CHALLENGING MATHS (JUNIORS)

Day- 2

1) 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


2) 7: 32 :: 28 : ?
A) 128. B) 228 C) 328 D) 428

3) BCFG: HILM :: NORQ: ?
A) TUXW. B) TXUW C) TWXU D) TWUX

4) ACEG: ZXVT:: BDFH: ?
A) SUWY B) YEUS C) YUES D) N

5) 8: 9:: 56 : ?
A) 27 B) 63 C) 72. D) 36

6) 25: 37: : 49: ?
A) 26 B) 62 C) 56 D) 65.

7) JkL, AbC, MnO, DeF, PqR, Gh?
A) A B) D C) I. D) K

8) 6, 24, 60, 120, 210, ?
A) 6 B) 33 C) 36 D) 336

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

10) R Q O L H ?
A) A B) B C) C. D) D

11) 2, 6, 12, 20, 30, ?, 56
A) 2 B) 4 C) 24 D) 42.

12) 1, 4, 10, 19, 31, ?
A) 4 B) 6 C) 46. D) 64

13) 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

14) 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

15) 9: 26:: 81: ?
A) 2 B) 4 C) 42 D) 242.

16) 3: 26: : ? : 124
A) 142 B) 124. C) 241 D) 214

17) 4: 27:: 9: ?
A) 46 B) 64. C) 83 D) 38

18) 4, ? 144, 400, 900, 1764
A) 69 B) 96 C) 102 D) 44

19) 2, 10, 30, 68, ?
A) 110 B) 120 C) 130. D) 140

20) Odd one out: 9,16,25,36,49,61
A) 9 B) 25 C) 61 D) N

21) 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.

22) 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

23) 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

24) 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

25) 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

26) 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.


27) 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

28) If 2= 5, 4 = 18, 6 = 39 and 8 = 68 then 10 = ?
A) 10 B) 100 C) 105 D) 110

29) Odd one out:
a) 2160, 360, 69., 18, 6, 3
b) 7, 8, 18, 57, 228., 1165, 6996.

30) 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

31) 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. 
A) 1 hr B) 1hr 5min  C) 1hr 12m D) none 

32) ₹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. 
A) 6000  B) 7000  C) 7500 D) none 

33) 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.            
A) 1500 B) 2000 C) 2500 D) none 


Day -1

1) (2⁴ -2)/(2³ -1) = ?
A) 2 B) 4 C) 8 D) 16 E) none

2) Which is larger, 2²³⁴ or 5¹⁰⁰

3) 2²(x +3) + 9 - 5 = 32. Then x = ?
A) 4 B) 8 C) 1 D) 16 E) none

4) 4x/6 = 2 + 3x/15. Then x = ? 
A) 17 B) 30 C) 30/17 D) 17/30 E) none

5) 2ˣ + 2ˣ + 2ˣ + 2ˣ = 2²⁰²³
A) 2000 B) 2001 C) 2021  D) none 

6)  Find the correct option:
If 9x² = 360 then
A) x= 40 B) x= -40 & x= 40 C) x=√40 D) x= - √40 & x= √40

7) If 16ˣ = 81 then (2ˣ ⁻¹)² = ?
A) 3 B) 2 C) 3/2 D) 9/4 E) none

8) 20% of 60 is equal to what percent of 80
A) 10 B) 15 C) 20 D) 25 E) none

9) If (8ˣ⁺¹ - 2ˣ⁺³)/(4ˣ - 2ˣ) = 136 then find x.
A) 3 B) 4 C) 5 D) 6 E) none

10) If 3²ʸ -30 = 6 then 3⁻ʸ= ?
A) 6 B) -6 C) 1/6 D) -1/6 E) none

11) 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

12) What is the remainder when 2x⁴ - 3x² - x +3 is divided by x+1
A) 1 B) 2 C) 3 D) 4 E) none

13)  Find the number of digits by multiplying these two numbers
(16⁵) × (5¹⁶)
A) 5 B) 16 C) 21 D) 20 E) none

14) (49)¹⁵ - 1 is exactly divisible by:
A) 50 B) 51 C) 8 D) 29

15) If 1/98! + 1/99! ° x/100! Then x=?
A) 100 B) 1000 C) 10000 D) 1/10 E) none

16) If 5ˣ⁻¹ = 1 then simplify 5ˣ⁺¹ = ?
A) 265 B) 275 C) 225 D) 25

17) If 9x² = 144y² then the value of x/y is
A) 12 B) 4 C) 3 D) 1

18) i √{√(i)²²}= ?
A) √-1 B) -1 C) +1 D) None

19) 2¹⁰⁰ - 2⁹⁹ = ?
A) 2¹ B) 2⁹⁹ C) 2¹⁰⁰ D) none

20) If ˣ√(122² - 121²) = 3 then x is
A) 11 B) 21 C) 31 D) none

21) If 3ˣ = 4 then find the value of 9⁵ˣ⁺³ is
A) 3² B) 81 C) 243 D) none

22) Value of √[2 ³√{2} ⁴√(2)}]= ?
A) 1 B) 2 C) 4 D) none

23) (2¹⁰ - 2⁹ - 2⁸)²/16 = ?
A) 256 B) 512 C) 4096 D) none 

24) If 4x - = 2/3 then the value of 81³ˣ/27ʸ is
A) 4/9 B) 8/27 C) 16/81 D) none

25) What is the half of 8⁸
A) 4⁴ B) 8⁷ C) 8⁴ D) 4⁸ E) 2²³ F) none

26) Value of √(9% × 4%) is
A) 6 B) 6% C) 60% D) 600% E) none 

27) (90²+ 30²)/{(90+30)²+(90-30)²} =?
A) 1 B) 2 C) 1/2 D) 3 

28) 9 - 3 ÷ 1/3 + 1 = ?
A) 0  B) 1 C) 2 D) 

29) Value of
A) 11/7 B) 7/11 C) 1/7 D) none 

30) 

31) 

32) 

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