If the set A has m elements, B has n elements then the number of elements in A x B is ______.

2

(a)

m + n

(b)

m + n + 1

(c)

mn

(d)

n²

Let R be a relation from a set A to B, then ______.

2

(a)

R=A\(\cup\)B

(b)

R =A\(\cap\)B

(c)

R\(\subset\)A x B

(d)

R \(\subset\) B x A

If R is a relation from a finite set A having m elements to a finite set B having n elemen.ts, then the number of relations from A to B is ______.

2

(a)

2^mn

(b)

2^mn-1

(c)

2mn

(d)

mⁿ

Which one of the following is not a function

2

(a)

{(x, y) (:) x, y \(\in\) R, x² = y}

(b)

{(x, y) (:) x, y \(\in\) R, y² = x}

(c)

{(x, y) (:) x, y \(\in\) R, x = y³}

(d)

{(x, y) (:) x, y \(\in\) R, y = x³}

Let f(x) = Ix-1I then ______.

2

(a)

f(x²) = [f(x)]²

(b)

f(x +y) = f(x) f(y)

(c)

f(IxI) = I f(x) I

(d)

none of these

If f(x) = log\({1+x\over 1-x}\) and g(x) = \({3x+x^3\over 1+3x^2}\) then f(g(x)) is equal to ______.

2

(a)

f(2x)

(b)

\([f(x)]^2\)

(c)

3f(x)

(d)

- f(3x)

If \(f(x)={2^x+2^{-x}\over 2}\) then f(x+y) f(x-y)is equal to ______.

2

(a)

\({1\over2}[f(2x)+f(2y)]\)

(b)

\({1\over2}[f(2x)-f(2y)]\)

(c)

\({1\over3}[f(2x)+f(2y)]\)

(d)

\({1\over3}[f(2x)-f(2y)]\)

If f(x) =\({x+1\over x-1}\) is a real function,\(\neq\) 1, then \(f[f\{f(2)\}]\) is ______.

2

(a)

-1

(b)

-3

(c)

3

(d)

4

If f: R\(\rightarrow\) R be given by f(x) =\({4^x\over 4^x+2}\) for all x \(\in\) R, then ______.

2

(a)

f(x) = f(1 + x)

(b)

f(x) + f(1 + x) = 0

(c)

f(x) + f(1 - x) = 1

(d)

none of these

The domain of the function \(f(x)=\sqrt{x-1}+\sqrt{3-x}\) is ______.

2

(a)

(1,\(\infty\))

(b)

(\(\infty\),5)

(c)

(1, 3)

(d)

[1, 3]

In a ∆ABC, if ∠A = 45^o, ∠B = 60^o and ∠C = 75^o, then the ratio of sides is ______.

2

(a)

2 : \(\sqrt { 6 } :(\sqrt { 3 } +1)\)

(b)

\(\sqrt { 2 } :6:(\sqrt { 3 } +1)\)

(c)

\(2:\sqrt { 6 } :(\sqrt { 3 } -1)\)

(d)

None

In a ΔABC if a = 5, b = 6 and c = 5, then ∠B is ______.

2

(a)

cos^-1 \(\left( \frac { 7 }{ 24 } \right) \)

(b)

cos^-1\(\left( \frac { 7 }{ 25 } \right) \)

(c)

cos^-1 \(\left( \frac { 7 }{30 } \right) \)

(d)

None

In a ΔABC, if the sides are 7cm, 4\(\sqrt { 3 } \) cm and .\(\sqrt { 13 } \) cm, then the smallest angle is ______.

2

(a)

45^o

(b)

60^o

(c)

30^o

(d)

90^o

If x = r sin\(\alpha\) cos \(\beta\), y = r sin\(\alpha\) sin \(\beta\)and z = r cos\(\alpha\), then X² + y² + Z² is independent of ______.

2

(a)

\(\alpha , \beta\)

(b)

\(\gamma , \alpha\)

(c)

\(\gamma , \beta\)

(d)

none of these

sin⁶\(\theta\) + cos⁶\(\theta\) + 3 sin²\(\theta\) cos²\(\theta\) is equal to ______.

2

(a)

0

(b)

1

(c)

4

(d)

2

If tan\(\theta\) + cot \(\theta\) = 5 then tan³ \(\theta\) + cot³ \(\theta\) is equal to ______.

2

(a)

135

(b)

140

(c)

110

(d)

90

If tan \(\theta\) + sec \(\theta\) = e^x then cos\(\theta\) is equal to ______.

2

(a)

\({e^x+e^{-x}\over 2}\)

(b)

\({e^x-e^{-x}\over 2}\)

(c)

\({e^x-e^{-x}\over e^x+e^x}\)

(d)

\({2\over e^x+e^{-x}}\)

If tan \(\theta={\alpha\over \alpha+1}\) and tan \(\phi ={1\over 2\alpha+1}\) , then (A+ B) is equal to ______.

2

(a)

0

(b)

\(\pi\over4\)

(c)

\(\pi\over6\)

(d)

\(\pi\over2\)

In a\(\triangle\) ABC, if tan A +tanB+ tan C = o then cot A cot B cot C is equal to______.

2

(a)

6

(b)

3

(c)

\(1\over6\)

(d)

\(1\over3\)

If sin \(\theta\) + sin \(\phi\)= \(\alpha\) and cos\(\theta\) - cos\(\phi\)= b then tan\({\theta -\phi\over 2}\) is equal to ______.

2

(a)

\(\sqrt{a^2+b^2}\)

(b)

\(-{a\over b}\)

(c)

\(-{b\over a}\)

(d)

\(1\over \sqrt{a^2-b^2}\)

If A, B, C are in A.P. then \({sinA-sinC\over cosC-cosA}\) is equal to ______.

2

(a)

sin B

(b)

cot B

(c)

sin 2B

(d)

cot 2B

If 4 sin²\(\theta=1\) then the values of \(\theta\) are ______.

2

(a)

\(2n\pi\pm{\pi\over3},n\in Z\)

(b)

\(n\pi\pm{\pi\over3},n\in Z\)

(c)

\(n\pi\pm{\pi\over6},n\in Z\)

(d)

\(2n\pi\pm{\pi\over6},n\in Z\)

The solution of the equation cos² \(\theta\) -+sin\(\theta\)+ 1=0lies in the interval ______.

2

(a)

\(({\pi\over 4},{3\pi\over4})\)

(b)

\((-{\pi\over 4},{3\pi\over4})\)

(c)

\(({3\pi\over 4},{5\pi\over4})\)

(d)

\(({5\pi\over 4},{7\pi\over4})\)

Find the general solutions of\(\sqrt{3}\) sin x-cos x =2 ______.

2

(a)

X = n\(\pi +{\pi\over 6}+(-1)^n{\pi\over2}\)

(b)

X = n\(\pi -{\pi\over 6}+(-1)^n{\pi\over2}\)

(c)

X = n\(\pi +{\pi\over 6}+(-1)^{n+1}{\pi\over2}\)

(d)

None