Free Printable 12 DIAMOND: INTEGRATION: VECTORS

1.

$\Pr ojection\ of\$

i\ -\ j\ an\ i\ +\ j\

is -

a)

$\frac{3}{2}$

b)

$\frac{5}{2}$

c)

$2$

d)

0

2.

$Solution\ of\$
$\frac{dy}{dx}=\ \frac{1+y^2}{1+x^2}$
is

a)

$\tan^{-1}y\ =\ \tan^{-1}x\ +\ c$

b)

$\sin^{-1}y\ =\ \sin^{-1}x\ +\ c$

c)

tanx.tany = c

d)

$\cos^{-1}y\ =\ \cos^{-1}x\ +\ c$

3.

$\int_{ }^{ }\ \operatorname{cosec}^2x\ dx\ =$

a)

- cot x + c

b)

cot x +c

c)

tan x + c

d)

- tanx +c

4.

$\int_0^{\frac{\pi}{2}}\ \frac{\sin^nx}{\sin^nx\ +\ \cos^nx}\ dx\ =$

a)

0

b)

$\frac{\pi}{4}$

c)

1

d)

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

5.

$The\ general\ solution\ of$
$\frac{dy}{dx}=\ \frac{y}{x}\ is$

a)

$\log y\ =\ kx$

b)

$y=kx$

c)

$xy\ =\ k$

d)

$y=k\log x$

6.

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

a)

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

b)

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

c)

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

d)

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

7.

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

a)

cos x

b)

- cos x

c)

tan x

d)

cot x

8.

$\int_{ }\ \frac{dx}{\sqrt{1\ -\ x^2}}\ =$

a)

x

b)

$\cos^{-1}x$

c)

$\tan^{-1}x$

d)

$\sin^{-1}x$

9.

$\int_{ }^{ }\operatorname{cosec}x\ \cot x\ dx\ =\$

a)

cosec x

b)

$\ -\ \operatorname{cosec}\ x$

c)

tan x

d)

$\ -\ \tan\ x$

10.

$\int_{ }^{ }e^{ax}\ dx\ =$

a)

$e^x$

b)

$e^{ax}$

c)

$\frac{e^{ax}}{a}$

d)

$\frac{1}{x}$

12 DIAMOND: INTEGRATION: VECTORS

Total questions: 10

Worksheet time: 5mins

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