The number of constant functions from a set containing m elements to a set containing n elements is

(a)

mn

(b)

m

(c)

n

(d)

m+n

Let f:R➝R be defined by f(x) = 1 - |x|. Then the range of f is

(a)

R

(b)

(1,∞)

(c)

(-1,∞)

(d)

(-∞,1]

The function f:R➝R be defined by f(x) = sinx + cosx is

(a)

an odd function

(b)

neither an odd function nor an even function

(c)

an even function

(d)

both odd function and even function

Given A = {5,6,7,8}. Which one of the following is incorrect?

(a)

Ø ⊆ A

(b)

A⊆A

(c)

{7,8,9}⊆A

(d)

{5}⊆A

If A = {(x,y) : y = e^x, x∈R} and B = {(x,y) : y = e^-x, x ∈ R} then n(A∩B) is

(a)

Infinity

(b)

0

(c)

1

(d)

2

If A = {(x,y) : y = sin x, x ∈ R} and B = {(x,y) : y = cos x, x ∈ R} then A∩B contains

(a)

no element

(b)

infinitely many elements

(c)

only one element

(d)

cannot be determined

Let A and B be subsets of the universal set N, the set of natural numbers. Then A^'∪[(A⋂B)∪B^'] is

(a)

A

(b)

A'

(c)

B

(d)

N

The number of students who take both the subjects Mathematics and Chemistry is 70. This represents 10% of the enrollment in Mathematics and 14% of the enrollment in Chemistry. The number of students take at least one of these two subjects, is

(a)

1120

(b)

1130

(c)

1100

(d)

insufficient data

If f(x) = 2x - 3 and g(x) = x² + x - 2 then gof(x) is __________

(a)

2(2x²- 5x + 2)

(b)

(2x²- 5x - 2)

(c)

2(2x²+ 5x + 2)

(d)

2x²+ 5x - 2

Let f : R➝R be given by f(x) = x + \(\sqrt { { x }^{ 2 } } \) is __________

(a)

injective

(b)

Surjective

(c)

bijective

(d)

none of these

For non-empty sets A and B, if A ⊂ B then (A \(\times\)B) ⋂ (B \(\times\)A) is equal to

(a)

A ⋂ B

(b)

A \(\times\)A

(c)

B \(\times\)B

(d)

none of these.

\(n(p(A))=512,n(p(B))=32,n(A\cup B)=16,\) find \(n(A\cap B) \)  ___________

(a)

2

(b)

9

(c)

4

(d)

5

The domain of the function \(f(x)=\sqrt{ x - 5 }+ \sqrt{6 - x}\) is 

(a)

[5, ∞)

(b)

(- ∞, 6)

(c)

[5, 6]

(d)

(-5, ≠6)

The function f(x) = log (x + \(\sqrt{x^2+1}\)) is ___________

(a)

an even function

(b)

an odd function

(c)

a periodic function

(d)

neither an even nor an odd function

If \(f(x)={1-x\over 1+x},(x\neq0)\) then f^-1(x) =

(a)

f(x)

(b)

\(1\over f(x)\)

(c)

-f(x)

(d)

-\(1\over f(x)\)

If A and B are any two finite sets having m and n elements respectively then the cardinality of the power set of A \(\times\) B is ___________

(a)

2^m

(b)

2ⁿ

(c)

mn

(d)

2^mn

If |x+2| \(\le\) 9, then x belongs to

(a)

\((-\infty ,-7)\)

(b)

[-11, 7]

(c)

\((-\infty ,-7)\cup (11,\infty)\)

(d)

(-11, 7)

Given that x, y and b are real numbers x < y, b > 0, then

(a)

xb < yb

(b)

xb > yb

(c)

xb ≤ yb

(d)

\(\frac { x }{ b } \ge \frac { y }{ b } \)

If 3 is the logarithm of 343, then the base is

(a)

5

(b)

7

(c)

6

(d)

9

If a and b are the roots of the equation x²- kx + 16 = 0 and a²+ b² = 32, then the value of k is

(a)

10

(b)

-8

(c)

-8, 8

(d)

6

The equation whose roots are numerically equal but opposite in sign to the roots 3x²- 5x -7 = 0 is

(a)

3x²- 5x - 7 = 0

(b)

3x²+ 5x - 7 = 0

(c)

3x²- 5x + 7 = 0

(d)

3x² + x - 7

If 8 and 2 are the roots of x²+ ax + c = 0 and 3, 3 are the roots of x² + dx + b = 0; then the roots of the equation x²+ ax + b = 0 are

(a)

1, 2

(b)

-1, 1

(c)

9, 1

(d)

-1, 2

If a and b are the real roots of the equation x²- kx + c = 0, then the distance between the points (a, 0) and (b, 0) is

(a)

\(\sqrt { { k }^{ 2 }-4c } \)

(b)

\(\sqrt { { 4k }^{ 2 }-c } \)

(c)

\(\sqrt { 4c-{ k }^{ 2 } } \)

(d)

\(\sqrt { k-8c } \)

The number of roots of (x + 3)⁴+ (x + 5)⁴ = 16 is

(a)

4

(b)

2

(c)

3

(d)

0

The value of log₃ 11.log₁₁ 13.log₁₃ 15.log₁₅ 27.log₂₇ 81 is

(a)

1

(b)

2

(c)

3

(d)

4

If - 3x + 17 < -13 then ___________

(a)

x ∈ (10, ∞)

(b)

x ∈ [10, ∞)

(c)

x ∈ (-∞, 10]

(d)

x ∈ [10, 10)

If |x + 3| ≥ 10 then ___________

(a)

x ∊ (-13, 7]

(b)

x ∊ [-13, 7)

(c)

x ∊ (-∞, -13] \(\cup\) [7, ∞)

(d)

x ∊ (-∞, -13] \(\cup\) [7, ∞)

\((\sqrt { 5 } -2)(\sqrt { 5 } +2)\) is equal to ___________

(a)

1

(b)

3

(c)

23

(d)

21

Solve \(\sqrt{7+6x-x^2}=x+1\)

(a)

(1, -3)

(b)

(3, -1)

(c)

(1, -1)

(d)

(3, -3)

The value of 2 log₁₀ 3 + log₁₀ 16 - 2 log₁₀ \(6\over 5\) is ___________

(a)

1

(b)

0

(c)

2

(d)

3

The value of \({3^{-3}\times6^4\times 12^{-3}\over 9^{-4}\times 2^{-2}}\) is ___________

(a)

3⁵

(b)

3⁶

(c)

3⁴

(d)

3

The number of real solutions of the equation |x²| - 3|x| + 2 = 0 is ___________

(a)

1

(b)

2

(c)

3

(d)

4

If a and b are roots of x² + x + 1 = 0 then the value of a² + b² = ___________

(a)

1

(b)

-1

(c)

cannot be determined

(d)

0

Zero of the polynomial p(x) = x² - 4x + 4

(a)

1

(b)

2

(c)

-2

(d)

-1

\(\frac { 1 }{ cos{ 80 }^{ 0 } } -\frac { \sqrt { 3 } }{ sin{ 80 }^{ 0 } } \)=

(a)

\(\sqrt{2}\)

(b)

\(\sqrt{3}\)

(c)

2

(d)

4

If cos 28⁰+ sin 28⁰ = k³, then cos 17⁰ is equal to

(a)

\(\frac { { k }^{ 3 } }{ \sqrt { 2 } } \)

(b)

-\(\frac { { k }^{ 3 } }{ \sqrt { 2 } } \)

(c)

±\(\frac { { k }^{ 3 } }{ \sqrt { 2 } } \)

(d)

-\(\frac { { k }^{ 3 } }{ \sqrt { 3 } } \)

If tan40⁰ = λ, then \(\frac { tan{ 140 }^{ 0 }-tan{ 130 }^{ 0 } }{ 1+tan{ 140 }^{ 0 }.tan{ 130 }^{ 0 } } \) =

(a)

\(\frac { 1-\lambda ^{ 2 } }{ \lambda } \)

(b)

\(\frac { 1+{ \lambda }^{ 2 } }{ \lambda } \)

(c)

\(\frac { 1+{ \lambda }^{ 2 } }{ 2\lambda } \)

(d)

\(\frac { 1-{ \lambda }^{ 2 } }{ 2\lambda } \)

Let f_k(x) = \(\frac { 1 }{ k } \)[sin^kx + cos^kx] where x\(\in \)R and k ≥ 1. Then f₄(x) - f₆(x) =

(a)

\(\frac { 1 }{ 4 } \)

(b)

\(\frac { 1 }{ 12 } \)

(c)

\(\frac { 1 }{ 6 } \)

(d)

\(\frac { 1 }{ 3 } \)

cos 2ፀ cos 2ф + sin²(ፀ - ф) - sin²(ፀ + ф) is equal to

(a)

sin2(ፀ+\(\phi \))

(b)

cos2(ፀ+\(\phi \))

(c)

sin2(ፀ-\(\phi \))

(d)

cos2(ፀ-\(\phi \))

If f(ፀ) = |sin ፀ| + |cos ፀ|, ፀ\(\in \)R, then f(ፀ) is in the interval     

(a)

[0, 2]

(b)

[1,\(\sqrt { 2 } \)]

(c)

[1, 2]

(d)

[0, 1]

If the angles of a triangle are in A.P., then the measure of one of the angles in radians is ___________

(a)

\(\frac { \pi }{ 6 } \)

(b)

\(\frac { \pi }{ 3 } \)

(c)

\(\frac { \pi }{ 2 } \)

(d)

\(\frac { 2\pi }{ 3 } \)

If tan x = \(\frac { -1 }{ \sqrt { 5 } } \) and x lies in the IV quadrant, then the value of cos x is ___________

(a)

\(\sqrt { \frac { 5 }{ 6 } } \)

(b)

\(\frac { 2 }{ \sqrt { 6 } } \)

(c)

\(\frac { 1 }{ 2 } \)

(d)

\(\frac { 1 }{ \sqrt { 6 } } \)

\(\frac { cos3x }{ 2cos2x-1 } \) is _______________

(a)

cos x

(b)

sin x

(c)

tan x

(d)

cot x

If tanx = \({1\over 7}\) ,tan y = \({1\over 3}\) then x + y is ____________ 

(a)

\({\pi\over 4}\)

(b)

\({\pi\over 3}\)

(c)

\({\pi\over 2}\)

(d)

\({\pi}\)

In \(\triangle\)ABC, \(\hat{C}\) = 90° then a cos A + b cos B is _______________

(a)

2R sin B

(b)

2 sin B

(c)

0

(d)

2a sin B

(sec A + tan A-1) (sec A - tan A+1)-2 tan A = _______________

(a)

0

(b)

1

(c)

2

(d)

2 tan A

If sin θ = sin \(\alpha\), then the angles θ and \(\alpha\) are related by _______________

(a)

\(\theta=n\pi\pm\alpha\)

(b)

\(\theta=2n\pi+(-1)^n\alpha\)

(c)

\(\alpha=n\pi\pm(-1)^n\theta\)

(d)

\(\theta=(2n+1)\pi+\alpha\)

The value of tan^-1 (1) + cos^-1(\(\frac{-1}{2}\)) + sin^-1(\(\frac{-1}{2}\)) _______________

(a)

\(\frac{\pi}{4}\)

(b)

\(\frac{5\pi}{4}\)

(c)

\(\frac{3\pi}{4}\)

(d)

\(\frac{\pi}{2}\)

Number of solutions of the equation tan x + sec x = 2 cos x lying in the interval [0, 2π] is _______________

(a)

0

(b)

1

(c)

2

(d)

3

Area of triangle ABC is _______________

(a)

\(\frac{1}{2}\)ab cos C

(b)

\(\frac{1}{2}\)ab sin C

(c)

\(\frac{1}{2}\)ab cos B

(d)

\(\frac{1}{2}\)bc sin B

The number of five digit telephone numbers having at least one of their digits repeated is

(a)

90000

(b)

10000

(c)

30240

(d)

69760

There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two points is

(a)

45

(b)

40

(c)

39

(d)

38

The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines.

(a)

6

(b)

9

(c)

12

(d)

18

Number of sides of a polygon having 44 diagonals is

(a)

4

(b)

4!

(c)

11

(d)

22

If 10 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then the total number of points of intersection are

(a)

45

(b)

40

(c)

10!

(d)

2¹⁰

In a plane there are 10 points are there out of which 4 points are collinear, then the number of triangles formed is

(a)

110

(b)

¹⁰C₃

(c)

120

(d)

116

In ²ⁿC₃ : ⁿC₃ = 11 : 1 then n is

(a)

5

(b)

6

(c)

11

(d)

7

The number of 10 digit number that can be written by using the digits 2 and 3 is

(a)

¹⁰C₂+⁹C₂

(b)

2¹⁰

(c)

2¹⁰-2

(d)

10!

If P_r stands for ^r P_r then the sum of the series 1+ P₁ + 2P₂ + 3P₃ +...+ nP_n is

(a)

P_n+1

(b)

P_n+1-1

(c)

P_n-1+1

(d)

⁽ⁿ⁺¹⁾P_(n-1)

The number of ways to average the letters of the word CHEESE are _________

(a)

120

(b)

240

(c)

720

(d)

6

5c₁ + 5c₂ + 5c₃ + 5c₄ + 5c₅  is equal to _________

(a)

30

(b)

31

(c)

32

(d)

33

Among the players 5 are bowlers. In how many ways a team of 11 may be formed with atleast 4 bowlers?

(a)

265

(b)

263

(c)

264

(d)

275

For all n \(\in \) N, 3\(\times\) 5²ⁿ⁺¹+2³ⁿ⁺¹ is divisible by _________

(a)

19

(b)

17

(c)

23

(d)

25

The number of diagonals of a decagon _________

(a)

10

(b)

20

(c)

35

(d)

40

The number of ways of selecting of 3 poets and 4 scientists such that poets are in even places _________

(a)

12

(b)

36

(c)

72

(d)

144

If ⁿC_r-1 = 36, ⁿC_r = 84 and ⁿC_r+1 = 126 then r = _________

(a)

2

(b)

2

(c)

3

(d)

4

If ⁿC₁₀ = ⁿC₆, then ⁿC₂ =  _________

(a)

16

(b)

4

(c)

120

(d)

240

The remainder when 38¹⁵ is divided by 13 is

(a)

12

(b)

1

(c)

11

(d)

5

The n^th term of the sequence 1, 2, 4, 7, 11,... is

(a)

n³ + 3n² + 2n

(b)

n³ - 3n² + 3n

(c)

\(\frac { n(n+1)(n+2) }{ 3 } \)

(d)

\(\frac { { n }^{ 2 }-n+2 }{ 2 } \)

The value of the series\(\frac { 1 }{ 2 } +\frac { 7 }{ 4 } +\frac { 13 }{ 8 } +\frac { 19 }{ 16 } +\).....is

(a)

14

(b)

7

(c)

4

(d)

6

The coefficient of x⁵ in the series e^-2x is

(a)

\(\frac { 2 }{ 3 } \)

(b)

\(\frac { 2 }{ 3 } \)

(c)

\(\frac { -4 }{ 15 } \)

(d)

\(\frac { 4 }{ 15 } \)

The value of \(\frac { 1 }{ 2! } +\frac { 1 }{ 4! } +\frac { 1 }{ 6! } +....is\)

(a)

\(\frac { { e }^{ 2 }+1 }{ 2e } \)

(b)

\(\frac { { (e+1) }^{ 2 } }{ 2e } \)

(c)

\(\frac { { (e-1) }^{ 2 } }{ 2e } \)

(d)

\(\frac { { e }^{ 2 }+1 }{ 2e } \)

The Co-efficient of x^-17 in \({ \left( { x }^{ 4 }-\frac { 1 }{ { x }^{ 3 } } \right) }^{ 15 }\)is _____________ 

(a)

1365

(b)

-1365

(c)

3003

(d)

-3003

The first and last term of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be ______________

(a)

5

(b)

6

(c)

7

(d)

8

The series 1+4x+8x² + \(\frac { 32 }{ 3 } { x }^{ 3 }+.....+\infty \ is\) ______________

(a)

e^x

(b)

e^4x

(c)

e^2x

(d)

e^8x

The value of 2 + 4 + 6 + + 2n is

(a)

\(\frac { n\left( n-1 \right) }{ 2 } \)

(b)

\(\frac { n\left( n+1 \right) }{ 2 } \)

(c)

\(\frac { 2n\left( 2n+1 \right) }{ 2 } \)

(d)

n(n + 1)

With usual notation C₀ + C₂ + C₄ + ... is ______________

(a)

2^n-1

(b)

2ⁿ

(c)

2ⁿ⁺¹

(d)

2ⁿ⁺²

In the expansion of (2x + 3)⁵ the coefficient of x² is ______________

(a)

720

(b)

1080

(c)

810

(d)

5

\(\sqrt \frac{1-2x}{1+2x}\) is approximately equal to ______________

(a)

1- 2x-x²

(b)

1 + 2x+ x²

(c)

1+ 2x

(d)

1-2x+x²

The coefficient of a⁵ in the expansion of (3a + 5b)⁵ is ______________

(a)

1

(b)

243

(c)

6750

(d)

9375

\(\frac{2}{1!}+\frac{4}{3!}+\frac{6}{5!}+. . .\infty =\) ______________

(a)

e

(b)

2e

(c)

\(\frac{1}{e}\)

(d)

e²

If a,b, c are in A.P, as well as in G.P then ______________

(a)

a = b ≠ c

(b)

a ≠ b = c

(c)

a ≠b ≠ c

(d)

a = b = c

2^1/4 4^1/8 8^1/16 16^1/32 . . . = ______________

(a)

1

(b)

2

(c)

\(\frac{3}{2}\)

(d)

\(\frac{5}{2}\)

The slope of the line which makes an angle 45^o with the line 3x- y = -5 are:

(a)

1, -1

(b)

\(\frac{1}{2},-2\)

(c)

\(1,\frac{1}{2}\)

(d)

\(2,-\frac{1}{2}\)

If a vertex of a square is at the origin and its one side lies along the line 4x + 3y - 20 = 0, then the area of the square is

(a)

20 sq. units

(b)

16 sq. units

(c)

25 sq. units

(d)

4 sq.units

The value of x so that 2 is the slope of the line through (2, 5) and (x, 3) is ______________

(a)

-1

(b)

1

(c)

0

(d)

2

If the points (a, 0) (0, b) and (x, y) are collinear, then ______________

(a)

\(\frac{x}{a}-\frac{y}{b}=1\)

(b)

\(\frac{x}{a}+\frac{y}{b}=1\)

(c)

\(\frac{x}{a}+\frac{y}{b}=-1\)

(d)

\(\frac{x}{a}+\frac{y}{b}=0\)

Distance between the lines 5x + 3y - 7 = 0 and 15x + 9y + 14 = 0 is ______________

(a)

\(\frac{35}{\sqrt{34}}\)

(b)

\(\frac{1}{3\sqrt{34}}\)

(c)

\(\frac{35}{2\sqrt{34}}\)

(d)

\(\frac{35}{3\sqrt{34}}\)

If the lines x + q = 0, y - 2 = 0 and 3x + 2y + 5 = 0 are concurrent, then the value of q will be ______________

(a)

2

(b)

2

(c)

3

(d)

5

The equating straight line with y-intercept -2 and inclination with x-axis is 135° is ______________

(a)

x + y - 2 = 0

(b)

y - x + 2 = 0

(c)

y + x + 2 = 0

(d)

none

If(1, 3) (2,1) (9, 4) are collinear then a is ______________

(a)

\(\frac{1}{2}\)

(b)

2

(c)

0

(d)

-\(\frac{1}{2}\)

The lines x + 2y - 3 = 0 and 3x - y + 7 = 0 are ______________

(a)

parallel

(b)

neither parallel nor perpendicular

(c)

perpendicular

(d)

parallel as wellas perpendicular

The length of perpendicular from the origin to a line is 12 and the line makes an angle of 120° with the positive direction of y-axis. then the equation of line is ______________

(a)

\(x+y\sqrt 3=24\)

(b)

\(x+y=12\sqrt 2\)

(c)

x + y = 24

(d)

\(x+y=12\sqrt 3\)

The value \(\lambda\) for which the equation 12x²- 10xy + 2y²+11x-5y+\(\lambda\) = 0 represent a pair of straight lines is ______________

(a)

\(\lambda\) = 1

(b)

\(\lambda\) = 2

(c)

\(\lambda\) = 3

(d)

\(\lambda\) = 0

The points (k + 1, 1), (2k + 1, 3) and (2k + 2, 2k) are collinear if ______________

(a)

k = -1

(b)

\(k=\frac{1}{2}\)

(c)

k = 3

(d)

k = 2

The points (a, 0),(0, b) and (1, 1) will be collinear if ______________

(a)

a + b = 1

(b)

a + b = 2

(c)

\(\frac{1}{a}+\frac{1}{b}=1\)

(d)

a + b = 0

The equation x²+ kxy + y²- 5x - 7y + 6 = 0 represents a pair of straight lines then k = ______________

(a)

\(\frac{5}{3}\)

(b)

\(\frac{10}{3}\)

(c)

\(\frac{3}{2}\)

(d)

\(\frac{3}{10}\)

The distance between the parallel lines 3x - 4y + 9 = 0 and 6x - 8y -15 = 0 is ______________

(a)

\(\frac{-33}{10}\)

(b)

\(\frac{10}{33}\)

(c)

\(\frac{33}{10}\)

(d)

\(\frac{33}{20}\)

The point (2, 1) and (-3, 5) are on ______________

(a)

Same side of the line 3x - 2y + 1 = 0

(b)

Opposite sides of the line 3x - 2y + 1 = 0

(c)

On the line 3x - 2y + 1 = 0

(d)

On the line x + y = 3

The co-ordinates of a point on x + y + 3 = 0 whose distance from x + 2y + 2 = 0 is \(\sqrt 5\), is ______________

(a)

(9, 6)

(b)

(-9, 6)

(c)

(6, -9)

(d)

(-9, -6)