If A = {(x,y) : y = sin x, x ∈ R} and B = {(x,y) : y = cos x, x ∈ R} then A∩B contains

(a)

no element

(b)

infinitely many elements

(c)

only one element

(d)

cannot be determined

Let R be the set of all real numbers. Consider the following subsets of the plane R x R: S = {(x, y) : y =x + 1 and 0 < x < 2} and T = {(x,y) : x - y is an integer} Then which of the following is true?

(a)

T is an equivalence relation but S is not an equivalence relation

(b)

Neither S nor T is an equivalence relation

(c)

Both S and T are equivalence relation

(d)

S is an equivalence relation but T is not an equivalence relation.

Domain of the function \(y={x-1\over x+1}\) is __________

(a)

1R

(b)

Q

(c)

R-(-1)

(d)

R-1

The number of solution of x² + |x - 1| = 1 is

(a)

1

(b)

0

(c)

2

(d)

3

Choose the incorrect statement

(a)

Matrix multiplication is non commutative

(b)

Matrix addition is associative

(c)

Singular matrices have inverse

(d)

Non singular matrices have inverse

A function f(x) is said to be continuous at x=a if  \(\lim _{ x\rightarrow a }{ f\left( x \right) } \)is equal to

(a)

\(f\left( a \right) \)

(b)

\(f\left( -a \right) \)

(c)

\(2f\left( a \right) \)

(d)

\(f\left( \frac { 1 }{ a } \right) \)

Choose the correct or the most suitable answer from the given four alternatives.
If f(x) is an even functions, thenf^'(x) is an ______function

(a)

even

(b)

odd

(c)

even and odd

(d)

even or odd

Assertion (A) : f (x) =\(\begin{cases} \begin{matrix} x+1, & x<2 \end{matrix} \\ \begin{matrix} 2x-1, & x\ge 2 \end{matrix} \end{cases}\) then f'(2) does not exist.
Reason (R) : f(x) is not continuous at 2.

(a)

Both A and it are true and R is the correct explanation of A

(b)

Both A and R are true but R is not the correct explantion of A

(c)

A is true R is false

(d)

A is false R is true

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

(a)

x²+c

(b)

2x²+c

(c)

\({x^2\over2}+c\)

(d)

\(-{x^2\over2}+c\)

\(\int { \frac { { 4x }^{ 3 }+1 }{ { x }^{ 4 }+x } } \) dx = _______ + c.

(a)

log (4x³  +1)

(b)

log (x⁴ + x)

(c)

log (4x³)

(d)

\(\frac { 1 }{ log({ x }^{ 4 }) } \)