\(n(p(A))=512,n(p(B))=32,n(A\cup B)=16,\) find \(n(A\cap B) \)  ___________

(a)

2

(b)

9

(c)

4

(d)

5

If 3 is the logarithm of 343, then the base is

(a)

5

(b)

7

(c)

6

(d)

9

\(\frac { cos3x }{ 2cos2x-1 } \) is _______________

(a)

cos x

(b)

sin x

(c)

tan x

(d)

cot x

The number of positive integral solution of \(x\times y\times z=30\) is  _________

(a)

3

(b)

1

(c)

9

(d)

27

The sum of the digits in the unit's place of all the 4- digit numbers formed by 3, 4, 5 and 6, without repetition, is _______.

(a)

432

(b)

108

(c)

36

(d)

72

The value of \({ 9 }^{ \frac { 1 }{ 3 } }\) ,\({ 9 }^{ \frac { 1 }{ 9 } }\)\({ 9 }^{ \frac { 1 }{ 27}}\),\(\infty \) is ______________

(a)

1

(b)

3

(c)

9

(d)

none of these

The locus of a point which is collinear with the points (a, 0) and (0, b) is ______________

(a)

x + y = 1

(b)

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

(c)

x + y = ab

(d)

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

On using elementary row operation R₁⟶R₁-3R₂ in the following matrix equation \(\begin{pmatrix} 4 & 2 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)________.

(a)

\(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & -7 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)

(b)

\(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 0 & 3 \end{pmatrix}\begin{pmatrix} -1 & -3 \\ 1 & 1 \end{pmatrix}\)

(c)

\(\begin{pmatrix} -5 & -7 \\ 3 & 3 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ 1 & -7 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)

(d)

\(\begin{pmatrix} 4 & 2 \\ -5 & -7 \end{pmatrix}=\begin{pmatrix} 1 & 2 \\ -3 & -3 \end{pmatrix}\begin{pmatrix} 2 & 0 \\ 1 & 1 \end{pmatrix}\)

The value of the expression \({ \left| \overrightarrow { a } \times \overrightarrow { b } \right| }^{ 2 }+{ (\overrightarrow { a } .\overrightarrow { b } ) }^{ 2 }\) is ___________ .

(a)

cos² \(\theta\)

(b)

sin² \(\theta\)

(c)

\({ |\overrightarrow { a } | }^{ 2 }|{ \overrightarrow { b } | }^{ 2 }\)

(d)

\({ (|\overrightarrow { a } |+|\overrightarrow { b } |) }^{ 2 }\)

\(lim_{x \rightarrow 0}{e^{sin \ x}-1\over x}=\)

(a)

1

(b)

e

(c)

\({1\over e}\)

(d)

0