20
Marks: --/1
In the nineteenth century a person was X years old in the year X2. How old was he in 1884?
Choose one answer.
| a. 43 | ||
| b. 68 | ||
| c. 78 | ||
| d. 58 |
21
Marks: --/1
A three-digit number in base 10 is written in base 9 and base 11 to give two numbers N1 and N2,respectively. What is the probability that N1and N2 are also three-digit numbers?
Choose one answer.
| a. 0.67 | ||
| b. 0.33 | ||
| c. 0.88 | ||
| d. 0.55 | ||
| e. 0.42 |
22
Marks: --/2
What is the remainder when (17)36 + (19)36 is divided by 111?
Choose one answer.
| a. 2 | ||
| b. 0 | ||
| c. 1 | ||
| d. 109 |
23
Marks: --/2
If 
, then x is equal to
, then x is equal to
Choose one answer.
| a. 2 | ||
| b. 1/2 | ||
| c. -1 | ||
| d. 1 |
24
Marks: --/1
The smallest positive integer N such that sqrt(N) - sqrt(N - 1) is less than 0.01 is
Choose one answer.
| a. 2499 | ||
| b. 2501 | ||
| c. 2498 | ||
| d. 2502 | ||
| e. 2500 |
25
Marks: --/1
The numbers 123 456 789 and 999 999 999 are multiplied. How many times does digit ‘9’ come in the product?
Choose one answer.
| a. 2 | ||
| b. 3 | ||
| c. 0 | ||
| d. 9 |
26
Marks: --/1
All the divisors of 360, including 1 and the number itself, are summed up. The sum is 1170. What is the sum of the reciprocals of all the divisors of 360?
Choose one answer.
| a. 2.75 | ||
| b. 1.75 | ||
| c. 3.25 | ||
| d. 2.5 |
27
Marks: --/1
The sum of the digits of Kallu’s nightclub number is
Choose one answer.
| a. an even number | ||
| b. a perfect square | ||
| c. a perfect number | ||
| d. a prime number |
28
Marks: --/1
(x, y are integers)
Choose one answer.
| a. 7 | ||
| b. 9 | ||
| c. 3 | ||
| d. 5 |
29
Marks: --/1
To number the pages of a book, exactly 300 digits were used. How many pages did the book have?
Choose one answer.
| a. 136 | ||
| b. 135 | ||
| c. 138 | ||
| d. 137 |
30
Marks: --/1
The product of three consecutive odd numbers is 531117. What is the sum of the three numbers?
Choose one answer.
| a. 273 | ||
| b. 213 | ||
| c. 183 | ||
| d. 243 |
31
Marks: --/1
In a national hockey single elimination tournament, 303 teams are participating. How many games will be played before a team becomes the national champion?
Choose one answer.
a. 152
b. 77
c. 303
d. 302
32
Marks: --/1
The value of A + B that satisfies (630 + 6-30)(630 - 6-30) = 3A8B - 3-A8-B is
Choose one answer.
a. 40
b. 20
c. 60
d. 80
33
Marks: --/1
The digits 1, 2, 3, 4, and 5 are each used once to compose a five-digit number abcde such that the three-digit number abc is divisible by 4, bcd is divisble by 5, and cde is divisble by 3. Find the digit a.
Answer:
34
Marks: --/1
The number A4531B, where A and B are single-digit numbers, is divisible by 72. Then A + B is equal to
Choose one answer.
a. 8
b. 4
c. 7
d. 5
35
Marks: --/1
What is the value of n such that n! = 3! × 5! × 7!
Answer:
36
Marks: --/2
What is the remainder when 1 + (11)11 + (111)111 +....
+ (111...111)111...111 is divided by 100? The last term contains ten 1's within the bracket as well as the power.
Choose one answer.
a. 30
b. 10
c. 40
d. 0
37
Marks: --/1
What is the sum of the real values of x satisfying the equation
4 × 32x+2 – 92x = 243?
Choose one answer.
a. 5/2
b. 3/2
c. 3
d. 1
38
Marks: --/1
The last two digits of 41997 are
Choose one answer.
a. 36
b. 84
c. 64
d. 24
39
Marks: --/1
Let S = p2 + q2 + r2, where p and q are consecutive positive integers and
r = p × q. Then (S)1/2 is
Choose one answer.
a. always irrational
b. an even integer
c. an odd integer
d. sometimes irrational
40
Marks: --/1
If the remainder when x100
is divided by x^2 - 3x + 2 is ax+b, then value of a and b are :--Choose one answer.
a. 2^100 and 1
b. 2^100 and 2 - 2^100
c. 2^100 and 1- 2^100
d. 2^100 - 1 and 2 - 2^100
41
Marks: --/2
What is the remainder when the number is divided by 99?
Choose one answer.
a. 18
b. 36
c. 33
d. 27
42
Marks: --/1
5353 – 2727 is certainly divisible by
Choose one answer.
43
Marks: --/1
What is the largest prime whose cube divides 1!2!…1001!?
Choose one answer.
44
Marks: --/1
The difference between the cubes of two consecutive positive integers is 1027. Then the product of these integers is
Choose one answer.
45
Marks: --/2
Let
 , where a, b, c, and d are not equal to zero. Then the set of intersection of all values of S and T is
Choose one answer.
46
Marks: --/1
Let q and r be the quotient and remainder when M, a five digit number, is divided by 100. For how many values of M is q + r divisible by 99?
Choose one answer.
47
Marks: --/1
A two-digit number is divided by the sum of its digits. The answer is 6. What is the product of the digits?
Choose one answer.
48
Marks: --/1
(CAT 2006)
When you reverse the digits of the number 13, the number increases by 18. How many other two-digit numbers increase by 18 when their digits are reversed?
Choose one answer.
49
Marks: --/2
Let n be the smallest positive number such that the number S = (8n)(5600) has 604 digits. Then the sum of the digits of S is
Choose one answer.
50
Marks: --/2
If n is a natural number such that 1012 < n < 1013 and the sum of the digits of n is 2, then the number of values n can take is
Choose one answer.
51
Marks: --/1
The number (2n)! is divisible by
I. (n!)2 II. ((n − 1)!)2 III. n! × (n+1)!
Choose one answer.
|
51
Marks: --/1
The number (2n)! is divisible by
I. (n!)2
II. ((n − 1)!)2
III. n! × (n+1)!
I. (n!)2
II. ((n − 1)!)2
III. n! × (n+1)!
Choose one answer.
| a. II and III only | ||
| b. I and II only | ||
| c. I and III only | ||
| d. I, II and III |
52
Marks: --/2
Vinay has 128 boxes with him. He has to put least 120 oranges in one box and 144 oranges at the most. Then the least number of boxes containing the same number of oranges is
Choose one answer.
| a. 24 | ||
| b. 6 | ||
| c. 103 | ||
| d. 5 |
53
Marks: --/1
In a village of 2029 inhabitants, at least x villagers have the same English initials for their first name and their surname. The least possible value of x is
Choose one answer.
| a. 4 | ||
| b. 3 | ||
| c. 6 | ||
| d. 5 | ||
| e. 2 |
54
Marks: --/1
If 
, then
(CAT 2005)
, then(CAT 2005)
Choose one answer.
| a. R > 1.0 | ||
| b. 0.1 < R ≤ 0.5 | ||
| c. 0 < R ≤ 0.1 | ||
| d. 0.5 < R ≤ 1.0 |
55
Marks: --/2
The unit digit of 
is
is
Choose one answer.
| a. 3 | ||
| b. 1 | ||
| c. 9 | ||
| d. 7 |
56
Marks: --/1
In how many ways can the number 105 be written as a sum of two or more consecutive positive integers?
Choose one answer.
| a. 4 | ||
| b. 6 | ||
| c. 5 | ||
| d. 7 |
57
Marks: --/1
For how many values of k is 1212 the least common multiple of 66, 88, and k?
Choose one answer.
| a. 1 | ||
| b. 25 | ||
| c. 12 | ||
| d. 24 |
58
Marks: --/1
(CAT 2006)
The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?
The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?
Choose one answer.
| a. 25 | ||
| b. 67 | ||
| c. 21 | ||
| d. 41 | ||
| e. 73 |
59
Marks: --/1
The single digits a and b are neither both nine nor both zero. The repeating decimal 0.abababab... = V />= O /><!--[if !vml]--><!--[endif]-->is expressed as a fraction in lowest terms. How many different denominators are possible?
Choose one answer.
| a. 5 | ||
| b. 4 | ||
| c. 6 | ||
| d. 3 |
60
Marks: --/1
The sum of 20 distinct numbers is 801. What is their minimum LCM possible?
Choose one answer.
| a. 360 | ||
| b. 42 | ||
| c. 840 | ||
| d. 480 |
61
Marks: --/1
What is the remainder when is divided by 13?
is divided by 13?
Choose one answer.
| a. 6 | ||
| b. 7 | ||
| c. 1 | ||
| d. 10 |
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