If the function f:[-3,3]➝S defined by f(x) = x² is onto, then S is

(a)

[-9,9]

(b)

R

(c)

[-3,3]

(d)

[0,9]

The function f:R➝R is defined by f(x)=\(\frac { \left( { x }^{ 2 }+cosx \right) \left( 1+{ x }^{ 4 } \right) }{ \left( x-sinx \right) \left( 2x-{ x }^{ 3 } \right) } +{ e }^{ -\left| x \right| }\) 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.

If A⊆B, then A\B is  ________

(a)

B

(b)

A

(c)

Ø

(d)

\(\frac{B}{A}\)

If A = {1, 2, 3}, B = {1, 4, 6, 9} and R is a relation from A to B defined by "x is greater than y". The range of R is __________

(a)

{1, 4, 6, 9}

(b)

{4, 6, 9}

(c)

{1}

(d)

None of these

Let R be the relation over the set of all straight lines in a plane such that l₁Rl₂ ⇔ l₁丄l₂ . Then  R is __________

(a)

symmetric

(b)

reflexive

(c)

transitive

(d)

an equivalent relation

If n(A) = 2 and n(B ∪ C) = 3, then n[(A \(\times\) B) ∪ (A \(\times\) C)] is

(a)

2³

(b)

3²

(c)

6

(d)

5

The number of relations on a set containing 3 elements is

(a)

9

(b)

81

(c)

512

(d)

1024

Let R be the universal relation on a set X with more than one element. Then R is

(a)

not reflexive

(b)

not symmetric

(c)

transitive

(d)

none of the above

Let X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4),(4, 1)}. Then R is

(a)

reflexive

(b)

symmetric

(c)

transitive

(d)

equivalence

The range of the function \({1\over 1-2sinx}\) is

(a)

\((-∞,-1)\cup\left( {1\over 3},\infty\right)\)

(b)

\(\left( -1,{1\over 3}\right)\)

(c)

\(\left[ -1,{1\over 3}\right]\)

(d)

\((-∞,-1]\cup [\frac { 1 }{ 3 } ,∞)\)

If \(f:[-2,2]\rightarrow A\) is given by f(x) = 3³ then f is onto, if A is ___________

(a)

[3, 3]

(b)

(3, 3)

(c)

[-24,24]

(d)

(-24, 24)

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 domain of the function \(f(x)=\sqrt{log_{10}{3-x\over x}}\)is

(a)

\((0,{3\over2})\)

(b)

(0, 3)

(c)

\((-\infty, {3\over2}]\)

(d)

\((0, {3\over2}]\)

If \(f(x)={1-x\over 1+x}, x≠0\) then \(f[f(x)]+f\left[f\left(1\over x\right)\right]\)

(a)

<2

(b)

> 2

(c)

> 2

(d)

None

n[P[P[p(Ø)]]] =

(a)

2

(b)

1

(c)

4

(d)

8

If A, B and C are three sets and if A ∈ B and B ⊂ C then

(a)

A ⊂ C

(b)

A need not be a subset of C

(c)

A = B

(d)

C ⊂ A

The solution 5x-1<24 and 5x+1 > -24 is

(a)

(4,5)

(b)

(-5,-4)

(c)

(-5,5)

(d)

(-5,4)

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

If  \(\frac { 1-2x }{ 3+2x-{ x }^{ 2 } } =\frac { A }{ 3-x } +\frac { B }{ x+1 } \), then the value of A + B is

(a)

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

(b)

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

(c)

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

(d)

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

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

(a)

4

(b)

2

(c)

3

(d)

0

If x < 7, then ___________

(a)

-x < -7

(b)

- x ≤ -7

(c)

-x > -7

(d)

-x ≥ -7

The rationalising factor of \(\frac { 5 }{ \sqrt [ 3 ]{ 3 } } \) is

(a)

\(\sqrt [ 3 ]{ 6 } \)

(b)

\(\sqrt [ 3 ]{ 3 } \)

(c)

\(\sqrt [ 3 ]{ 9 } \)

(d)

\(\sqrt [ 3 ]{ 27 } \)

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

(a)

1

(b)

3

(c)

23

(d)

21

If the roots of x²-bx + c = 0 are two consecutive integer,then b²- 4c is ___________

(a)

0

(b)

1

(c)

2

(d)

none of these

The value of log₁₀⁸ + log₁₀⁵- log₁₀⁴ = ___________

(a)

\({ log }_{ 10 }^{ 9 }\)

(b)

\({ log }_{ 10 }^{ 36 }\)

(c)

1

(d)

-1

The factors of the polynomial \(6\sqrt { { 3x }^{ 2 } } -47x+5\sqrt { 3 } \) are ___________

(a)

\((2x-5\sqrt { 3 } )(3\sqrt { 3 } x-1)\)

(b)

\((2x-5\sqrt { 3 } )(3\sqrt { 3 } x+1)\)

(c)

\((2x+5\sqrt { 3 } )(3\sqrt { 3 } x+1)\)

(d)

\((2x+5\sqrt { 3 } )(3\sqrt { 3 } x-1)\)

If \(\alpha\) and \(\beta\) are the roots of 2x² + 4x + 5 = 0 the equation where roots are 2\(\alpha\) and 2\(\beta\) is ___________

(a)

4x²+ 4x + 5 = 0

(b)

2x² + 4x + 50 = 0

(c)

x² + 4x + 5 = 0

(d)

x²+ 4x + 10 = 0

Solve 3x² + 5x - 2≤0

(a)

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

(b)

[2,\(\frac{1}{3}\)]

(c)

(-2,\(\frac{1}{3}\))

(d)

(-2,\(\frac{-1}{3}\))

The zero of the polynomial function f(x) = 9x²-16 are ____________

(a)

(9, 16)

(b)

(3, 4)

(c)

\((\frac{4}{3},-\frac{4}{3})\)

(d)

\((\frac{3}{4},-\frac{3}{4})\)

The value of a when x³- 2x²+ 3x + a is divided by (x - 1), the remainder is 1, is ___________

(a)

-1

(b)

1

(c)

2

(d)

-2

If \(\frac{x}{x^2-5x+6}=\frac{A}{x-2}+\frac{B}{x-3}\) then value of A is _____________

(a)

2

(b)

0

(c)

3

(d)

-2

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

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 \(\pi <2\theta <\frac { 3\pi }{ 2 } \), then \(\sqrt { 2+\sqrt { 2+2cos4\theta } } \) equals to

(a)

-2 cosፀ

(b)

-2 sinፀ

(c)

2 cosፀ

(d)

2 sinፀ

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)

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

If cos pፀ + cos qፀ = 0 and if p ≠ q, then ፀ is equal to (n is any integer)

(a)

\(\frac { \pi (3n+1) }{ p-q } \)

(b)

\(\frac { \pi (2n+1) }{ p\pm q } \)

(c)

\(\frac { \pi (n\pm 1) }{ p\pm q } \)

(d)

\(\frac { \pi (n+2) }{ p+q } \)

\(\frac { cos6x+6cos4x+15cos2x+10 }{ cos5x+5cos3x+10cosx } \) is equal to

(a)

cos 2x

(b)

cos x

(c)

cos 3x

(d)

2 cos x

If sin α + cos α = b, then sin 2α is equal to

(a)

b²- 1, if b ≤\(\sqrt { 2 } \)

(b)

b²- 1, if b >\(\sqrt { 2 } \)

(c)

b²-1, if b ≥ 1

(d)

b²- 1, if b ≥\(\sqrt { 2 } \)

The angle between the minute and hour hands of a clock at 8.30 is ___________

(a)

80⁰

(b)

75⁰

(c)

60⁰

(d)

105⁰

If tan A = \(\frac { a }{ a+1 } \) and B = \(\frac { 1 }{ 2a+1 } \) then the value of A + B is ___________

(a)

0

(b)

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

(c)

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

(d)

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

If cos x = \(\frac { -1 }{ 2 } \) \(0 < x < 2\pi\) and, then the solutions are _______________

(a)

x = \(\frac { \pi }{ 3 } ,\frac { 4\pi }{ 3 } \)

(b)

x = \(\frac { 2\pi }{ 3 } ,\frac { 4\pi }{ 3 } \)

(c)

x = \(\frac { 2\pi }{ 3 } ,\frac { 7\pi }{ 6 } \)

(d)

x = \(\frac { 2\pi }{ 3 } ,\frac { 5\pi }{ 3 } \)

If the arcs of same lengths in two circles sustend central angles 30° and 40° find the ratio of their radii _______________

(a)

3 : 4

(b)

4 : 3

(c)

7 : 12

(d)

none of these

The general solution of cosec_\(\theta\) = -2 is _______________

(a)

\(2n\pi +(-1)^n({\pi\over 6})\)

(b)

\(n\pi +(-1)^n({-\pi\over 6})\)

(c)

\(2n\pi \pm({\pi\over 6})\)

(d)

\(-{\pi\over 6}+n\pi\)

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

(a)

0

(b)

1

(c)

2

(d)

2 tan A

The value of cos 20°- sin 20° is _______________

(a)

positive

(b)

negative

(c)

0

(d)

1

If cos \(\alpha\) = \(\frac{3}{5}\) and cos \(\beta=\frac{5}{13}\), then _______________

(a)

cos\((\alpha+\beta)=\frac{33}{65}\)

(b)

\(sin(\alpha+\beta)=\frac{56}{65}\)

(c)

\(sin^2\frac{(\alpha-\beta)}{2}=\frac{4}{65}\)

(d)

\(cos(\alpha-\beta)=\frac{66}{65}\)

If in a triangle a = 5, b = 4 and cos(A - B) = \(\frac{31}{32}\) then the third side C is equal to _______________

(a)

5

(b)

6

(c)

3

(d)

12

\(\frac{1}{360}\) of a complete rotation clockwise is _______________

(a)

-1°

(b)

-360°

(c)

-90°

(d)

1°

The number of ways in which the following prize be given to a class of 30 boys first and second in mathematics, first and second in physics, first in chemistry and first in English is

(a)

30⁴\(\times\) 29²

(b)

30³\(\times\) 29³

(c)

30²\(\times\) 29⁴

(d)

30\(\times\)29⁵

Number of sides of a polygon having 44 diagonals is

(a)

4

(b)

4!

(c)

11

(d)

22

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 ways of choosing 5 cards out of a deck of 52 cards which include at least one king is

(a)

⁵²C₅

(b)

⁴⁸C₅

(c)

⁵²C₅ + ⁴⁸C₅

(d)

⁵²C₅ - ⁴⁸C₅

The number of different signals which can be give from 6 flags of different colours taking one or more at a time is _________

(a)

1958

(b)

1956

(c)

16

(d)

64

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

(a)

19

(b)

17

(c)

23

(d)

25

If p(n):49ⁿ + 16ⁿ +\(\lambda \) is divisible by 64 for n \(\in \) N is true, then the least negative integral value of \(\lambda \) is _________

(a)

-3

(b)

-2

(c)

-1

(d)

-4

is _________

(a)

\(\lfloor{n}(n+2)\)

(b)

(c)

(d)

none of these

If ⁿP_r = 720, ⁿC_r = 120 then r is _________

(a)

2

(b)

4

(c)

3

(d)

5

The number of parallelogram formed if 5 parallel lines intersect with 4 other paralle llines is _________

(a)

10

(b)

45

(c)

30

(d)

60

How many words can be formed using all the letters of the word ANAND _________

(a)

30

(b)

35

(c)

40

(d)

45

The number of ways of disturbing 7 identical balls in 3 distinct boxes, so that no box is empty is  _________

(a)

7

(b)

6

(c)

35

(d)

15

Each of five questions is a multiple-choice test has 4 possible answers. The number of different sets of possible answers is  _________

(a)

4⁵-4

(b)

5⁴-5

(c)

1024

(d)

1023

The number of positive integral solution of \(x\times y\times z=30\) is  _________

(a)

3

(b)

1

(c)

9

(d)

27

The number of 4 digit numbers, that can be formed by the digits 3, 4, 5, 6, 7, 8, 0 and no digit is being repeated is  _________

(a)

720

(b)

840

(c)

280

(d)

560

If ⁿP_t = 720 nCr, then the value of r =  _________

(a)

6

(b)

5

(c)

4

(d)

7

The sequence \(\frac { 1 }{ \sqrt { 3 } } ,\frac { 1 }{ \sqrt { 3 } +\sqrt { 2 } }, \frac { 1 }{ \sqrt { 3 } +2\sqrt { 2 } },...... \)form an 

(a)

AP

(b)

GP

(c)

HP

(d)

AGP

If S_n denotes the sum of n terms of an AP whose common difference is d, the value of S_n - 2S_n-1 + S_n-2 is

(a)

d

(b)

2d

(c)

4d

(d)

d²

The sum up to n terms of the series \(\sqrt { 2 } +\sqrt { 8 } +\sqrt { 18 } +\sqrt { 32 } +\).....is

(a)

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

(b)

2n(n+1)

(c)

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

(d)

1

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 term without x in \({ \left( 2x-\frac { 1 }{ 2{ x }^{ 2 } } \right) }^{ 12 }\) is ______________

(a)

495

(b)

-495

(c)

-7920

(d)

7920

The nth term of a G.P is 128 and the sum of its n terms is 225. If its common ratio is 2, then its first term is ______________

(a)

1

(b)

3

(c)

8

(d)

none of these 

The Co-efficient of x³ in \(\sqrt { \frac { 1-x }{ 1+x } } ,\left| x \right| <1\ is\ \)______________

(a)

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

(b)

\(\frac { 3 }{ 8 } \)

(c)

\(\frac { -3 }{ 8 } \)

(d)

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

The coefficient of x⁶ in (2 + 2x)¹⁰ is

(a)

¹⁰C₆

(b)

2⁶

(c)

¹⁰C₆2⁶

(d)

¹⁰C₆2¹⁰

If ⁿC₁₀ > ⁿC_r for all possible r, then a value of n is

(a)

10

(b)

21

(c)

19

(d)

20

If a is the arithmetic mean and g is the geometric mean of two numbers, then

(a)

a \(\le \) g

(b)

a \(\ge\) g

(c)

a = g

(d)

a > g

AM, GM, HM denote the Arithmetic mean, Geometric mean and Harmonic mean respectively the relationship between this is ______________

(a)

AM < GM < HM

(b)

AM ≤ GM ≤ HM

(c)

AM>GM>HM

(d)

AM≥GM≥HM

\(\frac{1}{1!}+\frac{1}{3!}+\frac{1}{5!}+...\) is ______________

(a)

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

(b)

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

(c)

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

(d)

none of these

Sum of the binomial coefficients is ______________

(a)

2n

(b)

n²

(c)

2ⁿ

(d)

n+17

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)

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

If x, 2x + 2, 3x + 3 . . . are in G.P, then the 4^th term is ______________

(a)

27

(b)

-27

(c)

13.5

(d)

-13.5

If the point (8, -5) lies on the locus \(\frac{x^2}{16}-\frac{y^2}{25}=k\), then the value of k is

(a)

0

(b)

1

(c)

2

(d)

3

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)

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

The intercepts of the perpendicular bisector of the line segment joining (1, 2) and (3, 4) with coordinate axes are

(a)

5, -5

(b)

5, 5

(c)

5, 3

(d)

5, -4

The image of the point (2, 3) in the line y = -x is 

(a)

(-3, -2)

(b)

(-3, 2)

(c)

(-2, -3)

(d)

(3, 2)

The area of the triangle formed by the lines x² - 4y² = 0 and x = a is

(a)

2a²

(b)

\(\frac{\sqrt3}{2}a^2\)

(c)

\(\frac12a^2\)

(d)

\(\frac{2}{\sqrt3}a^2\)

Slope of x-axis or a line parallel to x-axis is ______________

(a)

0

(b)

positive

(c)

negative

(d)

infinity

The figure formed by the lines ax ± by ± c = 0 is a ______________

(a)

rectangle

(b)

square

(c)

rhombus

(d)

none of these

If 7x² - 8xy +A = 0 represents a pair of perpendicular lines, the A is ______________

(a)

7

(b)

-7

(c)

-8

(d)

8

The locus of a moving point P(a cos³θ, a sin³θ) is ______________

(a)

\({ x }^{ \frac { 2 }{ 3 } }+{ y }^{ \frac { 2 }{ 3 } }={ a }^{ \frac { 2 }{ 3 } }\)

(b)

x² + y² = a²

(c)

x + y = a

(d)

\({ x }^{ \frac { 3 }{ 2 } }+{ y }^{ \frac { 3 }{ 2 } }={ a }^{ \frac { 3 }{ 2 } }\)

If the straight line y = mx + c passes through the point (1, 2) and (-2, 4) then the value of m and c are ______________

(a)

\(\frac{8}{3},\frac{-2}{3}\)

(b)

\(\frac{-2}{3},\frac{8}{3}\)

(c)

\(\frac{2}{3},\frac{-8}{3}\)

(d)

\(\frac{-2}{3},\frac{-8}{3}\)

The equation of the straight line bisecting the line segment joining the points (2, 4) and (4, 2) and making an angle of 45^o with positive direction of x-axis is ______________

(a)

x + y = 6

(b)

x - y = 0

(c)

x - y = 6

(d)

x + y = 0

The equation of the straight line which passes through the point (2, 4) and have intercept on the axes equal in magnitude but opposite in sign is ______________

(a)

x - y = 2

(b)

x - y + 2 = 0

(c)

x - y + 1 = 0

(d)

x - y - 1 = 0

The lines ax + y + 1 = 0, x + by + 1 = 0 and x + y + c = 0(a ≠ b ≠ c ≠ 1) are concurrent, then the value of \(\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}=\) ______________

(a)

-1

(b)

1

(c)

0

(d)

abc

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 (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

Separate equation of lines for a pair of lines whose equation is x²+ xy -12y² = 0 are ______________

(a)

x + 4y = 0 and x + 3y = 0

(b)

2x - 3y = 0 and x - 4y = 0

(c)

x - 6y = 0 and x - 3y = 0

(d)

x + 4y = 0 and x - 3y = 0

The locus of a point which is equidistant from (-1, 1) and (4, 2) is ______________

(a)

5x + 3y + 9 = 0

(b)

5x + 3y - 9 = 0

(c)

3x - 5y = 0

(d)

3x + 5y - 9 = 0