 197
17) which of the following numbers is composite
a) 137 b) 147 c) 157 d) 167
18) If a * b = 2a - 3b + ab then 3*5+ 5*3 is equal to
a) 22 b) 24 c) 26 d) 28
19) If x* y = x²+ 2y, what is the value of p if 4 * (3* p)= 50
a) 4 b) 7 c) 8 d) 12.5
20) If p * q = (p+ q)/2 and p+ q =(2p + q)3 when what is the value of (4*6)*(12*4)?
a) 4 b) 6 c) 8 d) 10
21) which of the following numbers is a multiple of 8 ?
a) 923872 b) 923972 c) 923862 d) 923962
22) The numbers 24984, 26784 and 28584 are
i) divisible by 3 ii) divisible by 4 iii) divisible by 9
Which of these are correct ?
a) 1 and 2 b) 2 and 3 c) 1 and 3 d) 1, 2 and 3
23) 419562 is divisible by
a) 3, 4, 7, 9 and 11 b) 3,6, 7 and 9 c) 3, 4,6,9 and 11 d) 3,6, 9 and 11
24) A number divisible by 56 is always divisible by each of the following numbers except
a) 4 b) 7 c) 8 d) 9
25) How many three digit numbers can be formed using the digits 2, 6, 7 such that each number is divisible by 2 as well as 3? repetition of digits is not allowed.
a) 2 b) 3 c) 4 d) 6
26) Which of the following numbers is divisible by 99 ?
a) 114345 b) 135792 c) 913464 d) 3572404
27) A number is divisible by 18 if it is divisible by both ___and___
a) 2,9 b) 3,6 c) either a or b d) cannot say
28) Which of the following statements is not true ?
a) A number divisible by both 3 and 9 is divisible by 27.
b) a number divisible by both the 9 and 11 is divisible by 99.
c) A number division by both 3 and 4 is divisible by 12.
d) A number divisible by both 8 and 13 is divisible by 24.
29) in a five digit number abcde, if the values c,d and e are given we can test its divisibility by
a) 2, 3 and 5 only b) 2,4,5 and 11 only c) 2,3,5,6,9 in 10 only d) 2,4,5,8 and 10 only
30) A number is divisible by 90 if it is divisible by each one of the following except
a) 2 and 45 both b) 6 and 15 both c) 5 and 18 both d) 9 and 10 both
31) If a+ b+ c= 6 and c is an odd digit then the three digit number abc is
a) an odd multiple of 3 b) an even multiple of 6 c) an even multiple of 3 d) an even multiple of 9.
32) if the division N+ 5 leaves a remainder of 3, what might be the ones digit of N
a) 2 b) 3 c) 4 d) 6
33) if the division N + 5 leaves a remainder of 4 and the division N+2 leaves a remainder of 1 then the ones digit of N is
a) 3 b) 5 c) 7 d) 9
34) If 78 * 3945 is divisible by 11, where * is a digit then * is equals to
a) 0 b) 1 c) 3 d) 5
35) If a number 774958A96B is divisible by both 8 and 9, the respective values of A and B are
a) 5 and 8 b) 7 and 8 c) 8 and 10 d) none
36) If 56x32y is divisible by 18 then the least value of y is
a) 0 b) 2 c) 4 d) 6
37) If a 3 digit number abc is divisible by 11 then which of the following expressions must be a multiple of 11 ?
a) a+ b+ c b) a- b+ c c) a- b- c d) b+ c - a
38) A four digit number abcd is divisible by 11 if d+ b=___ or ___
a) 0, 11(a+ c) b) 0, (a+ c) c) (a+ c),11(a+ c) d) (a+ c),12(a+ c)
39) A 5 digit number AABAA is divisible by 33. How many such numbers are there ?
a) 3 b) 5 c) 9 d) more than 10
40) The digit in the tens place of a two digit number is 3 more than the digit in the unit place. Let the digit at units place be p. Then, the number is
a) 10p+3 b) 11p+3 c) 10p+30 d) 11p+ 30
41) A four digit number is formed by repeating a two digit number such as 2525, 3232 etc. anry number of this form of exactly divisible by
a) 7 b) 11 c) 13 d) smallest three digit prime number e) all the above
42) A six digit number is formed by repeating a three digit number, e.g., 657657, 789789 etc. Any number of this form is divisible by
a) 7 b) 11 c) 13 d) 1001 e) all of these
43) The product of any three consecutive natural numbers is always divisible by
a) 3 b) 6 c) 9 d) 15
44) The largest natural number which exactly divides the product of any four consecutive natural numbers is
a) 6 b) 12 c) 24 d) 120
45) The difference between a two digit number and the number formed by interchanging the digits is always divisible by
a) 5 b) 7 c) 9 d) 11
46) The sum of a two digit number and the number formed by interchanging the digits is always divisible by
a) 7 b) 9 c) 10 d) 11
47) let xyz be a 3 digit number. Then xyz- zyx is not divisible by
a) 9 b) 11c) 18 d) 33
48) ay 4 digit number 4xy5 is divisible by 55. Then , the value of y- x is
a) 0 b) 1 c) 4 d) 5
49) If abc is a 3 digit number then the number abc - a- b - c is divisible by
a) 9 b) 10 c) 11 d) 90
50) What is the remainder when the sum of the three consecutive even integers is divided by 6
a) 0 b) 1 c) 3 d) 4
51) What is the remainder when the sum of three consecutive odd integers is divided by 6 ?
a) 0 b) 1 c) 3 d) 4
52) Choose the incorrect statement .
a) The remainder obtained on dividing a number by3 is the same as the remainder obtained on dividing the sum of its digits by 3.
b) The remainder obtained on dividing a number by 9 is the same as the remainder obtained on dividing the sum of its digit by 9.
c) The remainder obtained on dividing a number by 4 is the same as the remainder obtained on dividing the number formed by its last two digit by 4.
d) The remainder obtained on dividing a number by 8 is the same as the remainder obtained on dividing the number formed by its last 4 digit by 8.
53) A 4 digit number ppqq is divisible by 55. Then, the possible value/s of q is/are
a) zero and two b) 2and 5 c) 0 and 5 d) 7
54) let abc 3 be a three digit number. Then , abc+ bca + cab is not divisible by
a) a+ b+ c b) 3 c) 9 d) 37
55) If the square of a number of 2 digit is decreased by the square of the number formed by reversing the digit then the result is not always divisible by
a) 9 b) the product of digits c) the sum of digit d) the difference of digit
56) Tarun ranky9th from the top and 38th from the bottom in a class. The total number of students in the class is
a) 45 b) 46 c) 47 d) 48
57) a group of boys stand in a single line. On boy 19th in order from both the ends. How many boys are there in the class ?
a) 37 b) 38 c) 39 d) cannot be determined
58) Nitin rano 18th in the class of 49 students . What is his rank from the last ?
a) 18 b) 19 c) 31 d) 32
59) Sumit is 8th from the left and Sachin is 9th from the right in a row of 15 students . How many students are there between Sumit and Sachin.
a) 0 b) 1 c) 2 d) 5
60) In a row of boys if A who is 10th from the left and B who is 9th from the right interchange their positions, A beco15th from the left. How many boys are there in the row.
a) 23 b) 27 c) 28 d) 31
61) In a division sum, the divisor is 12 times the quotient and 5 times the remainder. If the remainder is 48 then the dividend is
a) 2404 b) 3648 c) 4808 d) 4848
62) On dividing a number by 56, we will get 29 as remainder. On dividing the same number by 8, what will be the remainder?
a) 4 b) 5 c) 6 d) 7
63) a number when divided by 136 leaves remainder 36. if the same number is divided by 17, the remainder will be
a) 2 b) 3 c) 7 d) 9
64) when n is divided by 4, the remainder is 3. What is the remainder when 2n is divided by 4 ?
a) 1 b) 2 c) 3 d) 6
65) A number which divided by 5 leaves remainder 3. What is the remainder when the square of the same number is divided by 5 ?
a) 0 b) 3 c) 4 d) 9
66) The largest 5 digit number exactly divisible by 91 is
a) 99918 b) 99921 c) 99971 d) 99981
67) The smallest 6-digit number exactly divisible by 111 9
a) 111111 b) 110011 c) 100011 d) 110101
68) The difference between the squares of any two consecutive integers is equal to
a) an even number b) sum of given numbers c) difference of given numbers d) products of given numbers .
69) The number of boys in a class is three time the number of girls. Which of the following numbers cannot represent the total number of children in the class ?
a)!40 b) 42 c) 44 d) 48
70) If n≠ 0, Which of the following must be greater than n?
i) 2n ii) n² iii) 2- n
a) i only b) i and ii only c) ii and iii only d) none of i, ii, and iii
71) The middle digit number of a three digit number is zero and the sum of the other digits is 11. If the digit be reversed, the number so formed exceeds the original number by 495. The number is
a) 308 b) 407 c) 209 d) 506
72) if from a two digit number we substract the number formed by reversing its digits then the result so obtained is a perfect cube. How many such numbers are possible
a) 4 b) 5 c) 7 d) 8
73) When a certain number m is divided by 5 and added to 8, the result is equal to 3m subtracted from 4. The value of m is
a) 2 b) -5/4 c) 4/3 d) -1/3
74) Given 1+ 2 +3+ 4 +....+10 =55 then sum 6+12+ 18+ 24 +...+60 is equals to
a) 300 b) 330 c) 455 d) 655
75) let n be a natural number such that 1/2 +1/3 +1/7 +1/n is also natural number. Which of the following statements is not true?
a) 2 divides n b) 3 divides n c) 7 divides n d) n> 84
76) Four prime numbers are arranged in ascending order. The product of first three numbers is 385 and that of the last 3 is 1001. The largest prime numbers is
a) 9 b) 11 c) 13 d) 17
77) The sum of the four consecutive even numbers A, B , C and D is 180. What is the sum of the next 4 consecutive even numbers.
a) 196 b) 204 c) 212 d) 214
78) if you write down all the numbers from one to hundred, how many times do you write 7 ?
a) 11 b) 18 c) 20 d) 21
79) The total number of digits used in numbering the pages of a book having 366 pages is
a) 732 b) 990 c) 1098 d) 1305
80) 3/4 of a number is 20 more then half of the same number. The number is
a) 50 b) 80 c) 90 d) 180
81) If the sum of three consecutive even numbers is 234, which is the smallest among them ?
a) 68 b) 76 c) 78 d) 80
82) A number whose fifth part increased by 4 is equals to its fourth part deminished by 10, is
a) 240 b) 260 c) 270 d) 280
83) while solving a problem by mistake Aditya squared a number and then substracted 25 from it rather than first subtracting 25 from the number and then squaring it. But he got the answer right. What was the given number ?
a) 13 b) 38 c) 48 d) 58
84) The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocal of these numbers ?
a) 12/35 b) 1/35 c) 35/8 d) 7/32
85) The product of two natural numbers is 17, then, the sum of the reciprocals of their squares is
a) 1/289 b) 289/290 c) 290/289 d) 289
86) two different natural numbers are such that their product is less than their sum. One of the numbers must be
a) 1 b) 2 c) 3 d) none
87) The sum of two numbers is 75 and their difference is 25. The product of the two numbers is
a) 125 b) 1000 c) 1250 d) 1350
88) The difference of two numbers is 2. If the difference of their square is 18, what is their sum?
a) 20 b) a number between 8 and 16 c) A number between 5 and 8 d) can not be determined
89) 54 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780. The bigger part is
a) 24 b) 30 c) 32 d) 34
90) The sum of four numbers is 64. if you add 3 to the first number, 3 is subtracted from the second number, the third is multiplied by 3 and the fourth is divided by 3 then all the results are equal p. What is the difference between the largest and the smallest of the original numbers ?
a) 21 b) 27 c) 32 d) cannot be determined
91) If AB x AB = 6AB then A has the value
a) 2 b) 3 c) 4 d) 6
92) if we have 2B then A is equal to
+ AB
-----
8A
a) 4 b) 5 c) 6 d) cannot be determined
93) if we have AB then B is equal to
x B
----
96
a) 3 b) 4 c) 6 d) either 4 or 6
94) if AA x A =CAB then C is equals to
a) 6 b) 7 c) 8 d) 9
95) if we have B1 then B is equals to
x B
-----
49B
a) 3 b) 6 c) 7 d) 9
96) Let E= 3, B= 7 and A= 4, then, for the following addition sum
B A S E
+ B A L L
----------------
GAMES
which of the following is true
a) G= 1, S= 6 b) M=9, L= 5 c) G= 8, L= 7 d) S=7, M= 8
97) Evaluate (987534129)²- 987534133 x 987534125.
a) 4 b) 987534119 c) 987534138 d) 16
98) How many numbers are there between 200 and 800 which are divisible by both 5 and 7 ?
a) 16 b) 17 c) 35 d) cannot be determined
99) A motorist knows four different routes from Bristol to Birmingham. From Birmingham to Sheffield, he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle?
a) 4 b) 8 c) 12 d) 24
100) If every 2 out of 3 readymade shirts need alternations in the sleeves and every 4 out of 5 need it in the body, how many alterations will be required for 60 shirts.
a) 24 b) 123 c) 133 d) 143
EXERCISE - B
1) The generalised form of a four digit number abcd is ____
2) The usual form of 1000a + 10b + c is____
3) There are____ zeros in 1 million.
4) by just looking at the ones digit, we can test the divisibility of a number by___, ____ and _____.
5) 2 x 2 -2 ÷ 2 - 2 -2 ÷ 2+ 2(2-2)= ____
6) If aᵇ = bᵃ then a and b have the values ___ and ____
7) A number is divisible by 15 if it is divisible by both____ and ____
8) The number xy - yx, where x and y are digits and x > y, divisible by ____
9) If the sum of the digits of a number is divisible by 9 then it is divisible by both____ and ____
10) A natural N when divided by 5 leaves a remainder 1. The ones digit of N can be ____ or ____.
11) two numbers whose produced is a one digit number and the sum is a two digit number are _____ and ____
12) 3 natural numbers whose sum and product are equal are____, ___ and ___
13) There are _____prime numbers between 80 and 100.
14) If AB x B =9B then (A, B) can be equal to ____ or____
15) if B x B = AB then either A= 2, B= 5 or A= ____, B= ____
16) If AB + AB = CB then B can be only _____
17) If A and B are two natural numbers such that A+ B=13 then the least possible value of A x B is ____while the greatest possible value of Ax B is ____
18) A number which when divided by 3 leaves a remainder 2 is of the form ____,where N is a natural number.
19) A number of the form 63N+ 9 will leave a reminder____ when divided by 7.
20)If PQ x 6= QQQ if you divide the number 4 digit number by the number we get a special as value then a has the value 399 then the value of age 6 is equals to the difference of 3 digit number and the number of 10 by reverse in the order of digit is always divisible by and if is divisible by 11 the value of Y is the four digit number 450 is divisible by 6 then has the value in a 5 digit number exactly divisible by 9 divisible by 9 then the list value of ease and maximum value if abc at resisting digit of the number which is exactly divisible by the list value of exactly divisible by the three the least value of x + Y in the maximum value of x + Y is divisible by 3 the minimum and the maximum values of and respectively the number is divisible by 16 the number formed by its last digit is divisible by 60number divisible by 16 the number formed by its last is it is divisible by 16 all even number divisible by 9 or divisible by the largest number by which difference between a 3 digital number in the number obtained by reversible digits is always divisible age 252 then at the values and if 1480195 is divisible by 33 then value of seeds 872 then equal to 2 last digit has a remainder 1 minute is debit at 3 or 5 the list two digit number satisfying this condition is 1 multiplying a number by 7 the product is a number each of whose digit is 3 the smallest number as digits that 80001 million the number where A and B are digits are divisible by 9 if a number it divisible by both 3 and 980 divisible by 27 all even number divisible by 3 or divisible by 6 if the number exactly divide the sum of two numbers in must exactly divided by numbersly the two numbers are proprimes then at least one of them must be a prime numbers the sum of the two consecutive odd numbers is always divisible by 4number divide 3 numbers exactly must divided that some exactly a number of form 36 9 1 / 9700 and number division by both aim and n is always divisible by if a number leaves remainder of 1 / 2 then the unit digit of the number is ABCD is a 4 digit number say that the then the remainder obtained on dividing by 10 HD divisible by the number is divisible by 6 in the maximum possible values a is 9 even numbers is divisible by 3 in the minimum possible values is 3 at 3 digit number from by the digit A B and C then the sum of the numbers already divisible by 37
The total number of actress of 500 12 is 48 and 14 how many different positiv integers a capital of 33678 the sum of the power supply is 108192 is 57812 number of prime factors is 5656 112 HCF of 18365 41 to 60 LCM LCM of two number is 11 the LCM is 7700 if one of the number 6275 then other is 279 there is no two number is 12 times the ratio of the sum of the HCF and LCM is equal number in 96 in the other is 124 128 134 the product of two co-primes is 1 17 the LCM should be one 17 equals to their HCL cannot be reboot the greatest possible in which can be used to measure exactly the length 7 385 1295 15 25 42 three different continents contain different qualities of mixture of male converters measurement are 434 and 465 what we go to measure must be there to measure all the different quantity exactly 173141 kg the maximum number of students among one show 11 place in 19 pencils can be distributed in such a way that is student get the same number of Princess is 919 the list number of square tiles required to take the ceiling up a room 1517 cm long and 9 to broad is 656 738 and 14 majoring road sir 64896 in less the list length of closer can you measure exact number of times using any of the roads is 0.969.609 19.20 968 electric device make a bill after 60 seconds and other device nation be up to 62 second they beat together then the next time when they would be together the list is 10.30 10 31 10 5911 a.m. the traffic lights 3D front road crossing change after 48 second 72 second and one day second respective they also simultaneously 820 hours then what time will they again change simultaneously abnc started the same time in the same direction to run around a circular stadium a complete the round 252 sector B in 300 8 second see in 198 second all second in the same point after what time will then meet again at the starting research of English Mathematics and science books containing 336 to 1496 who is the expectivali have to be sketch in a such a way that all the books are started subject wise and the height of the each tag is the same the total number stack will be 14 21 22 48 which greatest number will divide 3000 26 and 543 under 11 and 13 respective 15 30 45 60 the greatest number which can be divided 1354 1856 2017 62 living the same in under 10 in rich case 64 124 156 to 60 what is the list number which when divided by 8 9 12 15 leaves remainder one in each case 179 181 229 361 what is the least number which one digit by 5 is divisible by each one of the 21 28 36 and 45 425 1259 1262 1265 what is the list number what is the list number which one divided by 5689121 image case and completed divisible by 13 361 721 1800 13601
AVERAGE
1) The average of all odd numbers up to 100 is
a) 49 b) 49.5 c) 50 d) 51
2) The average of 2, 7, 6 and x is 5 and the average of 18, 1, 6, x and y is 10. what is the value of y ?
a) 5 b) 10 c) 20 d) 30
3) adcd ER pipe consecutive average is a family consist of grandparents parents and 3 grams average age of the grandparents 67 years that of the parent is 35 years and that of the ground 6 years the average age of the family is if the average of M number series M and that of the n number is M then the average append plusing number is a minus and n + NM the average expenditure of a man for the first five months of the year is 5000 and for the next 7 months it is 5400 he saves 2300 during this year is average monthly income is 525 grocers has a sale of 6435 6927 685 7230 6562 for 5 consecutive months how much sale much he have in a 6 month so that you get an average cell of 650091 591 6000 16991 a company produces for the first three months how many items to average 3007510kar owner by the petrol rupees 7920 per litre for three consecutive years computer the average cost for lick his friends 6464 year 18.49 18.58 19.2 21.6 or 3 November the first is twice the second and half of the third is the average of the three number is 56 then the difference between the first and the third number is 12 20 24 28 the average age of 30 students In a class is 50 years its students of the class at the average age of 16 years in the average age of the remaining 24 students should be 14 years 14 years 3 months 14 years 6 months 14 years 9 months the average of 18 numbers is 15 the average of 15 of this numbers in 16 and average of another 25 number is 14 what is the average of the remaining numbers 14.75 to 10.25 cannot be to mind there are three groups of student consisting of 25 50 and 25 students separately the main marks obtained by the first to groups are 60 and 55 the combined mean of all the three groups 58 what is the mean of the marks scored by the third group 57 58 662 the average marks in a science test in a class of 20 students 68 the marks up to students were misreed as 48 and 65 instead of the actual mark 72 and 61 respectively what you would be the correct average 668.569 69.5 a people's marks were wrongly instered as 83 institute of 63 due to these the average marks for the class but increased by half the number of peoples in the class is 10 2014 73 the average of 11 number system.9 is the average of the first 6 number is 10.5 and that of the last 6 number is 11.4 then the middle number is 11 11.311.4 11.5 the average temperature for the first four days of the week is that are the last four days is 41.3 with the average temperature for the whole week is 40.6 then the temperature in the 4th day is 38.5 40.841.341.3 the average weight of a class of 24 students is 35 in the weight of the teacher is included the average by 400g the weight of the teacher is 45 kg 53 kg 55 kg the average age of a mother and Hershey's children is 12 years which is reduced by 5 years of the mother in excluded how old is the mother 40 years 42 years 48 years 50 yearsthe average weight of 8 man is increased by 1.5 kg which one one of the main who wait 65 kg is replaced by a new man the weight of the new man is 70 kg 74 kg 76 kg 77 kg the average height of 25 boys is 1.4 when 5 boys leave the group then the average height increases by 0.15 what is the average height of the five boys who lives 0.80.90.951.05 emoterist travels to a place 150 km away at an average speed of 50 and returns at 30 is average speed for the whole journey in each 3537 37.5 the average age of the husband and his wife was 23 years at the time of their marriage after 5 years they have a one year old child average age of the family now is 19 years 23 years 28.5 years the average age of an ideal classes 40 years to a new students with an average age of 24 years join the class there by decreasing the average by 4 years the original strength of the class was 10 11 1250 4 years ago the average age of a family of 4% was 18 years during the period of JB was born today the average age of the family still 18 years the age of the boy baby is 1.2 years 2 years 2.5 years 3 the average salary of all the workers in a workshop is 8000 the average salary of 7 technician is 12000 in the average salary of the race 6000 the total number of workers in the box office 221 22 the average weight of a b and c is 45 kg the average weight of a and a baby 40 kg in that a b and c43 kg then the weight of B is 17 kg 31 kg school mein 600 student the average age of the boys 12 years and that of the girls if the average age of the Student Of the school is 11 years 9 more than the number of girls in the school is 150 to 53 5450 the average age of a student of the class is 15.8 the average age of the boys in the class 16.4 years and that of the girls is 15.4 years the ratio of the number of the boys to the number of girls
ALGEBRAIC EXPRESSIONS. IDENTITIES AND FACTORISATION
The sum of - 8 ab and - 3ab is - 5 ab - 11 ab 5 ab 11 ab the coefficient of P in the terms of P3 is -1 - 3 13 - 30 which of the following are like terms the product of a monomial and a binomial is a monomial binomial trinomial subtract 3mm from MN we get the sum of which of the following is a binomial in a polynomial that exponents of the variables are always interiors positive integers non negative integer not positive integers which of the following algebraic expression is a polynomial the value of the expression minus 34 is 1012 which of the following algebraic expression is a polynomial the product of the monomial choose the incorrect statement the degree of the polynomial is a quadratic polynomial the degree of polynomials is a quadratic polynomial the highest common factors of the area of rectangle the length 4 PQ and the volume of a cuboid with length 2 MN break to 3MP and high 2 MB is what must be added to make it equals to X what the must be subtracted from water must be added to the sun and simplify evaluate it is divided the percentage the product of is equals to the percent obtained when is divided by 01 x choose the correct simplify identify the value of the product of and when x is equal to zero it is divided the remainder is then the value of a is the product of and is in the product of the coefficient of 81 24 given that the value each 5334 555 the question in the remainder when is divided by each find the remainder when is divided by if then the value will be in the value of 5 10 15 20 the value of two sides of rectangle sir units what is this area in square units the two are the sun side of rectangles are then its perimeter is area of square is the cost of a toys given by the expression expression for the total cost of toys is the value of each the value of each then the value of natural numbers only integers only real numbers cannot say then then the value of x y is 400 then 72 1272 in the value of these 140 14 the square of square of the value of 9154 544 what is equals to the value of 125 712 the value of the expression
The product of two terms with likes science is the term while the product of the two terms with the unlike signs is a term saving the same Coefficient and called like terms the coefficient in is the number of terms in the expression is a constant is a polynomial of degree the higher power of a variable is called the of the polynomial the side of the square of the area 81 age the sum of the areas of 2 square the product of two polynomial is the numerical factor of the term is called its writing + 10 ABC is the factorise form of the common factor method of factorization for a polynomial is based on property for to be a perfect square natural primo trinomial must be added to eat is a monomial theory substance from we get an identities to for all the value of the variable the product of two negative terms and negative terms the product of one negative and one positive term is a negative term is a binomial why is a factor of 2xy valuefactorization the factorize form the degree of the polynomials when we divide the monomial by another monomial the equation obtained is also known when he divided polynomial the question obtained is also a polynomial some of the factors the value of Z for weight to find the value of US identity the difference of the squares of two consecutive numbers is equal to the exam
LINEAR EQUATIONS
Which of the following is not a linear equation which are the following is a linear equation in one variable which of the following equation has x = 12 as the solution how many of the following statements are correct is a linear equation in one variable if he is an even numbers in the next odd numbers is to T + 1 the solution of the equation the terms linear equation and linear equation at the same is a linear equation for X 135 to 354798 1232 solve solution of the equation 2345 the value of PNB equation - 3.41 - 2.8 2.8 4.2 solve 4x 83 14876x0125 solve for y29 9929 if and then is equals to 0123 solve for x 89 10 12 x - 2 1 2 3 then value of x and y are expect the value of x in the equation is in the equation if the value of oxygen increased by 3 then the corresponding value of Y decreases by 15 decreases by 3 decreases by one get slipper linear equation in one variable has only one variable with any power only one term with a variable only one variable with power one only constant term a linear equation in one variable has only one solution can have two solution only can I more than two solution has a no solution the price of 10 shares equals to get a four table the price of 15 shares in two tables together is 4000 total price of 12 chairs and 3 table C 315003750 3840 39 the cost of 12 base in 30 valid season 940 what is the cost of 4 brain contain wallet 2017 289 2980 the cost of 21 tables in 35 years is 41825 what is the cost of 9 tables and 15 chair 1775 17925 1875 18725 if two jeans and 3 shirts cost 43 jeans into shirts cost the 500 how much do one jeans one such cost 12500 165750 A student was asked to divide a number by 1738 in street he actually multiplied by 178 and get to 25 more then the expected number the expected answer was 64 126 136a sum of 1360 has been divided among A B and C such that a guest 23 upward the gates and we get 14 of what Seagate be share is 12162 4300 tank is 25 full 16 to the tank it becomes 67 full the capacity of the tank is 28 l 32 l 35 l 42 L 18 of while watch 58 full Ben 10 bottle supplied was taken out of 8 bottle supplier was poled in Twitter by 35 full how many bottles of foil can be tin contents 20 13 48 inhen classroom there are certain number of benches if 6 students are made to sit on a Ben 10 to accommodate all of them one more bench is needed however it 7 students are made to switch on the bank accommodating all of them space for 5 students left the total number of student in the class is 3042 729 if it child is given 10 suite there are three sweets left over body fits is given 11 switch the number of sweets is four lay the total number of state is 3757 7375 180 oranges are distributed among 70 boys and girls such that each boy gets to and each girls 3 oranges the number of boys is 25 30 70schools annual day sweets where to be equality distributed and 12 children but on that particular day 32 children's how many sweets is child originally supposed to 15 18 24 cannot be written by in a hard of cow the number of lakes is 14 more than twice the number afraid the number of cows in the heart is 5710 SRK number of horse season in equal number of man are going somewhere half of the owners are on their hearts is back while the remaining once are working a long lating their hot the number of lakes walking on the ground 17 then how many hourses are there 10 12 14 16 and employee may claim 7 for each kilometre when he travel by taxi and 64- km he drive is own car if any one week he claim 6005 for travelling 90 km how many kilometre did he travel by taxi 135 155 162 170 in an examination student score 4 March for every correct answer and loses one mark for every wrong answer A student attempted all the 200 questions and sport 200 marks in all the number of question 3 answer correctly was 6068 882for any target a person get one it's time when he is hea time loses one when he says it if he get 30 after running at the last target 100 times then how many times dream is the target 25 35 40 45 a man basic pay for 40 hours week is 200 over time spread at 25% of the secret in a certain we keyword over time in total 300 there for work for a total of 52 hour 56 hour 58 62 hours and man agrees to purchase a gift for D three men drops are how much more will reach have to contribute toward the purchase of the book a total of 324 coins of 25 and 25 make a summer 71 the number 25.6 121 24 144 200 number of part increased by 4 is equals to the fourth part diminished by 10 is 242 62670 280 if 17th of a number except 611 part by 100 than the number is 770 11825 1925 in the sum of one half an 15th of a number is it one third of that number by 22 3 the number is 15 18 2013 2 digit number by one the number is 12 15 18 21 852 is added to the number of the sum multiplied by 92 and 3 is added to the productone fifth number is equals to 58 of another number is 35 is added to the first number becomes 4 time the second number the second number is 25 471 25 the difference between the two numbers is 16 of the smaller number is greater than 17th of the larger number by 4 then the two numbers are 9 and 25 12833 and 49 56 and 72 dashama poor country even integer is 1284 the greatest of them is 323 22 3 22 3 26 what is the sum of two consecutive even numbers the difference of square is 84 34 38 4246 A train started from station with the certain number of passengers at the first of half of the passenger get down and 125 passengers in at the second fault half of the passing left then the train left for the destination is 250 passenger the number of passengers in the train at the start wall 253 54 5550 the number of 10 by inter changing the two digit of a two digit number is less than that the original number by 54 in the sum of the two digit of the number is 12 original number is 48 3984 A to Z number because 5 6 of the itself when it digits are reverse the two digit differ by one the number is 45 54 56 65A to Z number 7 times 2 digit the number of that is formed by reversing it digits 18 lesson the original number the number is 42 52 6272 the denominator of a factor if three more than the number HR is the numerator is well as the denominator is increased by 4 the fraction become 45 the original fraction was 58 710811 103 the difference between numerator and the denominator refraction is 5 if 5 is added to its denominator the fraction is decreased by 54 the fraction is 1694 1346 a number is greater than average of its third quarter in one 12th of 56 the number is 40 64 7285 bhejo FIR father 10 years ago was thrice the age of the sun 10 years and the father says will be twice that of eastern the ratio of the present ages 5:27 is to 38 is 259 is 25 had present size hai jis wise age of his daughter after 6 years the ratio of the ages of soil and his daughter will be 23 to 13 science presentation 36 years 40 years 46 years cannot be to mindthe sum of daughter and her mother is 56 years after 4 years age of the mother will be three time that of the daughter the present age is 10 years 46 years 12 years 44 years 11 years 45 years 13 years 43 years asha got married 8 years ago he present age 65 times the age at the time of a marriage Asad brother was 10 years longer to her at the time of a marriage the present the age of two persons de per by 20 years 5 years ago the older one be five times as old as the younger one their present ages are 25 years 5 years 30 years 10 years 25 years 15 years 50 years 20 years A man is aged three times more than his sons Ronit after 8 years he would be two and half times of Ronnie says after father eight years how many times would he be at the Rooney face 2562 6 years ago the ratio of the ages of Kunal and the summit was 6 to 54 years and the ratio of the wages will be 11 is to 10 samajh present age is 16 years 18 years 20 years cannot be determinedGaurav 150 marble Shweta 110 marbles how many marbles must Gaurav give to Tanmay so that the Tanmay will have four times as many Asgar 82980140 for a journey the cost of a charity cut is one third of the cost of an adult security the total cost of the tickets for adults and five children is 85 the cost of child tickets is 56 1050 Arun and sahjanchand print each has some money eat Arun give 30 to sajal will have take twice the money left into Arundhati left with sajal how much money does he chat 346242 245 2019 5190 one third of manik's marks in English exceed a half of his marks in science by 30 figure 240 marks in two subject together is marks in science is 42 56180 the sum of the three consecutive multiples of 7 is 357 the sum of digit in the smallest multiple is 489 there are 50 passenger se barbad launch luxury bus shared by resort summer 3 passengers at 20 tickets while the rest of 45° if the total collection them all the passengers how many passengers tickets 127 and 1250 distance between two places a and b is 210 2 car start simultaneously from A and B opposite direction in distance between them after 3 hours is 54 if the speed of one car is less than that of the other by 8 then the speed of the slower car is 1822 2430 St mar goes down stream and cover the distance between two parts in 3 hours the same distance the perimeter of a rectangle is 240 if its length is increased by 10% and its breath is decreased by 20% the perimeter in a sun change the length of the rectangle is 46800
The shifting of a number from one side of an equation to the other is called any value of the variable is makes both side of an equation equal is called or up the equation the solution of the equation is a number which is a much greater than 21 as is less 71 age the solution of the equation then X is equals to and the numerical value of 2x - 7 is the value of x for which expression 3x - 4 and 2x + 1 is a term of an equation can be transferred to the other side by changing its the equation can be solved by the method the number which one dividing by 60 minutes by 48 the solution of the equation number is the digit in the tense place of a 2 digit number is 4 more than that digit in the universe place in the digit at unit place then the number is 17 is subtracted from the products 5 times is a man is 56 years 987 will be three times as old as she was 9 years ago her present age years the sum of two consecutive multiple of 5 is 55 the smaller one is the sum of the three consecutive multiples of 666 the greatest one is 180 substed from pipe transistor settle number the result is 4 more than 4 times the number the number is the sum of two numbers is 84 and the difference is 12 the numbers are and out of 6th consecutive natural numbers in the sum of the first three is 27 then the sum of the other three age if one side of square is increased by 2 and the other side is decreased by 2 a rectangle of perimeter 48 is formed the side of the square is two different equation can never of the same answer very presence three consecutive original number then the number 16
Percentage
To fraction is equal to 25% is 141 1125 1251500 what is 25% of 25% equals to 0.00625 0.0625 0.625 6.25 the number 0.05 is what percentage of 20.025 0.2525 75% of the number is 900 then after number is 540 121350 hundred 27% of the value of the property is 2800 and the worth of the properties 80098 it cost to cut a copy a seat of paper however 2% discount is allowed on all photocopies done after first how much will it cost to 4580 Ritu pet 27.201 GST in the find the rate of GST person 9% 10% 12% Mrs Burma safe 2.5 zero in buying an item on sale at spent 25 for the item how much percent did she win the conjunction 8% 10% residual angle of measure 45 27 when he asked to draw an angle 45 the percentage error in his drawing
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