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6.

if  $\int \frac{1}{1-\cot x}dx=Ax+B\log |\sin x-\cos x|+c$   then A+B


A) 1

B) -1

C) 0

D) -2



7.

 if $\omega$  is a complex cube root of unity and 

$A=\begin{bmatrix}\omega & 0&0 \\0& \omega^{2} &0 \\ 0 & 0 &1\end{bmatrix}$  then A-1=


A) $\begin{bmatrix}\omega^{2} &0&0 \\0 & \omega^{} &0 \\ 0 & 0 &1\end{bmatrix}$

B) $\begin{bmatrix}1& 0&0 \\0& 1 &0 \\ 0 & 0 &1\end{bmatrix}$

C) $\begin{bmatrix}1 & 0&0 \\0& \omega^{2} &0 \\ 0 & 0 &\omega^{}\end{bmatrix}$

D) $\begin{bmatrix}0 & 0&\omega \\0& \omega^{2} &0 \\ 1 & 0 &0\end{bmatrix}$



8.

The edge of a cube is decreasing at the rate of 0.04 cm/sec . If the edge of the cube  is 10 cms, then the rate of decrease of surface area of the cube is 


A) 4.8 $cm^{2}/sec$

B) 4.08 $cm^{2}/sec$

C) .48 $cm^{2}/sec$

D) 4.008 $cm^{2}/sec$



9.

Let  $a: \sim (p \wedge \sim r)\vee (\sim q \vee s) $   and 

$b: \ (p \vee s)\leftrightarrow ( q \wedge r) $ .If the truth  values of p and q are true and that of r and s are false, then the truth values of a and b  be respectively...........


A) F, F

B) T, T

C) T, F

D) F,T



10.

 The vector equation of the plane 

$r= (2\hat{i}+\hat{k})+\lambda(\hat{i})+\mu(\hat{i}+2\hat{j}-3\hat{k})$   in scalar product form is  $r. (3\hat{i}+2\hat{k})=\alpha$ , then

 $\alpha$= ......


A) 2

B) 3

C) 1

D) 0



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