**Ques No 1:**

Which of the following has most number of divisors?

**Options:**

A. 182

B. 99

C. 176

D. 101

**Solution:**

**Ques No 2:**

The least number which on divided by 35 leaves a remainder of 25 and on division by 45 leaves the remainder 35 and on division by 55 leaves the remainder 45 is

**Options:**

A. 2515

B. 3455

C. 2875

D. 2785

**Solution:**

**Ques No 3:**

Which of the following is the smallest 6-digits number divisible by 111?

**Options:**

A. 111111

B. 110011

C. 100011

D. 100111

**Solution:**

**Ques No 4:**

Find out (A + B + C + D) such that AB × CB = DDD, where AB and CB are two-digit numbers and DDD is a three-digit number.

**Options:**

A. 21

B. 19

C. 17

D. 18

**Solution:**

**Ques No 5:**

Number of values of a (from 0 to 9) for the number N = 2345631143a4 is divisible by 12 is

**Options:**

A. 0

B. 1

C. 2

D. More Than 2

**Solution:**

**Ques No 6:**

If is real number, then the number of integral values of n is

**Options:**

A. 3

B. 5

C. 7

D. Infinite

**Solution:**

**Ques No 7:**

The number of positive n in the range 12 ≤ n ≤ 40 such that the product (n – 1)(n – 2)…3.2.1 is not divisible by n is

**Options:**

A. 5

B. 7

C. 13

D. 14

**Solution:**

**Ques No 8:**

How many 4-digit numbers are there with the property that it is a square and the number obtained by increasing all its digits by 1 is also a square?

**Options:**

A. 0

B. 1

C. 2

D. 4

**Solution:**

**Ques No 9:**

1^{13} + 2^{13} + 3^{13} + … + 60^{13} is divisible by

**Options:**

A. 61

B. 63

C. 65

D. 60

**Solution:**

**Ques No 10:**

The number of positive fractions m/n such that 1/3 ≤ m/n < 1 and leaving the property that the fraction remains the same by adding some positive integer to the numerator and multiplying the denominator by the same positive integer is

**Options:**

A. 1

B. 3

C. 6

D. Infinite

**Solution:**

**Ques No 11:**

If the eight digits’ number 2575d568 is divisible by 54 and 87, then the value of the digit d is

**Options:**

A. 4

B. 7

C. 0

D. 8

**Solution:**

**Ques No 12:**

The number of integer a such that 1 ≤ a ≤ 100 and a^{a} is a perfect square is

**Options:**

A. 50

B. 53

C. 55

D. 56

**Solution:**

**Ques No 13:**

A girl wrote all the numbers from 100 to 200. Then she started counting the number of one’s that has been used while writing all these numbers. What is the number that she got?

**Options:**

A. 111

B. 119

C. 120

D. 121

**Solution:**

**Ques No 14:**

The number of ordered pairs (a, b) of positive integers such that a + b = 90 and their greatest common divisors is 6 equals

**Options:**

A. 5

B. 4

C. 8

D. 10

**Solution:**

**Ques No 15:**

If aabb is a four-digit number and also a perfect square, then the value of a + b is

**Options:**

A. 12

B. 11

C. 10

D. 9

**Solution:**

**Ques No 16:**

The product of three consecutive positive integers is 8 times their sum. The sum of their square is

**Options:**

A. 50

B. 77

C. 100

D. 149

**Solution:**

**Ques No 17:**

If we write down all the natural numbers from 259 to 492 side by side get a very large natural number 259260261….491492 How many 8’s will be used to write this large natural number?

**Options:**

A. 52

B. 32

C. 43

D. 53

**Solution:**

**Ques No 18:**

What is the remainder when 7^{187} is divided by 800?

**Options:**

A. 143

B. 243

C. 343

D. 443

**Solution:**

**Ques No 19:**

The four-digit number 2652 is such that any two consecutive digits from it make a multiple of 13. Another number N has this same property is 100 digits long and begins in a 9. The last digit of N is

**Options:**

A. 2

B. 3

C. 6

D. 9

**Solution:**

**Ques No 20:**

Three consecutive positive integers are raised to the first, second, third powers respectively and then added. The sum so obtained is a perfect square whose square root equals the total of the three original integers. Which of the following best describe the minimum say m of the three integers?

**Options:**

A. 1 ≤ m ≤ 3

B. 4 ≤ m ≤ 6

C. 7 ≤ m ≤ 9

D. 10 ≤ m ≤ 12

**Solution:**