If n is an odd natural number, 3²ⁿ + 2²ⁿ is always divisible by
A) 13
B) 15
C) 17
D) 19

There is a circular path around a sports field. Anand takes 18 minutes to drive one round of the field while Prakash takes 12 minutes for the same. Suppose they both start at the same point and at the same time and go in the same direc¬tion. After how many minutes will they meet again at the starting point ?
A) 36 minutes
B) 19 minutes
C) 48 minutes
D) 56 minutes

A number 10x + y is multiplied by another number 10a + b and the result comes as 100p + 10q +r, where r = 2y, q = 2(x + y) and p = 2x; x, y < 5, q ≠ 0. The value of 10a + b may be:

1. 1. 11
   2. 13
   3. 31
   4. 22

Ramu has two vessels which contain 720 ml and 405 ml of milk respectively. Milk in each vessel is poured into glasses of equal capacity to their brim. Find the minimum number of glasses which can be filled with milk.
A) 25
B) 36
C) 48
D) 65

If log₃2 log₃(2^x – 5) log₃(2^x – 72) are in A.P then x is
A) an odd positive integer
B) a positive fraction
C) an even positive integer
D) an odd positive integer or even positive integer

If two positive integers p and q can be expressed as p = ab²and q = a³b; a, b being prime numbers, then LCM (p, q) is

1. 1. ab
   2. a²b²
   3. a³b²
   4. a³b³

1. If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is
   1. 4
   2. 2
   3. 1
   4. 3

If the product of two irrational numbers is rational, then which of the following can be concluded ?
A) The ratio of the greater and the smaller numbers is an integer.
B) The sum of the numbers must be rational.
C) The excess of the greater irrational number over the smaller irrational number must be rational.
D) The sum of the numbers must be irrational

If two positive integers p and q can be expressed as p = ab²and q = a³b; a, b being prime numbers, then LCM (p, q) is

• 1. ab
  2. a²b²
  3. a³b²
  4. a³b³

If A ⊆ B, then which one of the following is false?
A) A – B = A
B) B – A ≠ Φ
C) A ∪ B = B
D) A ∩ B = A

If A = {x : x is a letter in the word HEADMASTER}; then its Roster form is ……………………
A) A = {h, e, a, d, m, a, s, t, e, r}
B) A = {h, e, a, d, m, s, t, r}
C) A = {h, e, a, d, m, s, t, e, r}
D) A = {h, e, a, d, m, a, s, t, r}

S = {3,π,2–√,−5,3+7–√,27}. Which of the following is a sub-set of ‘S’ containing all irrational numbers ?
A) {3,π,27,−5,3+7–√}
B) {3+7–√,2–√,π}
C) {3,π,2–√}
D) {3,−5,27}

If A and B are two sets then (A – B) ∩ (B – A) =
A) A
B) B
C) A Δ B
D) Φ

Set builder form of {1, 3, 5, 7…. 19}
A) {x/x is odd number and x ≤ 19}
B) {2x/x ∈ N,x ≤ 1}
C) {x + 2/x ∈ N}
D) {x/x is even number and x > 19}

If A is any set such that n[p(A)] = 64, then n(A) =
A) 6
B) 16
C) 32
D) 8

If two zeroes of the polynomial x³ – 5x² + 6x are 2 and 3, then the third zero is
A) 0
B) 5
C) 6
D) 1

If ‘4’ is one of the zeroes of p(x) = x² + kx – 8, then the value of k = ………………
A) 1
B) -1
C) 2
D) -2

A quadratic polynomial, the sum of whose zeroes is zero and one zero is 4, is ………………..
A) x² – 16
B) x² + 16
C) x² – 4
D) x² + 4

The length of a rectangular dining hall is twice of its breadth. If x represents the breadth of the hall and its area is 5 sq. units, then the polynomial equation which represents the situation is
A) 5x² – 2 = 0
B) 2x² – 5 = 0
C) x² – 25 = 0
D) None

Find the values of “a” and “b” so that (x + 2) and (x – 1) may be factors of x³ + 10x² + ax + b.
A) a = 7,b = -18
B) a = 7, b = -17
C) a = 7, b = -15
D) a = 7, b = 17

If α, β are the zeroes of x² + x + 1, then 1α+1β = ……………………
A) 1
B) -1
C) 2
D) -2

The larger of two supplementary angles exceeds the smaller by 18°. The angles are ………………..
A) 80°, 100°
B) 81°, 99°
C) 82°, 98°
D) 83°, 97°

The value of k for which the pair of equations 3x + 4y + 2 = 0 and 9x + 12y + k = 0 represent coincident lines is ……………..
A) 2
B) 3
C) 6
D) 12

If the perimeter of a rectangular room is 34 and the length of the diagonal is 13, then the dimensions of the room are …………………
A) 7, 6
B) 11, 6
C) 12, 5
D) 12, 6

The 21^st term of an A.P., whose first two terms are -3 and 4 is …………………
A) 143
B) -143
C) 137
D) 17

In an A.P., if a = 1, a_n = 20 and S_n = 399, then n = ………………
A) 19
B) 42
C) 28
D) 38

Which term of G.P. 3, 3√3,9, …………….. equals to 243?
A) 6
B) 7
C) 8
D) 9

Which term of the A.P -18, -16, -14, …………………. is first positive term ?
A) t₉
B) t₁₀
C) t₁₁
D) t₁₂

What will be the value of x if 8x + 4 , 6x – 2 and 2x + 7 are in arithmetic progression?
A) −15/2
B) 15/2
C) 15
D) -15

The n^th term of an arithmetic progression is -11 while sum of the first n terms is 66, when its first term is 22 then the value of n is
A) 12
B) 13
C) 14
D) 15

If a line is passing through (2, 3) and (2, -3), then
1) the line is parallel to X – axis.
2) the line is parallel to Y – axis.
3) the slope of the line is not defined.
4) the slope of the line is zero.

If A(log₂8, log₅25) and B(log₁₀10, log₁₀100), then the mid-point of AB is
A) (2, 2)
B) (3, 2)
C) (1, 2)
D) (4, 4)

If origin is the centroid of a triangle, whose vertices are (3, 2), (-6, y) and (3,-2), then y = ………………….
A) 0
B) 3
C) 2
D) 6

The distance between two points A(a cosθ, 0), B(0, asinθ) is ……………….
A) a
B) a²
C) √a
D) 0

The ratio in which the line segment joining the points (4, 6) and (-7, -1) divided by X- axis is ………………….
A) 6 : 1
B) 1 : 6
C) 4 : 7
D) 7 : 4