Let X = {1, 2, 3, 4}, Y = {a, b, c, d} and f = {(1, a), (4, b), (2, c), (3, d), (2, d)}. Then f is

(a)

an one-to-one function

(b)

an onto function

(c)

a function which is not one-to-one

(d)

not a function

If \(\frac { |x-2| }{ x-2 } \ge 0\), then x belongs to

(a)

\([2,\infty]\)

(b)

\((2,\infty )\)

(c)

\((-\infty,2)\)

(d)

\((-2,\infty )\)

\(\left( 1+cos\frac { \pi }{ 8 } \right) \left( 1+cos\frac { 3\pi }{ 8 } \right) \left( 1+cos\frac { 5\pi }{ 8 } \right) \left( 1+cos\frac { 7\pi }{ 8 } \right) \) =

(a)

\(\frac { 1 }{ 8 } \)

(b)

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

(c)

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

(d)

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

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

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

(a)

10

(b)

6

(c)

5

(d)

4

Which of the following point lie on the locus of 3x²+ 3y²- 8x - 12y + 17 = 0

(a)

(0, 0)

(b)

(-2, 3)

(c)

(1, 2)

(d)

(0, -1)

Find the angle between the lines 3x²- 10xy - 3y² = 0 ______________

(a)

90°

(b)

45°

(c)

60°

(d)

30°

If A is a square matrix, then which of the following is not symmetric?

(a)

A + A^T

(b)

AA^T

(c)

A^T A

(d)

A − A^T

It is given that f '(a) exists, then \(lim_{x\rightarrow a}{xf(a)-af(x)\over x-a}\) is

(a)

f(a) - af '(a)

(b)

f '(a)

(c)

- f '(a)

(d)

f(a) + af '(a)

If \(\int f '(x)e^{x^2}dx=(x-1)e^{x^2}+c\), then f(x) is

(a)

\(2x^3-{x^2\over 2}+x+c\)

(b)

\({x^3\over 2}+3x^2+4x+c\)

(c)

x³ + 4x² + 6x + c

(d)

\({2x^3\over3}-x^2+x+c\)