If A = {1, 2, 3}, B = {1, 4, 6, 9} and R is a relation from A to B defined by "x is greater than y". The range of R is __________

(a)

{1, 4, 6, 9}

(b)

{4, 6, 9}

(c)

{1}

(d)

None of these

If \({ log }_{ \sqrt { x } }\) 0.25 = 4, then the value of x is

(a)

0.5

(b)

2.5

(c)

1.5

(d)

1.25

Assertion (A) : cos x = \(\frac{-1}{2}\) and 0\(\frac{2\pi}{3},\frac{4\pi}{3}\).
Reason (R) : cos is negative in the first and fourth quadrant only.

(a)

Both A and (R) 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

The sum up to n terms of the series \(\frac { 1 }{ \sqrt { 1 } +\sqrt { 3 } } +\frac { 1 }{ \sqrt { 3 } +\sqrt { 5 } } +\frac { 1 }{ \sqrt { 5 } +\sqrt { 7 } } +\)....is 

(a)

\(\sqrt { 2n+1 } \)

(b)

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

(c)

\(\sqrt { 2n+1 } -1\)

(d)

\(\frac { \sqrt { 2n+1 } -1 }{ 2 } \)

The sum of the series C₀²- C₁² + C₂² .....+ (- 1)ⁿC²_n where n is an even integer is ______________

(a)

2nC_n

(b)

(-1)ⁿ2nC_n

(c)

(-1)ⁿ2nC_n-1

(d)

(-1)^n/2nC_n/2

The direction cosines of the vector \(2\hat{i}+2\hat{j}-\hat{k}\) are ___________ .

(a)

\(\frac { 2 }{ 3 } ,\frac { 2 }{ 3 } ,-\frac { 1 }{ 3 } \)

(b)

\(\frac { 2 }{ 3 } ,\frac { 2 }{ 3 } ,\frac { 1 }{ 3 } \)

(c)

\(-\frac { 2 }{ 3 } ,-\frac { 2 }{ 3 } ,\frac { 1 }{ 3 } \)

(d)

\(-\frac { 2 }{ 3 } ,-\frac { 2 }{ 3 } ,-\frac { 1 }{ 3 } \)

Find the odd one out of the following

(a)

\(\hat { i } +2\hat { j } +3\hat { k } \)

(b)

\(2\hat { i } +4\hat { j } +6\hat { k } \)

(c)

\(7\hat { i } +14\hat { j } +21\hat { k } \)

(d)

\(\hat { i } +3\hat { j } +2\hat { k } \)

Choose the correct or the most suitable answer from the given four alternatives.
If \(x=a(\theta+\sin \theta), y=a(1+\cos \theta)\) then \(\frac{dy}{dx}\) is ______

(a)

\(\tan { \frac { \theta }{ 2 } } \)

(b)

\(-\tan { \frac { \theta }{ 2 } } \)

(c)

\(\cot { \frac { \theta }{ 2 } } \)

(d)

\(-\cot { \frac { \theta }{ 2 } } \)

\(\int { sin } \)e^x . d (e^x) = ________+c.

(a)

cos (e^x)

(b)

sin(e^x)

(c)

- cos (e^x)

(d)

-sin(e^x)

Choose the incorrect pair:

(a)

A and B disjoint - P(A⋂B) = peA) + PCB

(b)

A and B independent - P(A⋂B) = p(A) P(B)

(c)

A and B disjoint - P(A⋂B) = 0

(d)

A and B independent - P(A/B) = P(B/A)