12 A / INTE/DIFF/VECTORS / 14 - DEC -2020

The angle that vector  $\sqrt{2}\ i\ +\ j\ +\ k$  
makes with y - axis is 

•  $\frac{\pi}{2}$  

•  $\frac{\pi}{3}$  

•  $\frac{\pi}{6}$  

•  $0\degree$  

For what value of p vectors

 $3i+2j+\ 3k$  and  $i-\ 2pj+3k$  
are parallel.

• 1 / 3

• - 1/3

• 2 / 3

•  - 2/ 3

 $If\ y\ =\ \tan^{-1}\left[\ \frac{\sqrt{1+\ \sin x}+\sqrt{1-\ \sin x}}{\sqrt{1+\ \sin x}-\sqrt{1-\ \sin x}}\right]$  

•  $then\ \frac{dy}{dx}=\ \frac{1}{3}$  

•  $then\ \frac{dy}{dx}=\ -\frac{1}{3}$  

•  $then\ \frac{dy}{dx}=\ \frac{1}{2}$  

•  $then\ \frac{dy}{dx}=\ -\ \frac{1}{2}$  

 $\int_{ }^{ }\ \log\ x\ dx\ =$  

•  $x\log x\ -x+C$  

•  $x\log x\ +\ x+C$  

•  $x\log x\ -1+C$  

•  $x\log x\ +1+C$  

 $\int_{ }\ \frac{dx}{\left(x+1\right)\left(x+2\right)}=\$  

•  $\log\ \left|\ \frac{x+\ 1}{x+\ 2}\right|\ +\ C$  

•  $\log\ \left|\ \frac{x-\ 1}{x-\ 2}\right|\ +\ C$  

•  $\log\ \left|\ \frac{x+\ 2}{x+\ 1}\right|\ +\ C$  

•  $\log\ \left|\ \frac{x-2}{x\ -\ 1}\right|\ +\ C$  

 $\int_{ }\ \frac{dx}{\sqrt{x^2+a^2}}=$  

•  $\log\ \left[\ x\ +\sqrt{x^2\ +\ a^2}\right]\ +\ C$  

•  $og\ \left[\ x\ +\sqrt{x^2\ -\ a^2}\right]\ +\ C$  

•  $og\ \left[\ x\ -\sqrt{x^2\ +\ a^2}\right]\ +\ C$  

•  $og\ \left[\ x^2\ +\sqrt{x^2\ +\ a^2}\right]\ +\ C$  

 $\int_0^{\frac{\pi}{2}}\ \frac{\tan^{7\ }x}{\cot^7x\ +\ \tan^{7\ }x}\ dx\ =$  

•  $\frac{\pi}{2}$  

•  $\frac{\pi}{4}$  

•  $\pi$  

•  $\frac{\pi^2}{2}$  

 $\frac{d}{dx}\ \tan^{-1}x\ =\$  

•  $\frac{1}{x}$  

•  $\frac{1}{\sqrt{1+x^2}}$  

•  $\frac{1}{1+x^2}$  

•  $\frac{1}{\sqrt{1-x^2}}$  

 $If,\ y\ =\ e^{a-x\ }\ then\ \frac{dy}{dx}=$  

•  $y$  

•  $y\ e^{a-x}$  

•  $-\ y$  

•  $e^{a-x}$  

Find the area of the triangle whose two sides are represented by the vectors 2i and −3j .

• 3 sq units

• 4 sq units

• 5 sq units

• 6 sq units