MIXED QUESTIONS - X
1) On What sum of money, the difference between the simple interest and compound interest in 2 years at 5% per annum is Rs15 ?
2) A certain sum of money invested at 5% intrest, compounded annually, for 3 years. If the interest computes to Rs2522, determine the principal.
3) In how many years will a sum of Rs800 at 10% per annum compounded semi-annually become Rs926.10 ?
4) Suraj has a fixed deposit in Bank of India of Rs40000 for a period of 3 years. The bank allows a compound interest of 13% compounded half yearly. Find the maturity value.
5) Sita deposit Rs400 per month in a bank in recurring deposit. On maturity she gets Rs97854.40. Find the period of which she had deposited .
6) Which is the better investment 8% Rs100 shares at Rs 20 premium or 6% Rs100 shares at 20 discount?
7) A company declares a semi-annual dividend of 5%. Sanjay owns 25 shares of par value Rs12.50 each . How much annual dividend must he receive ?
8) A company having a capital stock of Rs 450000 declares a dividend of 4% semi-annually.
a) What is the annual income a stock holder owning 135 share at par of Rs 10 ?
b) What is the total amount of dividend paid annually by the company ?
9) Vinoy owns 150 Rs 25 shares of a company which declares a dividend of 12%. What is Vinay's dividend income? If he sells the shares at Rs40 and invests the proceeds in 7% stock (par value Rs100) at Rs80, what is the change in his dividend income ?
10) Mr Gupta purchased 360 Rs50 shares at Rs20 premium. The company declares an annual dividend 12%.
a) Find his dividend income from the shares.
b) Find his total investment in the shares.
11) A man invests Rs1426 in 5% stock at Rs115. He sells this stock at Rs125 and invests the proceeds in 3% stock at 93. Find the change in his income.
12) Solve : (11- 2x)/(9- 3x) ≥ 5/8, x ∈ R, x < 3.
13) Solve: 8/3 ≤ x + 1/3 < 10/3, x ∈ R. Hence represent the solution on a number lines.
14) A= {x: -1< x ≤ 5, x ∈ R}
B={x : -4 ≤ x < 3, x ∈ R}
Represent a) A ∩ B b) A' ∩ B on different number lines, where universal set is R.
15) Solve the equation 3x²- x - 7= 0 and give your answer correct to 2decimal places.
16) Find the roots of x²- 6x +2= 0, using formula method.
17) Find the roots of √3 x²- 9x + 6 √3= 0, using formula method.
18) Solve for x, (4x²-1) - 3(2x +1) + x(2x +1)= 0.
19) Solve for x, using formula method, x² - 1/x² = (29/10) (x - 1/x).
20) Solve the following quadratic equation: √(x +15) = x + 3, x ∈ N.
21) Solve: √(x(x -3))= √10, State sum of the roots.
22) Solve : √(6x -5) - √(3x -2)= 2 using formula method.
23) A two-digit number is 4 times the sum and two times the product of its digits . Find the number.
24) A says to B, ' I am twice as old as you were when I was old as you are'. If the product of their ages is 588. Find their present ages.
25) A number consists of two digits such that the square of the digit in the ten's place exceeds the digits in the unit place by 11. If the number is 5 times the sum of the digits, find the number.
26) 10 years ago, the sum of the ages of two sons was half of their father's age. The ratio of the present ages of the two sons is 4:3 and the sum of the present ages of all the three is 117 years. Find the present ages of the father and each of the two sons.
27) A party of students arranged an excursion costing Rs540, whose amount was to be shared equally by all of them. But later, it was found that three of the students, could not pay, though they had joined the excursion . As a result , the rest of the students had each to pay Rs2 more. Find the total number of students in the party.
28) In a certain examination, the those number of candidates passed was 4 times the number of those who failed. If the number of candidates that appeared had been 35 less, and the number been twice the number failing. Find the total number of candidates that appeared at the examination.
PROBABILITY - TEST
1) A coin is tossed 500 times. We obtain a head 260 times. On tossing the coin at random, find the probability of getting
A head
a) 12/25 b) 13/25 c) 14/25 d) 16/25
A tail
a) 12/25 b) 13/25 c) 14/25 d) 16/2
2) A die is rolled 50 times and the number 6 is obtained 8 times. Now, if the die is rolled at random, find the probability of getting the number 6.
a) a) 4/25 b) 13/25 c) 14/25 d) 16/25
3) There are 10 cards in a bag bearing numbers from 1 to 10. A card is drawn from the bag 60 times. Each time, the number obtained is noted and the card drawn is replaced. It was found that the card number bearing number 7 was drawn 4 times. Now, if a card is drawn at random, find the probability of getting the card bearing 7.
a) 1/15 b) 2/15 c) 4/15 d) 7/15
4) A die is rolled 100 times and the outcomes are noted and tabulated as shown :
Outcomes: 1 2 3 4 5 6
Frequency: 9 15 19 21 24 12
When a die is rolled at random, find the probability of getting the number
2
a) 3/20 b) 21/100 c) 3/25 d) 6/25
4
a) 3/20 b) 21/100 c) 3/25 d) 6/25
6
a) 3/20 b) 21/100 c) 3/25 d) 6/25
ASSASSIN REASONS QUESTIONS:
DIRECTIONS: In the following questions , a statement of Assertion(A) is followed by a statement of Reason(R). Choose the correct option:
1) Assertion (A): A coin is tossed 16 times and the outcomes are recorded as below:
H T T H T H H H T T H T H T T H
The probability of occurrence of a bad is 50% .
Reason : When a coin is tossed, there are two possible outcomes-- Head and Tail.
a) both Assertion (A) and Reason(R) are true and Reason(R) is the correct explanation of Assertion (A).
b) both Assertion (A) and Reason(R) are true and Reason(R) is not the correct explanation of Assertion (A).
c) Assertion (A) is true but Reason(R) is false.
d) Assertion (A) is false but Reason (R) is true.
2) Assertion (A): When a spinner with 3 colour Red(R), Green (G) and Black (B) as shown is rotated , red and green colours have equal probability to show up with arrow.
Reason (R): The probability of occurrence of an event E is given by
P(E)= total number of trials/number of trials in which occurs
a) both Assertion (A) and Reason(R) are true and Reason(R) is not the correct explanation of Assertion (A).
b) both Assertion (A) and Reason(R) are true and Reason (R) is not correct explanation of Assertion (A).
c) Assertion (A) is true but Reason (R) is false
d) Assertion (A) is false but Reason (R) is true.
PROBABILITY
1) A fair die is thrown once. Find the probability that the number on it is :
a) an odd number
b) greater than 4.
c) at the most 4.
d) between 7 and 10.
2) Two fair coin are tossed. Find the probability that:
a) head turns up exactly once.
b) Tail turns up at least once.
c) Tail does not turn up at all.
3) A coin is tossed thrice. Find the probability that
a) Tail turns up atleast twice.
b) Head does not turn up at all.
c) Tail comes on the second toss.
d) head turns up atleast once.
4) Two fair dice are tossed. Find the probability that
a) The sum of the schore is 9.
b) the product of the score is 12.
c) the score on the second die is greater than the score on the first die.
d) the sum of the scores is a prime number.
e) the sum of the scores is a multiple of 4.
f) the sum of the score is a perfect square.
5) One card is drawn from a pack of well-shuffled pack of cards. Find the probability that the card drawn is:
a) A queen.
b) not a queen
c) A face card
d) red card
e) bears a number less than 4
f) king or black card
6) In a match between A and B, the probability of winning of A is 0.43. What is the probability of winning of B ?
7) A bag contains 3 red, 4 white, 5 blue marbles. All the marbles are identical in shape and size. One marble is drawn at random from the bag. Find the probability that the marble drawn is:
a) red
b) red or white
8) An unbiased coin is tossed. Find the probability that :
a) A head turns up.
b) A tail turns up
c) both head and tail turns up.
d) never head nor tail turns up.
9) A uniform die is thrown. Find the probability of the event A, B, and E where.
a) A= score is an even number
b) B= score is a number less than 5 but not less than 2.
c) score is a number that is a multiple of 3 or 5.
10) A perfect cubic die is thrown. Find the probability that
a) A prime number comes up
b) A perfect square comes up.
11) Two coins are tossed simultaneously. Find the probability of getting exactly one head.
12) 3 coins are tossed simultaneously. Find the probability getting at least one head.
13) Three unbiased coins are tossed. Find the probability of getting atleast two heads up.
14) A coin is tossed three times. Write the sample space. Find the probability of
E₁: getting two or more heads. E₂: the second is not a head.
15) Two unbiased dies are thrown in the air. find the probability that the sum of the scores is a multiple of 3.
16) Two dice are thrown. What is the probability that the sum of the points obtained is greater than 4 ?
17) Two unbiased dies are thrown. Find the probability that the sum of the numbers on their faces is at most five.
18) two fair die are thrown. Find the probability of getting the same score on the first die as on the second.
19) two unbiased dice are thrown in the air. Find the probability that the sum of the scores is greater than 9 or an even number.
20) if two pair die are thrown , find the probably that the sum of the points on their uppermost face is the perfect square or a multiple of 3.
21) a box contains 5 red, 11 white and 7 black balls. One ball is drawn at random. Find the probability that the ball drawn is a white ball.
22) A bag contains 6 red, 5 blue, 3 white and 4 black balls. A ball is drawn at random. Find the probability that the ball is red or black.
23) In a bag there are 6 black, 4 white and 3 yellow balls. A ball is taken at random. find the probability of getting a yellow or a white ball.
24) A box contains 7 red, 5 white and 8 green balls identical in all respects except colour. One ball is drawn at random. Find the probability that it is not white .
25) a card is drawn from a pack of well 52 playing cards. Find the probability that the card is drawn is
a) a diamond
b) a red card
c) A king
d) an ace or a queen
e) a face card
f) a card bearing number between and including 2 and 6.
26) six token bearing numbers 1 to 6 are placed in one box and seven tokens bearing number 1 to 7 are placed in another box. if one token is drawn from each box, what is the probability that the sum of the number is
a) 6
b) 11
27) If P(E)= 0.95, find P(not E).
28) A bag contains a certain number of the blue balls. A ball is drawn . Find the probability that the ball is black drawn is
a) black
b) blue.
29) The probability that two boys do not have the same birthday is 0.394. What is the probability that the two boys have the same birthday ?
30) Which of the following cannot be the probability of an event?
a) 5/7 b) 0.28 c) √2 d) -2.4
31) From a deck of 52 cards, all the face cards are removed and then the remaining cards are shuffled . Now one card is drawn from the remaining deck. Find the probability that the card is:
a) A black card.
b) 8 of red colour.
c) a king a black colour.
32) A box contains 1000 balls out of which 25 are defective. It is not possible to just look at the bulb and tell whether or not it is defective. One bulb is taken out at random from the box. Calculate the probability that the bulb taken out is
a) A good one
b) A defective one .
33) A bag contains 50 identical cards which are numbered from 1 to 50. If one card is drawn at random from the bag, find the probability that it bears
a) A perfect square number.
b) A number divisible by 4
c) A number divisible by 5
d) A number divisible by 4 or 5.
e) A number divisible by 4 and 5.
34) a bag contains 6 red, 8 white and x blue balls which are identical in shape and size. The probability that a ball drawn at random is blue or white is 5/7. Find x.
1) a) 1/2 b) 1/3 c) 2/3 d) 0
2) a) 1/2 b) 3/4 c) 1/4
3) a) 1/2 b) 1/8 c) 1/2 d) 7/8
4) a) 1/9 b) 1/9 c) 5/12 d) 5/12 e) 1/4 f) 7/36
5) a) 1/13 b) 12/13 c) 3/13 d) 1/2 e) 3/13 f) 7/13
6) 0.57
7) a) 1/4 b) 7/12
8) a) 1/2 b) 1/2 c) 0 d) 0
9) a) 1/2 b) 1/2 c) 1/2
10) a) 1/2 b) 1/3
11) 1/2
12) 7.8
13) 1/2
14) 1/2, 1/2
15) 1/3
16) 5/6
17) 5/18
18) 1/6
19) 5/9
20) 5/12
21) 11/23
22) 5/9
23) 7/13
24) 3/4
25) a) 1/4 b) 1/2 c) 1/13 d) 2/13 e) 3/13 f) 5/13
26) a) 5/42 b) 1/14
27) 0.05
28) a) 0 b) 1
29) 0.606
30) √2 and -2.4
31) a) 1/2 b) 1/20 c) 0
32) a) 39/40 b) 1/40
33) a)7/30 b) 6/25 c) 1/5 d) 1/25
34) 7
PAPER -2
1)The lines given by ax + 4y = 8 and 2x + 3y + 2 =0 are mutually perpendicular find the value of a. -6
2) AB and CD are two chords of a circle intersecting at a point P outside the circle. If PC =30cm, CD =14cm and PA=24cm, determine AB . 4cm
3) find the value of sec60 sin30+ cosec450 cos 90.
4) Find the total surface area of an open pipe of length 50cm, external diameter 20 cm and internal diameter 6 pcm. 4657.71
5) The perimeter of a semicircle in 90cm. Calculate its area. 481.2cm²
6) Find the equations of the lines which passes through the point (-2,3) and are equally inclined to the coordinanates axes. x- y+5= 0, x+ y-1= 0
7) If P= 2 6 & Q= 3 x
3 9 y 2 find x and y such that PQ = null matrix -6,-1
8) Using remainder theorem, factorize the expression
3x³+ 10x²+ x -6.
9) If (a²+ b²)(x²+ y²)= (ax + by)², show that a/x = b/y.
10) If a= 4√6/(√2+ √3), find the value of (a+ 2√2)/(a -2√2)=(a+ 2√3)/(a- 2√3). 2
11) A square Lawn is bounded on three sides by a path 4 m widr. If the area of the path is 7/8 that of the lawn, find the dimensions of the lawn. 16m each
12) Mr Ahuja invests equal sums of money in two companies offering 8% shares of Rs100 at a premium of Rs25 at 6% shares of Rs100 at a discount of Rs25. He finds that if with his total investment he had bought equal number of shares of each company, his income would have been Rs142 less. Find his total investment.
13) simple interest on certain sum of money for 4 years at 4% per annum, exceeds the compound interest on the same sum for 3 years at 5% by Rs228. Find the sum.
14) A recurring deposit account of Rs1200 per month has a maturity value of Rs12440.00 if the rate of interest is 8% and the interest is calculated at the end of the every month. find the time of recurring deposit.
15)i) plot the point A(3,5) and B(-2,-4).
ii) A' is the image of A when reflected in the x-axis . write down the coordinate of A' and plot it.
iii) B' is the image of bpB when reflected in the y-axis, followed by reflection in the origin. Write down the coordinate of B'.
iv) Write down the geometrical name of the figure AA'BB'.
v) name two invariant points under reflection in the x-axis .
the point 54 / 9 in the figure in the ratio 2:5 find the coordinate of the point A and B the vertices of 0512 write down the equation of find the equation construct the quadrilateral ABCD 5 BC 7 and ABC 120 given that AC is the only line of symmetry write down the geometrical name of the quadrilateral measure and record the length of the day in cm find the mean of the given datawith reference to the given figure a man stands on the ground at a point which is on the same horizontal plane the foot of the vertical point the height of the pole is 10 the main size 2 m above the groundly observe the angle of elevation the top of the pole where calculate the distance of ab the angle of the elevation of the top of the pole when a standing 15 m from the pool give your answer correct a circular running track is the portion bounded by two concentric circle in the cost of 15 along the outer circumference of the track is 3696 at rupees 24 permission in the cost of leveling the track is 66@12 square metre find the weight of the train abr the point 06000 the origin is a median and an altitude find the equation of Prove the side of the quadrilateral touch a circle prove that
PAPER-1
1) The shadow of a flag post 25m high is 25√3m. Find the angle of elevation of the Sun. 30°
2) A conical tent has a circular base of area 0.375 hectares . If its height is 20m, find its capacity. 2500m³
3) The sum of two radii of two circles is 18.5cm and the difference of their circumference of their circymference is 22cm. Find the radius of the bigger circle. 11cm
4) In the given figure, AB || CD and O is the centre of the circle.
If angle BED=35°, find angle ACD.
5) The line x - y = 3 divides the join of (3,4) and (8,3) in the ratio m: n. Find the ratio. 2:1
6) If A= 2. 0 & B= 14 0
-3 4 -45 44
Find the values of scalar factors X and y, such that xA²+ yA = B.
7) 4x³-12x²+ ax + b has x-3 is a factor but when it is divided by x + 2 the remainder is - 75. Find a and b. -1,3
8) A's income is Rs140 more than B's and C's income is Rs80 more than D's. If the ratio of A's and C's income is 2:3 and the ratio of B's and D's income is 1:2, find the income of each. 400,260,600,520
9) Three numbers are in continued proportion. Their sum is 38 and the sum of their squares is 532. Find the numbers. 8,12,18 or 18,12,8
10) Mrs Mehta plans to invest Rs8456 in shares . She partly invests in 17% share at Rs140 and the remaining amount in 9% share at Rs112. Her income from the second investment is Rs58 more than the first investment. How much did she invest in shares at Rs112? Rs5376
11) If the loan is returned after one year, a person would have to pay Rs6240 only. If it is returned after 2 years he would have to pay Rs6489.60 with compound interest. Calculate the amount of loan and the rate of interest. 6000, 4%
12) Mrs Bhagat deposits Rs1500 every month for 36 months in a bank and receives Rs65655 at the end of 36 months. Find the rate of simple interest paid by the bank on the recurring deposit. 14%
13) Solve the inequation and represent it on the number line x/2 +3 ≤ x/3 +4 < 4x -7, x ∈ R.
14) Find the values of x and y if the matrix
A= x+ y y & B= 2 & C= 3
2x x- y -1 2 with the relation AB = C. -1,5
15) From the following table, find the frequency distribution and calculate the mean marks:
Marks no of students
less than 8 4
less than 16 10
less than 24 22
less than 32 41
Less than 40 50 23.68
16) Prove sin⁶x + cos⁶x = 1- 3 sin²x + 3sin⁴x.
17) Two spheres of the same metal weight 1 kgf and 7 kgf. The radius of the smaller sphere is 2.5cm. the sphere are melted to form a single big sphere. Find the diameter of big sphere. 10cm
18) Draw a ∆ ABC in which AB= 4.6cm, BC= 5.4cm and angle B= 60°. With centre A, draw a circle of radius 2cm. Draw another circle to touch BC at C and which also touches the given circle externally.
19) MT and NT are tangent to two circles.
Prove that M, B, N and T are concyclic points.
20) If A(3,2), B(-2,4) and C(3,-2) are the vertices of ∆ ABC, find the equation of the line perpendicular to AB and passing through the mid point of BC. 10x - 4y-1= 0
21) The difference between the reciprocals of two consecutive multiples of 3 is 1/468, find the numbers. 36,39
22) A man borrowed a certain sum of money. He can pay Rs242000 after 2 years or pay Rs292820 after 4 years to clear the debt alongwith compound interest. find
a) the rate percent per annum
b) the sum borrowed. 10%, 200000
) OX and OY are the coordinanate axes.
AB= 6cm. The point A slides along OX and point B slides along OY. Find the locus of the midpoint of AB.
) In the figure,
E is the midpoint of AC and BE perpendicular to AC. AX bisects angle BAC meeting BC at D and BE at Y. Prove that
a) the point Y is equidistant from A and C.
b) The point S is equidistant from AB and AC.
) The ordinate of a point P is greater than its abscissa by 3 units . Its distance from a point A(-4,-8) is 17 units . Find the coordinates of the point P if it lies in the first quadrant.
) A function f is defined as a set of integers.
f(x)= 2x+5, 2< x ≤ 4
3x-4, 0<x≤ 2
a) find f and the domain and range of the function.
b) Can you find f(1/3). If not, why?
c) Find the value of x, if f(x)= 11.
) Given A={x:x²+ 3x-4=0}; B={x: 3≤ x ≤ 5, x ∈N} and C={5,6}, Ax(B U C)
) abscissa of a point P is twice its ordinate. If the point P is equidistant from A(2,-5) and B(-3,6), find its coordinates.
) A man sold a briefcase at 8% profit. Had he purchased it for at 10% less and sold for Rs72 less, he would have gained 50/3%. For how much did the man purchase the briefcase .
) A regular 10 sided polygon is inscribed in a circle of radius 20cm. Find each side of the polygon.
) ∆ ABC and ∆ PQR are similar and their areas are 1089 cm² and 2304 respectively. If AB = 22cm, find PQ. 32cm
COMPOUND INTEREST
2) Vijay borrowed Rs5000 and agreed to pay intrest at the rate of 10%, 12% and 14% for the first, second and third year respectively. Find the total amount he had to pay after 3 years. Rs7022.40
3) The machinery of a certain factory is valued at Rs550000. It depreciates each year at 10% of its value. Find the value of the machinery at the end of 3 years. 400950
4) A certain sum money invested at compound interest amounts to Rs2420 at the end of second year and Rs2662 at the end of third year. 10%, 2000
5) At what rate percent per annum, compound interest , will Rs3000 amount to Rs3370.80 in two years ? 6%
6) In how many years will Rs8000 amount to Rs10648 at 10% per annum CI ? 3yrs
7) The difference between simple interest and compound interest is Rs19.20 for 2 years. If the principal is Rs3000, find the rate of interest. 8%
8) A sum of money is invested at compound interest payable. The interest in two successive years is Rs225 and Rs240. Find the rate of interest. 20/3%
9) The compound interest for the 3rd on a certain sum is Rs726. If the simple interest on the same sum is Rs1800, find the rate and the sum. 10%, Rs6000
10) Saurav borrowed a certain sum of money and paid it back in 2 years in two equal installments. If the rate of compound interest was 4% per annum and if he paid back Rs4056 annually, what sum did he borrow ? Rs7650
Sales Tax
1) Sneha purchased an article costing Rs820. If the rate of sales tax charged is 6%, find the total bill . Rs869.20
2) A transistor is sold for Rs1242 including sales tax. If the rate sales tax is 8%, find the listed price of it. Rs1150
3) Sunita bought a TV for Rs18810. The rate of sales tax was 14%. The listed price of the TV was Rs18810. Find the reduction she got on the set. Rs2310
BANKING
1) Mr. Desai opens a recurring deposit of Rs2000 per month for 30 months playing simple interest of 12% p.a. Calculate the amount he receives at the time of maturity. 69,300
SHARES AND DIVIDEND
1) Which is the better investment---12% shares at 90 or 15% at 120 ? 12% at 90 is better
2) A man invests a sum of money in Rs20 shares, paying 15% dividend, quoted at 20% premium. If his annual dividend is Rs720, calculate
a) his total investment.
b) the rate of interest on his investment. Rs5760, 12.5%
3) A man bought 3200 shares of Rs10 paying 15% per annum. He sold them when the price rose to Rs28 and invested the proceeds in Rs50 shares paying 11% per annum at 12% premium. Find the annual change in his income. Rs4000
PROFIT, LOSS AND DISCOUNT
1) A Manufacturers sells a TV set to a wholesaler dealer at a profit of 18%. The wholesaler sells the same to a retailer at a profit of 20%. The retailer, in turns sells to a customer for Rs150045 thereby earning of profit of 25%. Find the cost price for the manufacturer.
2) A tradesman marks an article at Rs410 more than the cost price. He allows a discount of 10% on the marked price. Find his profit percentage, if the cost price is Rs x. Leave your answer in terms of x.
3) A shopkeeper sells an article at 10% discount on the marked price which is 25% above the cost price. Find the profit he makes if he sells an article for 765.
4) Two successive discounts of 20% and 5% are given on a bill of Rs5500. Find the net amount of money payable to clear the bill if sales tax charge is 10%.
LINEAR INEQUATIONS
1) A is the solution set of 8x - 11 > 4x- 3 and B is the solution set of 6x - 2≤ 4x + 10 where x∈ N. Find the set A ∩ B. Hence, graph the solution set on the number line.
2) List the element of the solution set of the following equation: -3< x -2≤ 9 - 3x; x∈R.
3) Solve the inequation |2x - 9|< 6, x ∈Z. State the solution set.
4) List solution set of the inequation; 1/2 + 8x > 5x -3/2, x ∈Z.
5) Find the range of the values of x which satisfy -1/3 ≤ x/2 - 4/3 < 1/6, x ∈ R.
Graph these values of x on the real number line.
6) if - 2≤ 1/2 - 2x/3≤ 11 / 6, x ∈N, then find the solution set and graph it on the number line.
7) Write open mathematical sentences using x for the variables, whose graphs are given below :
QUADRATIC EQUATION
1) Solve: √(3x²+ x+5}= x - 3. -4,1/2
2) Roots of the quadric equation are 1/2 and -14. Find the equation. 2x²+ 27x -14= 0
3) 8(t²+ 1/t²)- 42(t - 1/t)+ 29= 0. Find the possible values of t. 15/4,3/2
4) Solve : x²- 6x -15= 0. Give your answer correct to two decimal places. -1.90, 7,9
5) Solve the following:
a) 6x²- x = 35.
b) x² - 8X - 1280 = 0.
c) 1/(2y -9) = 1/(y -3) + 4/5.
d) 2x²+ 11x -10 = 0. Give your answer correct to two decimal places.
e) 5ˣ⁺¹ + 5²⁻ˣ =126.
1) A two digit number is such that the product of digits is 12. When 9 is added to the number the digits are interchanged. Find the number.
2) The sides of a right angle triangle are x cm, 4(x + 1)cm, and (4 x + 5)cm. Find x.
3) A man purchased sheep for Rs4500. Three sheep were lost and the rest he sold for Rs30 more per sheep than he had paid. if his gain on the whole transaction is 8%, how many sheep did he buy ?
4) The sum of the ages of a man and his son is 46 years and the product of their ages is 168 years. Find the age of the son.
5) The total surface area of a cylinder is 75.24 cm² and its height is 3.6 cm. if its radius is x cm, find x.
6) The bill of a party for a certain number of people is Rs19200. If there were 10 more persons, the bill each person had to pay would have reduced by Rs160. Find the number of people at the party. 30
COORDINANATE GEOMTRY
Distance
1) Find the coordinanates of the point on the y-axis which are at a distance of √68 from the point (2,-5). (0,-13),(0,3)
2) A is the point in the y axis whose ordinate is 5 and B is a point (-3,1). Calculate the length of AB .
3) Find the coordinate of the points on the x-axis which are at a distance of 3√5 units from the point (8,-3).
4) Prove that the point A(-10,8), B(-2,-4) and C(10,4) are the vertices of an isosceles right angled triangle.
SECTION FORMULA
1) A point P divides the join of A(6,-2) and B(-5,8) in the ratio 2:3. Find the coordinanates of P.
2) Find the ratio in a which x-axis divides the join of A(7,2) and B(5,-4). 1:2
3) In what ratio is the line joining the points A(-8,6) and B(10,-4) divided by x-axis.
4) In what ratio is the line joining the points A(-12,9) and B(15,-6) divided by y-axis?
5) The midpoint of the line joining A(a,2) and B(3,6) is (2,b). Find the value of a and b.
6) ABCD is a parallelogram. The coordinates of the vertices are A(-4,-2), B(3,-2), C(x,4) and D(-1,2). Find the coordinates of the point C .
7) Find the coordinates of the points A and B where the line 5x + y=10 cuts the x-axis and y-axis respectively. Hence , find the coordinates of the midpoint of AB.
EQUATION OF STRAIGHT LINE
1) Find the equation of a line parallel to y= 2x + 3 and passing through (5,4). y= 2x -6
2) The coordinate of A and B are (3,-5) and (0,4) respectively. Find
a) slope of AB. 1/3
b) the equation of line passing through B and perpendicular to AB. 3y= x + 12
3) The lines x + 2 y=5 and 3x+ by= 3 are parallel. Find b. 6
4) If A(2, 8), B(6,4) and C(-6, y) are collinear points , find y.
5) 4x + a y - 7 = 0 and 6x + 3 y - 10 = 0 are parallel lines. Find a.
6) Find the value of k, given that the line y = 2x - 2K passes through (5,-2).
7) The coordinates of points A and B are (6,-4) and (8,12). Find the equation of
a) straight line AB .
b) the perpendicular bisector of AB.
8) The coordinates of the vertices of ∆ ABC are A(-2,5), B(6,1) and C(2,-1). Find
a) the equation of a line perpendicular to BC and passing through the vertex A.
b) the equation of a line perpendicular to AC and passing through the vertex B.
c) the coordinates of the orthocentre of ∆ABC.
9) A and B are points on positive side of the x-axis and y-axis respectively. The point P(4,3) divides the join of AB in the ratio 3:1. Find the equation of the line AB.
10) ABCD is a rhombus. The coordinates of A and C are (2,12) and (-6,-4) respectively. Find the equation of the diagonal BD.
Reflection:
1) find A(a,6) is reflected in the origin as A'( - 2, b). Write the value of a, b.
2) Point A(-4,0) is reflected in x-axis to A' and A' is reflected in y-axis to A". Write the coordinates of A' and A''.
3) Mₓ(a,8)= (c, b) and Mₒ(a, b)= -3, d), find a,b,c, d.
4) P(4,8) is reflected in the line L and its image is Q( 4,-2). Find the equation of the line l.
5) B (5,-4) is reflected in the line
a) x= 3
b) y= -4
c) y=2,
Write the coordinates of the image in each case,
d) State In which case the images is an invariant point.
METRICES
1) If A= -2 3 & B= 1 2
1 4 -3 -3, then Find AB.
2) If B= 1 5 & C= 4 0
-3 7 1 -3 with the relation as 2A - 2B = C, then find Matrix A.
3) If A= 1 2 B= -1 0 & C= 4 2
-3 -4 4 -5 -15 11 with the relation KB = C - A, then find the value of Matrix K.
4) If A= 3 -4
0 2 B= 3 8 with the relation MA= B, then find the matrix M.
5) If A= 3 4 B= 1 y C= 7 0
5 x 0 1 10 5 with the relation 2A + B = C, then, find the values of x and y.
6) A= sin²30° cos²45° & B= cos0° cos90°
sin0° sin90° find AB.
7) If A= 2 3 B= 7 15
-1 0 -5 -3 with the relation xA²+ yA = B, then find x and y.
8) If A= 3 0 & B= 2 -5 C= 2 -3
2 1 3 1 4 5
Find a) A(BC) b) (AB)C c) Is A(BC)= (AB)C
RELATIONS AND FUNCTIONS
FACTOR THEOREM
1) Find the remainder when x³- 5x²+ 9x - 6 by x-2.
2) Find the remainder when x³- 16x -26 is divided by x+3.
3) Find the remainder when x³+ 54 when divided by x+ 4.
4) If 2x³+ x²- 2x - k has 2x+1 as a factor, find k. Hence Factorize completely.
5) When 2x³+ x²- 2x - k is divided by 2x + 2, the remainder is 0. Find k.
6) if 3x³ + ax²- bx - 30 has x - 3 and 3x+ 5 as factors , find a, b.
7) Factorise completely by using factor theorem: 2x³- x²y - 36xy² - 45y³.
8) Given expression f(x)= x²+ n²x + m, h(x)= x²+ m²x + n and m≠ n, given that both the functions have x + a as a common factor, show that a(m + n)+ 1= 0.
RATIO AND PROPORTION
1) If 4, 5, 12 and x are in proportion, find x.
2) Find the mean proportion of 12.1 and 16.9.
3) What number may be substracted from 8, 14, 24, 46 so that the four numbers from a proportion ?
4) Two vessels contain a mixture of two liquids A and B in the ratio of 9:4 and 5:3. In which ratio must liquids be taken from each vessel to give a mixture of liquid A and liquid B in the ratio of 2:1 ?
5) Find the mean proportion of √48 - 2√3 and √48 + 2√3.
6) (a + b)/(c+ d)= (a - b)/(c - d), prove that (a²+ b²)/(c²+ d²)= ab/cd.
7) If x/p = y/q = z/r, show that (p²x²+ q²y²+ r²z²)/(p³x + q³y+ r³z)= √(xyz/pqr).
8) If p,q , r are in continued proportion, show that (x + y+ z)²/(x²+ y²+ z²)= (x + y+ z)/(x - y+z).
SIMILARITY
1) In the given figure,
DE is parallel to BC . Area of ∆ ABC=125 cm², area of trapezium BCDE is 105 cm², DE = 4cm. Calculate the length of BC.
2) The model of a school is made to a scale 1 :400
a) The length of the model is 60 cm. Calculate the length of the school.
b) The area of the ground occupied by it is 240000 m². Find the area of the ground occupied by the model.
c) The volume of the model is 60 litres. Find the volume of the building.
3) The volume of a boat is 81000cm³. The model of the boat is made with reduction factor 2 :15. Find the volume of a model .
4) In the given figure
PQ/BC = 3/5. Find
a) AP: PB
b) If area of ∆ APQ is 24.3 cm², find the area of the trapezium BCQP.
5) A scale of map 1:2000000. Find
a) how much does 1 cm on the map reparesent the number of kilometres on the ground ?
b) how much does 1 cm² on the map represent the number of km² on the ground.
c) how many square centimetres on map will represent 4400 km² on ground?
6) The volume of a figure drawn in space is 3375 cm³ and the figure is transformed by a magnification factor about any point in the space. If the volume of the image is 39304 cm³, find the magnification factor.
LOCUS
1) A field is of the shape of a quadrilateral ABCD in which AB=100m, BC =140m angle ABC= 120°. The vertex D is equidistant from B and C and 160m from A and angle BAD is obtuse . Measure CD.
2) Draw a line XYZ such that XY= YZ= 5cm. Construct angle XZA= 45°, AZ= 6cm. Find two points P and Q each at a distance of 2cm from XYZ and equidistant from A and Z. Measure PA and QA.
3) Two straight roads PQ and RS cross each other at P at an angle 75°. S is a stone on the road PQ, 800m from P, towards Q. By drawing a figure to scale (1cm=100m), locate the position of a flagstaff X, which is equidistant from P and S and is also equidistant from the roads. Measure the distance X from P, and calculate the actual distance.
SYMMETRY
1) a) Construct a quadrilateral ABCD with AB= 4 cm and BC =6.5 cm and angle ABC =135°.
b) Given that AC is its only line of symmetry.
2) Copy each of these figures and complete them with the help of the axis of symmetry l.
3) Use graph paper for this question. Plot the points on P(1,-3), Q(6,2) and R(1,7) to form angle PQR.
a) draw the line of symmetry of triangle PQR and write its equation.
b) Mark the point X, if the line in (a) and the line PR are both lines of symmetry of quadrilateral PQRX. Write coordinanates of the point X. Also write the equation of the line PR.
c) What kind of quadrilateral is PQRX ?
CIRCLE
1) AB and CD are parallel chords of a circle with centre O. AB= 10cm and CD= 24cm and they are on the same side of O. If the radius of the circles is 13cm, find the distance between the chords.
2) Two circles with radii 5cm and 7cm have their centres 15cm apart. Calculate
a) the length of the direct common tangent
b) the length of the transverse common tangent.
3) In the given figure,
AT is a tangent of a circle with centre O. Angel BAT= 70°, Calculate angle ACB.
4) In the given figure, AB is the diameter.
Calculate
a) angle PAB
b) angle ABQ.
5) In the given figure, ABCD is a cyclic quadrilateral in which angle BAD=75°, angle ABD= 58° and angle ADC= 77. Find
a) angle BDC
b) angle BCD
c) angle BCA
6) Two circles with centre P and Q interesect at C and D. PM = QM, AB perpendicular CM. Prove that AC= BC
7) ABC is a right angled triangle with AB = 6cm and BC= 8cm. A circle with centre O has been inscribed inside the triangle . Calculate the value of x, the radius of the inscribed circle.
8) P, Q and R are common tangents to the circles with centre A and B. Prove that
a) PS= SR = SQ
b) angle PRQ= 90°
9) In the given figure AB is a diameter of a circle with centre O .
AX, BY and XRY are tangents. Prove that angle XOY.
10) In the given figure,
O is the centre of the circle, angle POQ= 40° and TSP= 120°. Calculate the measure of angle PRS and angle QPR.
15) In the adjoining figure,
ED is a chord parallel to the diameter AC of the circle ABCDE. If angle CBE= 63°, calculate angle DEC.
16) In the given figure, two circles intersect at M and N.
ABC is a triangle. Prove that A, L, M and K are concyclic points.
17) In the given figure,
PAB is a secant and PT is a tangent to the given circle. The point T is the point of contact. Given PT= 6cm, AB= 5cm, find AP.
18) Draw a circle with radius 3.5cm and centre O. Take any point P such that OP= 5.8cm. From P construct two tangents to the circle.
19) Draw two circles with radii 4.2cm and 2.8 cm with their centres 8 cm apart . Construct
a) a direct common tangent.
b) a transverse common tangent.
20) Draw a circle of radius 3 cm. Circumscribe and inscribe a regular hexagon about it and inside it.
21) Construct a triangle in which AB= 5cm, BC= 3.6cm and angle ABC= 67.5°. Constrya Circle to touch AB at B and pass through C .
MENSURATION
CIRCLE
1) The area of a circular ring is 418 cm². If the radius of the smaller circle is 6cm, find the radius of the bigger circle.
2) The sum of two radii of two circles is 18.5cm and the difference of their circumference is 22cm. Find the radius of the bigger circle.
3) How many times will the wheel of a cycle rotate to cover a distance of 242 km, if its diameter is 77 cm ?
4) If the circumference of a circle is 440m, find its area.
5) Find the area of the largest circle that can be drawn in a square of side 21 cm.
6) The sum of the inner and outer circumference of a circular road is 770m. If the area of the road is 1540m², find its width .
7) The length of the minute hand of a clock is 8cm. Find the area swept by it in 18 minutes. (Leave your answer in terms of π).
8) The area of a circle inscribed in an equilateral triangle is 154cm². Find the perimeter of the triangle (π= 22/7, √3= 1.73). Give your answers correct to one decimal place.
9) The area of a circular field is 2464cm². Around it there is a circular path which has been built at the cost of Rs13860 at the rate of Rs10 per m². Find the radius of the outer circle.
10) The area of a circular ring enclosed between two concentric circles is 286 cm², find the diameters of the circle if their difference is 14cm.
11) A circular garden has a diameter of 84m. A boy takes a round on a bicycle, the diameter of the wheel being 70cm. Find the number of revolutions made by the wheel in completing 5 rounds of the garden. Also , find the distance covered in 5 rounds .
12) Each wheel of a car has a diameter of 35cm and makes 100 revolutions in 3 seconds. Calculate the speed of the car in kmph .
13) The diagram represents the area swept by the wiper of a car.
With the dimensions in the diagram, calculate the shaded area swept by the wiper.
CYLINDER
1) How many cubic meters of earth must be dug to make a cylindrical water tank, 4m in radius and 1.75m deep ? Also , find the cost of plastering its curved surface at the rate of Rs35.50 per m².
2) A cylindrical metallic tube has internal diameter 11.2cm and its length is 10 cm. The metal is uniformly 1.4cm thick . Calculate its volume.
3) The circumference of the base of a right circular cylinder is 37.25 cm and its height is 10cm. Find its curved surface area.
4) What length of solid cylinder of 5cm radius must be taken to the recast into a hollow cylinder of external diameter 20cm, 2cm thick and 25cm long?
5) A cylinder glass of diameter 12cm, contains some water. A metal sphere of diameter 6 cm, when placed in it, is fully submerged. Find the rise in water level in the glass.
6) A glass cylinder with diameter 14cm has 20cm height. It contains water to a depth of 8cm. Five cones each of radius 3cm and height 7cm are placed in it and are completely immersed. How many litres of water should be added to fill the glass !
7) The lower part of a solid is a right circular cylinder and its upper part is a right circular cone. The total height is 30cm and that of cylinderical part is 6 cm. If the diameter of its base is 14 cm, find
a) curved surface area
b) volume of the solid.
8) A cylindrical water tank of diameter 1.4m and height is 2.1m is being fed by a pipe of diameter 3.5cm through which water flows at the rate of 2m/s. Calculate in minutes the time it takes to fill the tank (π= 22/7)
9) Earth taken out on digging a circular tank of diameter 17.5m is spread all around the tank uniformly to a width of 4m, to form an embankment of height 2m. Calculate the depth of the circular tank correct to two decimal places (the depth of the tank is uniform everywhere).
CONE
1) A tent is in the form of a right circular cone. Its height is 4m and base diameter is 10.5m. If it can accommodate 15 persons , how many cubic meters of air is available for each person?
2) From a solid cone whose height 16 cm and radius is 12cm, a conical cavity of height 3cm and base radius 4cm is hollowed out. The base of the cones form concentric circles. Find the
a) total surface area
b) volume of remaining solid (leave your answer in π form).
3) a conical tent , 6 m in diameter and 4 m high is made of Canvas. How many such tents can be made from 1000m long, 110cm wide Canvas, allowing 10% for wastage?
4) A solid cone of height 12cm and base radius 6cm has the top 4cm removed as shown in the figure.
Find the whole surface area of the remaining solid.
SPHERE
1) A sphere has a radius of 10.5cm. Find its
a) volume
b) surface area
2) A spherical ball of metal, 6cm in diameter is melted and recest into three spherical balls. The diameters of the two balls at 3cm and 4cm. What is the diameter of the third ball ?
3) what is the least number of solid metallic sphere each of radius 4cm that should be melted and recast to form a hollow sphere of outer diameter 24cm and of uniform thickness of 2cm.
4) A vessel is in the form of an inverted cone. Its height is 8cm and the radius of its top which is open is 5cm. It is filled with water upto the rim. When lead shots, each of which is a sphere of radius 0.5cm, are dropped into the vessel, one fourth of the water flows out. Find the number of lead shots dropped into the vessel. (π= 22/7)
TRIGONOMETRY
1) 1/(1+ cosA) + 1/(1- cosA)= 2cosec²A
2) 2+ tan²x + cot²x = cosec²x sec²x.
3) In ∆ ABC, angle B= 60°, angle C= 30° and BC= 100m. Find AD.
4) In the figure angle ACD= 60°, angle B= 30°, BC= 100m. Find AD.
5) A guard observes an enemy boat, from an observation tower at a height of 180m above sea level, at an angle of depression of 30°.
a) Calculate the nearest metre, the distance between the boat and the foot of observation tower.
b) After sometime, it is observed that the boat is 200 m from the foot of the observation tower. Calculate the angle of depression.
6) A and B are two points, 80m apart, in a straight stretch of a bank of river. C is an object on the opposite bank such that angle CAB= 60° and angle CBA= 45°. Calculate the distance of C from the bank AB.
7) A vertical pillar and a tower 120m high are in the same horizontal plane. From the top of the tower, the angle of the depression of the top and foot of the pillar are 30° and 45° respectively. Find
a) the distance between the pillar and the tower.
b) the height of the pillar (give your answer and nearest correct to the nearest metre).
8) In the given figure. ∆ ABC is right angled triangle at C.
PQCR is a square. AC = 16cm, RC= 4cm. Calculate angle B.
9) In the figure, angle ADC= 30°, angle CDE= 45°, AB= 30cm. Find
a) BD
b) AE
10) In the given figure, ABC is a triangle in which angle ABC= 90°, angle C= 45° and AB= 12cm. BD perpendicular to AC. Find
a) BC
b) AD
c) AC
11) In the given figure,
all right angles have been marked. If DE= 18cm, EC= 8cm and BD= 40cm, Calculate
a) the measure of angle EDC
b) the length of the side FA to the nearest whole number, if DE|| FA.
12) A square ABCD of side 25cm rest on a plane of inclination 30°. Find the height of C above the horizontal, if AP= 30cm.
13) From a point P on level ground, the angle of elevation of the top of a tower is 30°. If the tower is 100m high , how far is P from the foot of the tower ?
14) A 60m high tree is broken by the wind. The broken part makes an angle of 30° with the ground. Find the length of the unbroken part of the tree.
15) The angle of depression from the top of a tower, 200m high, of an object on the ground is 30°. Find the distance of the object from the tower.
16) From a light house, the angle of depression of two ships on opposite sides of a light house were observed to be 30° and 45°. if the height of the light house is 90 metres and the line joining the two ships passes through the foot of the light house, find the distance between the two ships. Give your answer correct to one decimal places.
17) In the given figure,
AB represents a vertical pole and CD represents a 40m high tower, both of which are standing on the same horizontal plane, From the top of the tower, the angles of depression of the top and foot of the pole are 30° and 60° respectively. Calculate
a) the horizontal distance between the pole and the tower.
b) the height of the pole.
18) The angle of elevation of the top of a tower from a point A on the ground is 30°. On walking 50m towards the tower, the angle of elevation is found to be 60°. Calculate
a) the height of the tower correct to one decimal place.
b) the distance of the tower from A.
19) sinx(tanx - cotx)= secx - 2cosx.
20) (secx - cosecx)(secx + cosecx)(sin²x - sin⁴x)= sin²x - cos²x.
21) (sinx - cosx)(tanx + cotx)= secx - cosecx.
CENTRAL TENDENCY
1) Find the mean of 6,10, 4, 12, 8.
2) Find the mean of the following table by the direct method :
X: 10 15 20 25 30
F: 3 6 5 4 2
3) Calculate the mean marks in the given distribution by
a) direct method
b) shortcut method or assumed mean method
Marks frequency
0-9 4
10 -19 6
20- 29 12
30- 39 6
40- 49 7
50- 59 5
1) Calculate the median of 9, 2, 4, 7, 5, 0, 6.
2) Find the median of numbers 0, 2, 3, 5, 7, 7, 9, 10
3) Compute the median of the following distribution:
Marks: 5 10 15 20 25 30
F: 4 6 10 12 13 5
4) The following is a frequency distribution : draw an ogive and locate
a) median
b) semi-interquartile range
Class frequency CF
00-10 5 5
10-20 10 15
20-30 20 35
30-40 25 60
40-50 15 75
50-60 12 87
60-70 9 96
70-80 4 100
5) Draw an ogive for the following frequency distribution. Use your ogive to estimate
a) the median
b) the number of students to obtained the more than 75% marks.
Marks no. Of students
00-09 5
10-19 9
20-29 16
30-39 22
40-49 26
50-59 18
60-69 11
70-79 6
80-89 4
90-99 3
1) Find the mode of the following set of the number : 7, 2, 8, 5, 7, 9, 7, 8.
2) IQ of 50 students was recorded as follows. Draw a histogram and estimate the mode.
I. Q Score No. Of students
80-90 6
90-100 9
100-110 16
110-120 13
120-130 4
130-140 2
1) A boy scored the following marks in various class tests during a terminal examination, each test being marked out of 20:
17, 15, 16, 7, 10, 14, 12, 19, 16, 12
Find his average mean marks.
2) A test of 25 marks was given to 16 students and marks scored were recorded as given below:
25, 8, 14 ,20, 16, 22, 10 , 15, 8, 7, 24, 18, 19, 6, 11, 17.
a) find the mean marks.
b) in the report, marks were entered out 50. What is the mean of the recorded marks in the report ?
3) in a shooting competition , a marksman can score 0 to 5 points in each shot. After firing 20 shots, a competitor 's score was as follows:
Score: 0 1 2 3 4 5
F: 2 3 2 4 6 3
Find the mean score per shot.
4) The following are the marks obtained by 77 boy in a class test:
Marks No. Of boys
00-08 8
08-16 7
16-24 16
24-32 24
32-40 15
40-48 7
Calculate mean by
a) direct method
b) Short cut method
c) If the marks of each student are increased by 2, find the new mean marks.
5) Find the median for the each of the following sets of numbers:
a) 15, 8, 14, 20, 13, 12, 16.
b) 25, 11, 15, 10, 17, 6, 5, 12
6) A boy scored the following marks in various class during a term, each test being marked out of 20:
15, 17, 16,7,10,12,14,16,19,12,16
a) What is his model marks ?
b) What is his median marks?
c) What is his mean marks?
7) Given below is a cumulative frequency table showing the monthly savings of a group of people:
X: 10 20 30 40 50 60 70 80
C.F: 15 35 64 84 96 120 192 256
a) estimate the median .
b) estimate the semi-interquartile range for the distribution.
8) Using the data given below, construct the cumulative frequency table and draw the ogive . From the ogive determine:
a) the median
b) the inter-quartile range
Marks frequency
00-10 3
10-20 8
20-30 12
30-40 14
40-50 10
50-60 6
60-70 5
70-80. 2
9) Draw a histogram for the following data on graph paper labelling the axes properly and giving the scale for the axes. Also determine the mode and the modal class.
Height in cm no of students
50-60 8
60-70 3
70-80 4
80-90 10
90-100 2
MIXED QUESTIONS (1)
) Find the rate of sales tax levied on a car that was sold at a price three times its marked price.
) When ⁷x²- 3x +8 is divided by (x - 4), find the remainder (using reminder theorem).
) If cosx =2/5, without using table, find sin x.
) Calculate the length of the tangent drawn to a circle of diameter 8cm from a point 5cm away from a centre of the circle.
) if x², 4 and 9 are continued proportion , find the value of x.
) If x∈ Z, find the solution set for the equation 5 < 2x -3 ≤ 14 and graph the solution on a number line.
) find p and q if g(x)= x+ 2 is a factor of f(x)= x³- px + x + q anf f(2)= 4.
) Given A=1 -2 & B= 0
-3. 4 1
a) Find a matrix Z such that A+ B is zero matrix.
b) Find the matrix M such that A+ M= A.
c) Find AB.
) a) If 7 is the mean of 5, 3, 0.5, 4.5, b, 8.5, 9.5, find b.
b) If each observation is decreased in value by 1 unit, what would the new mean be?
) In the given figure below, AB is a chord with centre O and BT is tangent to the circle at B. If angle OAB= 32, find the value of x and y.
) Construct a regular pentagon of side 3cm. Draw the line of symmetry.
)a) A discount of 15% is allowed on the marked price of an article and sold for Rs2975. Calculate its marked price.
b) Given that the market price is 40% above the cost price of the article. Find its cost price and the profit made by the sale of the article in rupees.
) The volume of a cylinder 14cm long is equal to that of a cube having an edge 11cm. Calculate the radius of the cylinder.
) A piece of butter 3cm by 5cm by 12cm is placed in a hemispherical bowl of radius 3.25cm. Will in the butter overflow when it melts completely ?
) Construct a ∆ABC in which AB =5 cm, BC=8cm and CA= 7cm. Construct the circle which passes through A and B and has BC as tangent.
) A company with 10000 shares of Rs50 each, declares an annual dividend 5%.
a) What is the total amount of dividend paid by the company?
b) What would be the annual income of a man who 72 shares in the company ?
c) if he receives only 4% on his investment, find the price he paid for each share.
) a) State the equation of the mirror line, if point A(5,0) on reflection is mapped as A'(-5,0).
b) State the equation of the mirror line, if point B(4,-3) on reflection is mapped as B'(4,3).
c) Point C(-3,5) on reflection in y= 2 is mapped as C'. Find the coordinanates of C.
) Solve graphically: 2x + 3y = - 5, 2y+ 3x = 0.
) All function are symmetric about x-axis, Comment on this statement, giving clear reasons for it being true or false.
) In a ∆ABC, angle A is obtuse, PB perpendicular to AC and QC perpendicular AB. Prove AQ x AB = AP x AC.
) Taniya standing on a vertical cliff in a Jungle observes two rest-houses in line with her on opposite sides deep in the Jungle below. If their angles of depression are 30° and 45° and the distance between them is 222m, find the height of the cliff.
) AB is a fixed line. Write the locus of the point P so that AB²= AP²+ BP².
) Calculate the value of 2/(√5 -3) to 3 significant figures by rationalising the denominator.
) The base of a triangle is 2cm greater than twice its altitude area. If the area is 12cm², Calculate the base and the altitude.
) Find the equation of a line that passes through (1,3) and is parallel to the line y = - 3x + 2.
) In the given figure,
calculate:
a) angle APB
b) angle AOB.
) The midpoint of the line joining A(2, p) and B(q,4) is (3,5). Find the numerical value of p and q.
) From the following table, find:
a) average wage of a worker. Give your answer, to the nearest paise.
b) modal class.
Wages in Rs no of Workers
less than 10 15
less than 20 35
Less than 30 60
Less than 40 80
Less than 50 96
Less than 60 127
Less than 70 190
Less than 80 200
) The relation, f(x)= 2x is defined from the set X to set Y where X={0, 1, 2, 3} and Y={1, 2, 6}. The Venn diagram for sets X and Y are given in the figure. Copy the same and draw arrows to show the pairs that satisfy the relation. Is the relation a function ? Give reasons.
) Examine the ogive given below which shows the marks obtained out of 100 by a set of students in an examination and answer the following questions:
a) How many students are there in the set?
b) How many students obtained 40% marks ?
c) How many students obtained 90% and above ?
d) What is the median make?
) Prove that: √{(1+ cosx)/(1- cosx)}= cosecx + cotx.
MIXED QUESTIONS -(2)
) Calculate the compound interest on Rs8000 for 1 year at 12% per annum compounded half yearly.
) The point P(a,b) is reflected in the x-axis to obtain point Q(3, -4). Find a and b.
) if A= a 3a B= 2 & C= 5
b 4b 1 12 find a and b.
) The mean of the numbers 6 , y, 7, x and 14 is 8. Express y in terms of x.
) Given f(x)= x/(x²-1). Find f(-1/2).
) Solve using quadratic formula, x²- 5x -2= 0. Give your answer correct to 3 significant figures.
) If (8a+ 5b)/(8c + 5d)= (8a - 5b)/(8c - 5d). Prove that a/b = c/d.
) find the value of k, if x - k is a factor of x³- kx²+ x +4.
) Solve : 1< 3x -3 ≤12, x ∈R and mark it on a number line.
) Calculate the mean , median and mode of the following numbers:
12, 11, 10 ,11, 12, 13, 14, 13, 15. 13.
) In the diagram, chords AB and CD of the circular are produced to meet at O. Given that CD=4cm, DO=12cm and BO= 6cm, calculate AB.
) If cosx = 4/5 and cosy= 24/25; evaluate
a) cosec²x
b) cotx + coty.
) On a map drawn to a scale of 1:125000, a triangular plot of land has the following measurements: PQ =10cm, QR= 8cm, angle PRQ= 90°. Calculate
a) the actual length of PQ in km.
b) the area of the plot in square kilometres.
) AB is a diameter of a circle of radius 36cm. M and N are points on the diameter such that AM= MN= NB.
Semi-circles are drawn with AN and NB as diameters, as shown in the figure. Find :
a) The perimeter of the shaded region.
b) The area of the unshaded region (leave your answer in π form).
) The work done by (2x-3) men in (3x+1) days the work done by (3x+1) men in (x+8) days are in the ratio of 11:15. Find the value of x.
) If f(x)= (2x -7)/(x+4), find
a) f(2)
b) f(x³).
) Find the mean of the following frequency of distribution:
Class interval frequency
00- 30 3 3
30-60 7
60-90 15
90-120 14
120-150 7
150-180 4
) A man invests Rs30800 in buying shares of nominal value Rs56 at 10% premium. The dividend on the shares is 18% per annum. Calculate :
a) The number of shares he buys.
b) The dividend he receives annually.
c) The rate of interest he gets on his money.
) Show: sinx/(1- cotx) + cosx/(1- tanx) = sinx + cosx.
) A straight line passes through the points A(-2,8) and B(10,-4). It interesects the co-ordinate axes at point E and F. P is the midpoint of the segment EF.
Find :
a) The equation of the line.
b) The coordinate of E and F.
c) The co-ordinates of the point P.
) In an auditorium , seats were arranged in rows and columns. The number of rows was equal to the number of seats in each row. When the number of rows was doubled and the number of seats in each row was reduced by 15, the total number of seats increased by 400. Find :
a) The number of rows in the original arrangement.
b) The number of seats in the auditorium after rearrangement .
) Draw a histogram and hence estimate the mode for the following frequency distribution:
Class frequency
00-20 3
20-40 8
40-60 10
60-80 6
80-100 4
100-120 3
) A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60°. When he moves 40m away from the bank, he finds the angle of elevation to be 30°. Calculate
a) the width of the river
b) the height of the tree.
) Find a, b, if
A= 3 -2 B= 2a C= -4 & D= 2
-1 4 1 5 b with the relation AB+ 4C= 3D.
) A vessel is in the form of an inverted cone. Its height is 15cm and the diameter of its top which is open, is 5 cm. It is filled with water up to the rim. When lead shots, each of the which is a sphere of diameter 5 mm are dropped into the vessel, 1/3 of the water flows out. Find the number of lead shots dropped into the vessel .
) In the given circle with diameter AB , find the value of x.
) Construct an angle ABC=45°. Mark a point P on BC such that BP= 5.5cm. construct a Circle to touch AB at B and also to pass through P.
) Find the value of k for which the lines Kx - 7y +5= 0 and 6x - 2y +9= 0 are perpendicular to each other.
) If (a,b) ∈R, name the kind of relation between a and b if a R b => b R a, i.,e, a is related to b => is related to a.
Does R = {(a,b)= a< b, a, b ∈N} also show a relation of this kind ? Explain.
MIXED QUESTIONS -3
1) The price of a TV set inclusive of sales tax of 9% is Rs40221. Find the marked price.
2) If x: y= 4:3, find (5x + 8y): (6x - 7y).
3) Using the remainder theorem, find the remainder when y²- 7y²+ 15y -19 is divided by y - 3.
4) Without using table, evaluate 3cos70° cosec20°+ 2 cos65° cosec25°.
5) State and draw the locus of a point equidistant from two parallel lines.
6) In the given figure, the medians QS and RT of a ∆ PQR meet at G. Prove that :
a) ∆ TGS ~ ∆ RGQ
b) QG= 2GS from (a) above.
7) Solve the following inequation and graph the solution on the number line:
2x - 5≤ 5 x + 4< 11, x∈R.
) Given R={(x,y)∈ A x A: x= y} and A={0,1,2,3}, find:
a) list the elements of R
b) list the domain of R
c) List the range of R.
) Using only ruler and compass, construct angle ABC=120°, where AB= BC = 5cm. Mark two points P and Q which satisfy the condition that they are equal distant from both BA and BC and are also at a distance of 3 cm from the point B.
) The marks of 20 students in a test were as follows:
5, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14,14, 15,15,15, 16,16, 18, 19, 20, Calculate
a) the mean
b) the median
c) the mode
) Construct a ∆ ABC in which AB= AC= 4cm and BC= 3cm. Using a ruler and compasses only, draw the reflection A'BC of ∆ABC, in BC. Draw the lines of symmetry of the figure ABA'C.
) In the figure, BMD is the segment of a circle with centre O and angle BOD= 90°. BO= OD = 40 cm.Find
a) the area of shaded figure
b) the perimeter of the shaded figure (π=3.14)
) If A= 1 -4 B= -3 2 C) 4 0
4 1 4 0 0 -3 find
a) A²
b) BC
c) A²+ BC
) The point A(3,4) is reflected to A' in the x-axis, and O'clock is the image of O(the origin) when reflected in the AA'. Using graph paper, give
a) the coordinanates of A ' and O'.
b) the lengths of the segments AA' and OO'.
c) the perimeter of the quadrilateral AOA'O.
d) the geometrical name of the figure AOA'O'.
) Prove the following identity:
1/(Sinx + cosx) + 1/(sinx - cosx)= 2sinx/(2sin²x -1).
) In the given figure, AB is the diameter of a circle with centre O. Angel BCD is 130°. Find
a) angle DBA
b) angle BAD.
) Find the equation of a line passing through the point (-4,6) and having the x-intercept of 8 units .
) A man wants to buy 72 shares available at Rs130(per value of Rs100).
a) How much should he invest ?
b) if the dividend is 7.5%, what will be his annual income ?
c) if he wants to increase his annual income by Rs300, how many extra shares should be buy?
) Solve graphically the simultaneous equations given below. Take the scale as 2 cm= 1 unit on both the axes.
3x - 2y =4; 5x - 2y = 2.
) The following table gives the weekly wages of workers in a factory:
weekly wages(Rs) no of Workers
below 180 the number of workers getting 165 or more but less than 1805 was weekly poses using ruler compass only construct the triangle in which a circle of radius 3 in touch the answer the hollow sphere of internal and external diameter 8 and 16 respectively find the height of the tower and give the answer correct to a man sales and article of 15% above its cost price if he had but at 10% less than what he paid for it and sold it for rupees 140 less you have given 20% find the cost price of the article the function is given by formula such that the marks obtained by 24 students In a mathematics takes in given below 0 10 10 2018 20 30 32 30 44 dronazide for the given distribution of use a suitable scale for your Simon using estimate the medium the lowercottail the number of students who obtained more than 75% of taste the number of students who did not pass in the test in the past percentage was 14 24 3375 are the vertices of find the co-ordinate of the centroid the equation of a line through and parallel Mr print up with the saving bank account in the Bank of India is pass because the following and travel distance by 40 write down and expression for the time taken the return journey to 40 minutes then the onward journey write down any equation in X find the value
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