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

The relation R defined on a set A= {0,-1, 1, 2} by xRy if |x²+y²| ≤ 2, then which one of the following is true?

(a)

R = {(0,0), (0,-1), (0, 1), (-1, 0), (-1, 1), (1, 2), (1, 0)}

(b)

R^-1 = {(0,0), (0,-1), (0, 1), (-1, 0), (1, 0)}

(c)

Domain of R is {0,-1, 1, 2}

(d)

Range of R is {0,-1, 1}

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)

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

The domain and range of the function \(f(x)={|x-4|\over x-4}\)

(a)

R, [-1, 1]

(b)

R \ {4};{-1,1}

(c)

R \ {4};{-1,l}

(d)

R, (-1,1)

The value of \({ log }_{ 3 }\frac { 1 }{ 81 } \) is

(a)

-2

(b)

-8

(c)

-4

(d)

-9

\(\sqrt [ 4 ]{ 11 } \) is equal to ___________

(a)

\(\sqrt [ 8 ]{ 11^{ 2 } } \)

(b)

\(\sqrt [ 8 ]{ 11^{ 4 } } \)

(c)

\(\sqrt [ 8 ]{ 11^{ 8 } } \)

(d)

\(\sqrt [ 8 ]{ 11^{ 6 } } \)

The roots of the equation \(x+{1\over x}=3{1\over 3},x\ne 0\) are

(a)

1, 3

(b)

\({1\over 3},3\)

(c)

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

(d)

\(1,{1\over 3}\)

cos1⁰ + cos2⁰ + cos3⁰ +: : : + cos179⁰ =

(a)

0

(b)

1

(c)

-1

(d)

89

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)

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

If cos A = cos B and sin A = sin B then _______________

(a)

A + B = 0

(b)

A = B

(c)

A + B = 2nπ

(d)

A = B + 2nπ

Choose the incorrect pair:

(a)

sin x in II^nd quadrant

(b)

cos x in I^st quadrant 1

(c)

sec x in II^st quadrant -2

(d)

tan x in III^rd quadrant20

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

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

(a)

45

(b)

40

(c)

39

(d)

38

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

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

(a)

e^x

(b)

e^4x

(c)

e^2x

(d)

e^8x

The larget coefficients in the expansion of (1 + X)²⁴ is ______________

(a)

24C₂₄

(b)

24C₁₃

(c)

24C₁₂

(d)

24C₁₁

If the co-efficient of x in \({ \left( { x }^{ 2 }+\frac { \lambda }{ x } \right) }^{ 5 }\) is 270, then \(\lambda\) = ______________

(a)

3

(b)

4

(c)

5

(d)

6

Straight line joining the points (2, 3) and (-1, 4) passes through the point \((\alpha,\beta)\) if

(a)

\(\alpha+2\beta=7\)

(b)

\(3\alpha+\beta=9\)

(c)

\(\alpha+3\beta=11\)

(d)

\(3\alpha+\beta=11\)

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 distance between the line 12x - 5y + 9 = 0 and the point (2, 1) is ______________

(a)

\(\pm\frac{28}{13}\)

(b)

\(\frac{28}{13}\)

(c)

\(-\frac{28}{13}\)

(d)

none of these

The co-ordinates of the foot of the perpendicular drawn from the point (2, 3) to the line 3x - y + 4 = 0 is ______________

(a)

\((\frac{1}{10},\frac{37}{10})\)

(b)

\((\frac{-1}{10},-\frac{37}{10})\)

(c)

\((\frac{-1}{10},\frac{37}{10})\)

(d)

\((\frac{37}{10},\frac{-1}{10})\)

If h² = ab, then the lines represented by ax²+ 2hx + by² = 0 are ______________

(a)

parallel

(b)

perpendicular

(c)

coincident

(d)

None

If one of the lines by 6x²- xy + 4cy² = 0 is 3x + 4y = 0, then c = ______________

(a)

1

(b)

-1

(c)

3

(d)

-3