Free Printable 12 A / INTE/DIFF/VECTORS / 14

1.

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

a)

$\frac{\pi}{2}$

b)

$\frac{\pi}{3}$

c)

$\frac{\pi}{6}$

d)

$0\degree$

2.

For what value of p vectors

3i+2j+\ 3k

and

i-\ 2pj+3k

are parallel.

a)

1 / 3

b)

- 1/3

c)

2 / 3

d)

- 2/ 3

3.

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

a)

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

b)

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

c)

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

d)

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

4.

$\int_{ }^{ }\ \log\ x\ dx\ =$

a)

$x\log x\ -x+C$

b)

$x\log x\ +\ x+C$

c)

$x\log x\ -1+C$

d)

$x\log x\ +1+C$

5.

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

a)

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

b)

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

c)

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

d)

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

6.

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

a)

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

b)

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

c)

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

d)

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

7.

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

a)

$\frac{\pi}{2}$

b)

$\frac{\pi}{4}$

c)

$\pi$

d)

$\frac{\pi^2}{2}$

8.

$\frac{d}{dx}\ \tan^{-1}x\ =\$

a)

$\frac{1}{x}$

b)

$\frac{1}{\sqrt{1+x^2}}$

c)

$\frac{1}{1+x^2}$

d)

$\frac{1}{\sqrt{1-x^2}}$

9.

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

a)

$y$

b)

$y\ e^{a-x}$

c)

$-\ y$

d)

$e^{a-x}$

10.

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

a)

3 sq units

b)

4 sq units

c)

5 sq units

d)

6 sq units

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

Total questions: 10

Worksheet time: 18mins

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