## MATH

### MATH

• 1

A.

a +

B.

a − ɑ

C.

s’ab

D.

1

• 2

If l(x) is the least integer not less than x and g(x) is the greatest integer not greater than x, then

A.

9

B.

13

C.

1

D.

None of these

• 3

If 0 < a < 1, then the solution set of the inequation

A.

(1, 1/a)

B.

(0, a)

C.

(1, 1/a) ∪ (0, a)

D.

None of these

• 4

If the sum of the greatest integer less than or equal to x and the least integer greater than or equal to x is 5, then the solution set for x is

A.

(2, 3)

B.

(0, 5)

C.

[5, 6)

D.

None of these

• 5

A stick of length 20 units is to be divided into n parts so that the product of the lengths of the parts is greater than unity. The maximum possible value of n is

A.

18

B.

19

C.

20

D.

21

• 6

The number of ordered 4-tuples (x, y, z,w) where x, y, z,w ∈ [0,10] which satisfy the inequality
2sin2 x × 3>cos2 x × 4sin2 z + × 5>cos2 w N ≥ 120, is

A.

81

B.

144

C.

0

D.

Infinite

• 7

A.

Only positive values of s¥

B.

Only negative values of x

C.

All real numbers except zero

D.

Only for x > 1

• 8

Let x =

A.

2 ≤ 2

B.

x2 < 2

C.

x2 > 2

D.

x2 ≥ 2

• 9

The equation

A.

No solution

B.

One solution

C.

Two solutions

D.

More than two solutions

• 10

The number of roots of the equation sin πx = |log|x||, is

A.

2

B.

4

C.

5

D.

6

• 11

The number of real solutions of 1 + |s’x − 1| = s’x(s’x − 2), is

A.

1

B.

2

C.

3

D.

4

• 12

The number of positive integers satisfying the inequality n + 1cn-2 − n + 1cn-1 ≤ 50 is

A.

9

B.

8

C.

7

D.

6

• 13

The solution of the inequation log1/3(x2 + x + 1) + 1 < 0 is

A.

(−∞,−2) ∪ (1,∞)

B.

[−1, 2]

C.

(−2, 1)

D.

(−∞,∞)

• 14

If a, ɑ, s are sides of triangle, then

A.

[1, 2]

B.

[2, 3]

C.

[3, 4]

D.

[4, 5]

• 15

If 0 < x <

A.

√3

B.

C.

D.

1

• 16

Let y =

A.

−1 ≤ s¥ < 2 or s¥ ≥ 3

B.

−1 ≤ x < 3 or x > 2

C.

1 ≤ x < 2 or x ≥ 3

D.

None of these

• 17

If x, y, z are three real numbers such that x + y + z = 4 and x2 + y2 + z2 = 6, then the exhaustive set of values of x, is

A.

[2/3, 2]

B.

[0, 2/3]

C.

[0, 2]

D.

[−1/3, 2/3]

• 18

Non- negative real numbers such that a1 + a2+. . .+an

A.

B.

C.

D.

• 19

Solution set of inequality loge

A.

(2,∞)

B.

(−∞, 2)

C.

(−∞,∞)

D.

(3,∞)

• 20

(x − 1)(x2 − 5x + 7) < (x − 1),then x belongs to

A.

(1,2) ∪ (3,∞)

B.

(2, 3)

C.

(−∞, 1) ∪ (2,3)

D.

None of these

• 21

The value of nPr is equal to

A.

n-1Pr + r. n-1Pr-1

B.

n.n-1 Pr + n-1Pr-1

C.

n( n-1Pr+ n-1Pr-1)

D.

n-1Pr-1 + n-1Pr

• 22

A.

n+m+1Cn+1

B.

n+m+2Cn

C.

n+m+3Cn-1

D.

None of these

• 23

The number of straight lines can be formed out of 10 points of which 7 are collinear

A.

26

B.

21

C.

25

D.

None of these

• 24

A committee of 5 is to be formed from 9 ladies and 8 men. If the committee commands a lady majority, then the number of ways this can be done is

A.

2352

B.

1008

C.

3360

D.

3486

• 25

Consider the following statements : 1.These are 12 points in a plane of which only 5 are collinear, then the number of straight lines obtained 3.Three letters can be posted in five letter boxes in 35ways. Which of the statements given above is/are correct?

A.

Only (1)

B.

Only (2)

C.

Only(3)

D.

None of these