The function f:[0,2π]➝[-1,1] defined by f(x) = sin x is

(a)

one-to-one

(b)

on to

(c)

bijection

(d)

cannot be defined

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 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)

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

In an examination there are three multiple choice questions and each question has 5 choices. Number of ways in which a student can fail to get all answer correct is

(a)

125

(b)

124

(c)

64

(d)

63

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

Which of the following equation is the locus of (at², 2at)

(a)

\(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\)

(b)

\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\)

(c)

x² + y² = a²

(d)

y² = 4ax

What must be the matrix X, if 2x +\(\begin{bmatrix} 1& 2 \\ 3 & 4 \end{bmatrix}=\begin{bmatrix} 3 & 8 \\ 7 & 2 \end{bmatrix}?\)

(a)

\(\begin{bmatrix} 1& 3 \\ 2 &-1 \end{bmatrix}\)

(b)

\(\begin{bmatrix} 1& -3 \\ 2 &-1 \end{bmatrix}\)

(c)

\(\begin{bmatrix} 2& 6 \\ 4 &-2 \end{bmatrix}\)

(d)

\(\begin{bmatrix} 2& -6 \\ 4 &-2 \end{bmatrix}\)

If y = f(x²+2) and f '(3) = 5, then \({dy\over dx}\) at x = 1 is

(a)

5

(b)

25

(c)

15

(d)

10

\(\int \frac{x+2}{\sqrt{x^2-1}} d x\) is

(a)

\(\sqrt{x^2-1}-2 log|x+\sqrt{x^2-1}|+c\)

(b)

\(sin^{-1}x-2 log|x+\sqrt{x^2-1}|+c\)

(c)

\(2 log|x+\sqrt{x^2-1}|-sin^{-1}x+c\)

(d)

\(\sqrt{x^2-1}+2log|x+\sqrt{x^2-1}|+c\)

If m is a number such that m \(\le\) 5, then the probability that quadratic equation 2x² + 2mx + m + 1 = 0 has real roots is

(a)

\({1\over 5}\)

(b)

\({2\over 5}\)

(c)

\({3\over 5}\)

(d)

\({4\over 5}\)