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]

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

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

(a)

5

(b)

7

(c)

6

(d)

9

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

(a)

\(\sqrt{2}\)

(b)

\(\sqrt{3}\)

(c)

2

(d)

4

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

Everybody in a room shakes hands with everybody else. The total number of shake hands is 66. The number of persons in the room is

(a)

11

(b)

12

(c)

10

(d)

6

1+3+5+7+........+17 is equal to

(a)

101

(b)

81

(c)

71

(d)

61

The HM of two positive numbers whose AM and GM are 16, 8 respectively is

(a)

10

(b)

6

(c)

5

(d)

4

The equation of the locus of the point whose distance from y-axis is half the distance from origin is

(a)

x² + 3y² = 0

(b)

x²- 3y² = 0

(c)

3x²+ y² = 0

(d)

3x²- y² = 0

Equation of the straight line perpendicular to the line x - y + 5 = 0, through the point of intersection the y-axis and the given line

(a)

x - y - 5 = 0

(b)

x + y - 5 = 0

(c)

x + y + 5 = 0

(d)

x + y + 10 = 0

If A = \(\begin{bmatrix}\lambda & 1 \\ -1 & -\lambda \end{bmatrix}\), then for what value of \(\lambda\), A² = O?

(a)

0

(b)

\(\pm 1\)

(c)

-1

(d)

1

If x₁, x₂, x₃ as well as y₁, y₂, y₃ are in geometric progression with the same common ratio, then the points (x₁, y₁ ), (x₂, y₂), (x₃, y₃ ) are

(a)

vertices of an equilateral triangle

(b)

vertices of a right angled triangle

(c)

vertices of a right angled isosceles triangle

(d)

collinear

Let A and B be two symmetric matrices of same order. Then which one of the following statement is not true?

(a)

A + B is a symmetric matrix

(b)

AB is a symmetric matrix

(c)

AB = (BA)^T

(d)

A^T B = AB^T

If \(\overrightarrow{a}+2\overrightarrow{b}\) and \(3\overrightarrow{a}+m\overrightarrow{b}\) are parallel, then the value of m is

(a)

3

(b)

\(1\over3\)

(c)

6

(d)

\(1\over6\)

If ABCD is a parallelogram, then \(\overrightarrow{AB}+\overrightarrow{AD}+\overrightarrow{CB}+\overrightarrow{CD}\) is equal to

(a)

\(2(\overrightarrow{AB}+\overrightarrow{AD})\)

(b)

\(4\overrightarrow{AC}\)

(c)

\(4\overrightarrow{BD}\)

(d)

\(\overrightarrow{0}\)

If \(|\overrightarrow { a } |=10,|\overrightarrow { b } |=2,\) and \(|\overrightarrow { a } .\overrightarrow { b } |=12\) then the value of \(|\overrightarrow { a } \times \overrightarrow { b } |\) is ___________ .

(a)

5

(b)

10

(c)

14

(d)

16

The angle between two vectors \(\vec{a}\) and \(\vec{b}\) with magnitudes\(\sqrt{3}\) and 4 respectively and \(\vec{a}.\vec{b}=2\sqrt{3}\) is ________ .

(a)

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

(b)

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

(c)

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

(d)

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

\(lim_{x\rightarrow0}{\sqrt{1-cos 2x}\over x} \)

(a)

0

(b)

1

(c)

\(\sqrt{2}\)

(d)

does not exist

If the derivative of (ax - 5)e^3x at x = 0 is -13, then the value of a is

(a)

8

(b)

-2

(c)

5

(d)

2

The number of points in R in which the function \(f(x)=|x-1|+|x-3|+sin \ x\) is not differentiable, is

(a)

3

(b)

2

(c)

1

(d)

4

Write the following in roster form. 
{x\(\in \)N : x²<121 and x is a prime}

Simplify \({ 16 }^{ -\frac { 3 }{ 4 } }\)

Solve for x  \(\left| 3-x \right| <7\)

Prove that \(\cos { \left( \pi +\theta \right) } =-\cos { \theta } \)

A straight tunnel is to be made through a mountain. A surveyor observes the two extremities A and B of the tunnel to be built from a point P in front of the mountain. If AP = 3 km, BP = 5 Km and \(\angle APB\) 120^o, then find the length of the tunnel to be built.

Find the value of tan 120°.

How many strings can be formed from the letters of the word ARTICLE, so that vowels occupy the even Places?

By taking suitable sets A, B, C, verify the following results:
(A\(\times\) B)\(\cap \)(B\(\times\)A) = (A\(\cap \)B) \(\times\) (B\(\cap \)A)

If x=\(\sqrt { 2 } +\sqrt { 3 } \)  find \(\frac { { x }^{ 2 }+1 }{ { x }^{ 2 }-2 } \)

Find the direction cosines of the vector joining the points A(1,2, -3) and B(-1, -2,1) directed from A to B.

Use the graph to find the limits (if it exists). If the limit does not exist, explain why?
\(lim_{x\rightarrow{1}}sin \pi x\)

Prove that \(lim_{x\rightarrow 0}sin x=0\)

Find F'(x) if F(x) = \(\sqrt{x^2+1}\)

Differentiate y \(=x^{\sqrt{x}}\)

The function for exchanging American dollars for Singapore Dollar on a given day is f(x) = 1.23x, where x represents the number of American dollars. On the same day function for exchanging Singapore dollar to Indian Rupee is g(y) = 50.50y, Where y represents the number of Singapore dollars. Write a function which will give the exchange rate of American dollars in terms of Indian rupee

If \(f:R-\{ -1,1\}\rightarrow R\) is defined by \(f(x)={x \over x^2-1},\) verify whether f is one-to-one or not.

Find the square root of 7-4\(\sqrt{3}\)

A researcher wants to determine the width of a pond from east to west, which cannot be done by actual measurement. From a point P, he finds the distance to the eastern-most point of the pond to be 8 km, while the distance to the western most point form P to b 6 km. If the angle between the two lines of sight is 60⁰, find the width of the pond.

If A + B + C = \(\pi\), prove that cos²A + cos²B + cos²C = 1 - 2 cos A cos B cos C.

There are 11 points in a plane. No three of these lies in the same straight line except 4 points, which are collinear. Find,
(i) the number of straight lines that can be obtained from the pairs of these points?
(ii) the number of triangles that can be formed for which the points are their vertices?

lf P(2,-7) is a given point and Q is a point on (2x² + 9y² = 18), then find the equations of the locus of the mid-point of PQ.