CHALLENGING MATHS For ALL

Day -1

1) (2⁴ -2)/(2³ -1) = ?

2) The sum of all of the digits of the integers from 98 to 101 is

9+ 8+ 9 + 9+ 1+ 0+ 0 + 1 +0 + 1= 38 

The sum of all the digits of the integers from 1 to 2008 is

A) 30054  B) 27018 C) 28036 D) 30036 E) 28054

3) Which is larger, 2²³⁴ or 5¹⁰⁰ 

4) 

A) 1 B) 2 C) √2 D) 8 E) none

5) 2²(x +3) + 9 -5 = 32. Then x = ?

A) 4 B) 8 C) 1 D) 16 E) none

6) 4x/6 = 2 + 3x/15. Then x = ? 

A) 17 B) 30 C) 30/17 D) 17/30 E) none

7) Value of (3!)!/4! is

A) 20 B) 30 C) 40 D) 60 E) none

8) 

A) 2 B) 8 C) 64 D) 128

9)

10) 

11) Simplify: (3ⁿ⁺³ - 3ⁿ⁺¹)/3ⁿ⁺². 

A) 8/3 B) 2/3 C) 4/3 D) none

12) If 2ˣ + 2ˣ + 2ˣ + 2ˣ = 2²⁰²³ then x is:

A) 2000 B) 2001 C) 2021 D) none

13)

14) Find the correct option:

If 9x² = 360 then

A) x= 40 B) x= -40 & x= 40 C) x=√40 D) x= - √40 & x= √40

15) 

16) If 16ˣ = 81 then (2ˣ ⁻¹)² = ?

A) 3 B) 2 C) 3/2 D) 9/4 E) none

17)  Find n

        Note: n is a posotive integer

                 2ⁿ > 10¹⁰    

18) 

A) 0.1 B) 0.01 C) 0.001 D) 0.0001 E) none 

19) The sum of all divisors (Leaving 1 and number itself) of 720 is

A) 20 B) 19 C) 21 D) 18 

20) 20% of 60 is equal to what percent of 80

A) 10 B) 15 C) 20 D) 25 E) none

Day-2

1) 

2) If (8ˣ⁺¹ - 2ˣ⁺³)/(4ˣ - 2ˣ) = 136 then find x.

A) 3 B) 4 C) 5 D) 6  E) none

3) If 3²ʸ -30 = 6 then 3⁻ʸ= ?

A) 6 B) -6 C) 1/6 D) -1/6  E) none

4) If 2ˣ 3ʸ = 72 ×72 then the value of √{(xy+1)/(xy-8)} is

A) 5 B) 4 C) 5/4 D) 4/5  E) none

5) What is the remainder when 2x⁴ - 3x² - x +3 is divided by x+1

A) 1 B) 2 C) 3 D) 4 E) none

6) 

A) ⁵⁰√10 B) ¹⁰⁰√10 C) √10 D) ²⁰√10

7) 

A) 180 B) 180/7 C) 90/7 D) 45/7

8) Find the number of digits by multiplying these two numbers

(16⁵) × (5¹⁶)

A) 5 B) 16 C) 21 D) 20 E) none

9) (49)¹⁵ - 1 is exactly divisible by:

A) 50 B) 51 C) 8 D) 29

10) Given that the last four digits of 521¹⁰⁰⁰ is 0001, find the last four digits of 521⁹⁹⁹.

A) 001 B) 01 C) 00001 D) 1 E) none 

11) Value of x of

A) 2 B) 4 C) 16 D) 32 E) none 

12) If 1/98! + 1/99! ° x/100! Then x=?

A) 100 B) 1000 C) 10000 D) 1/10 E) none

13) If 5ˣ⁻¹ = 1 then simplify 5ˣ⁺¹ = ?

A) 265 B) 275 C) 225 D) 25

14) If 9x² = 144y² then the value of x/y is

A) 12 B) 4 C) 3 D) 1

Day- 3

1) i √{√(i)²²}= ?

A) √-1 B) -1 C) +1 D) None

2) 2¹⁰⁰ - 2⁹⁹ = ?

A) 2¹ B) 2⁹⁹ C) 2¹⁰⁰ D) none

3) If ˣ√(122² - 121²) = 3 then x is

A) 11 B) 21 C) 31 D) none

4) 

A) 1 B) 11 C) 21 D) none

5) If 3ˣ = 4 then find the value of 9⁵ˣ⁺³ is

A) 3² B) 81 C) 243 D) none

6) Value of √[2 ³√{2} ⁴√(2)}]= ?

A) 1 B) 2 C) 4 D) none

7) (2¹⁰ - 2⁹ - 2⁸)²/16 = ?

A) 256 B) 512 C) 4096 D) none 

8) If 4x - = 2/3 then the value of 81³ˣ/27ʸ is

A) 4/9  B) 8/27 C) 16/81 D) none

9) What is the half of 8⁸

A) 4⁴ B) 8⁷ C) 8⁴ D) 4⁸ E) 2²³ F) none

10) Value of √(9% × 4%) is

A) 6 B) 6% C) 60% D) 600% E) none 

11) (90²+ 30²)/{(90+30)²+(90-30)²} =?

A) 1 B) 2 C) 1/2 D) 3 

12) 

13) Choose the odd one:

A) a)13-22 b) 24-76. c)16-52 d)17-62

B) a)6-16 b)18-48 c)21-56 d)27-76.

C)a)39-77.b)51-119 c)33-88 d)52-91

D)a)26-4 b)226-14 c)274-16. d)82-8

E) a)2-4 b) 4-5 c) 6-18. d)8-32

F) 82, 15, 65, 26 

G) a)4-44 b) 6-64. c)3-30 d)5-35

H) 37, 47, 17, 27.

I) New Delhi, Kolkata, Chennai, Mumbai

14) 7: 32 :: 28 : ?

A) 128. B) 228 C) 328 D) 428

15) BCFG: HILM :: NORQ: ?

A) TUXW. B) TXUW C) TWXU D) TWUX

16) ACEG: ZXVT:: BDFH: ?

A) SUWY B) YEUS C) YUES D) N

17) 8: 9:: 56 : ?

A) 27 B) 63 C) 72. D) 36

18) 25: 37: : 49: ?

A) 26 B) 62 C) 56 D) 65.

19) JkL, AbC, MnO, DeF, PqR, Gh?

A) A B) D C) I. D) K

20) 6, 24, 60, 120, 210, ?

A) 6 B) 33 C) 36 D) 336

21) Y X H G W V F E U T D C S R B ?

A) A. B) B C) C D) D

22) R Q O L H ?

A) A B) B C) C. D) D

23) 2, 6, 12, 20, 30, ?, 56

A) 2 B) 4 C) 24 D) 42.

24) 1, 4, 10, 19, 31, ?

A) 4 B) 6 C) 46. D) 64

25) A husband and a wife had five married sons and each of them had four children. How many members are there in the family.

A) 32. B) 44 C) 30 D) 16

26) Two squads of soldiers A and B facing North and South respectively received the following command-- right turn, left turn, left turn, left turn, which direction could the squads A and B face at the end.

A) East, west       B) West, East

C) South, North  D) north, south

27) 9: 26:: 81: ?

A) 2 B) 4 C) 42 D) 242.

28) 3: 26: : ? : 124

A) 142 B) 124. C) 241 D) 214

29) 4: 27:: 9: ?

A) 46 B) 64. C) 83 D) 38

30) 4, ? 144, 400, 900, 1764

A) 69 B) 96 C) 102 D) 44

31) 2, 10, 30, 68, ?

A) 110 B) 120 C) 130. D) 140

32) Odd one out: 9,16,25,36,49,61

A) 9 B) 25 C) 61 D) N

33) Fatima while introducing Mustafa to her husband said, his brother's father is the only son of my grandfather. How is Fatima related to Mustafa ?

A) brother B) sister C) aunt D) niece

34) Tarun's age is the cube of a whole number. It was square of another whole number two years ago. How long must wait before his age is again the cube of a whole number.

A) 13 B) 23 C) 32 D) 39.

35) If GERMANY is written as 7, 5, 18, 13, 1, 14, 25. How can FRANCE be written.

A) 6,18,1,14,3,5

B) 6,8,1,14,3, 5

C) 6,18,1,4,3,5

D) 16,18,1,14,3,5

36) A man starts from a point 'X' and walks 3 km southwards, then he turns left and walks 6 km. In which direction is he from the starting point? 

A) south-east.     B) south-west

C) Northeast       D) northwest

37) C is to the west B and south west of A, D is to the North of C and is in line with AB. In which direction from the point of A, B is located?

A) south-east.     B) south-west

C) Northeast       D) northwest

38) Veena walked 5m towards north, took a left turn and walked 7m. She took a left turn again and walked 8m before taking a left turn and walking 7m. She then took a final left turn and walked 1m before stopping. How far is Veena from the starting point.

A) 1 B) 2. C) 3 D) 4

39) Study the following arrangement carefully and answer the questions given.

BUBDCEDBDEUBADCBEACDAEBAUACDBCAC.

a) Which of the following is the eighth to the left of the twentieth from the left end of the above arrangement.

A) A B). C) C D) D

b) How many meaningful words can be formed with the alphabets which are first, second, fifth and sixth from the left end of the above arrangement.

A) 1. B) 2 C) 3 D) 4.

c) How many such consonants are there in the above arrangement each of which is immediately preceded by a vowel and also immediately followed by a consonant ?

A) more than one

B) more than two

C) more than three

D) more than four

d) If all A's are dropped from the arrangement, which of the letter will be eleventh from the right end of the arrangement.

A) B B) C C) D D) E.

40) Pointing to a photograph of a girl, Rohit said "She has no sisters or daughters but her mother is the only daughter of my mother". How is the girl in the photograph related to Rohit ?

A) Nephew B) Niece C) brother D) sister

41) If √4096 = 64 then the value of √40.96 + √0.4096 + √0.004096 + √0.00004096

A) 7.1104. B) 0.71104 C) 0.071104 D) n

42) If 2= 5, 4 = 18, 6 = 39 and 8 = 68 then 10 = ?

A) 10 B) 100 C) 105 D) 110

43) Odd one out:

a) 2160, 360, 69., 18, 6, 3

b) 7, 8, 18, 57, 228., 1165, 6996.

44) One evening before sunset, two friends Shyam and Ram were talking to each other face to face. If Ram's shadow was exactly to his right side. Which direction was shyam facing.

A) South B) north C) southwest D) southeast

45) Five girls are standing in a circle facing the centre. Suman is between Lata and Asha. Mamta is to the right of Lata.

a) If Suman and Mamta interchange their positions, then who will be the fourth to the left of Rajni 

A) Asha. B) Mamta C) Suman D) Lata

b) If Rajani and Asha interchange their positions, then which of the following correct 

A) Asha would be second to the left of Lata

B) Mamta would be between Suman and Rajani

C) none of these 

c) Who is the left of Asha if Rajani is the fifth girl.

A) Rajani. B) Mamta C) Suman D) Lata

46) If the first and second digits in the sequence 5981327438 are interchanged, also the third and fourth digits, the fifth and sixth digits and so on, then which digits would be the seventh counting from the right

A) 4 B) 6 C) 8. D) 2

47) Walking at 6/7 th of his usual speed, a man is 12 minutes late. The usual time taken by hum to cover that distance is.       1hr 12m

48) ₹56250 are divided among A, B and C. So that A may receive half as much as B and C together, and B received one fourth of what A and C together receive. The share of A is more than that of B is.        7500

49) A and B having income ratio 5:3, The expense ratio of A, B, C are 8:5:2. If C spends ₹2000 and B saves ₹700, then A's savings are.            1500

Day - 4

1) Which one equals 13 ?

a) 4+3×2-1

b) 4(3+2)-1

c) 4×3 ÷2-1

d) 4+ 3(2+1)

2) Fill the box of the following by giving numbers:

a) 1,2,3,4= ∆ × ∆ = ∆∆

b) 1,2,3,4,5= ∆ × ∆∆= ∆∆

c) 1,2,3,4,5,6= ∆ × ∆∆= ∆∆∆

d) 2,3,4,5,6,7= ∆ × ∆∆ = ∆∆∆

e) 4,5,6,7,8,9= ∆ × ∆∆ = ∆∆∆

3) 81 ÷(3×3)+12 - (5+7)²=?

4) 3² - 3 ÷ 1/3 +6=?

5) Evaluate: - x²+1 when x=6

6) If ₓ√x = x³⁾² then find x.

7) Complete the Series:

a) 16, 89, 48, 36, 24,12, ?

b) 1, 4, 9, 16, 25, 36, ?

c) 2, 3, 4, -1, 18, 46, ?

d) 10, 19, 28, 37, ?

e) 3, 5, 9, 17, 33, 65

f) 4, 10, ?, 82, 244, 730.