Free Printable 12/DE/INTE/DIFF/VECT/24.12.2020

1.

Solution of

x\ \frac{dy}{dx}\ =\ \frac{y}{1+\log x}

is

a)

y = log x +c

b)

$y\ =\ \frac{c}{1+\log x}$

c)

$y\ =\ c\left(1\ +\ \log x\right)$

d)

y = x +logcx

2.

Solution of

\frac{dy}{dx}\ =\ 1+x+y+xy

is

a)

$\log\left(1+y\right)\ =\ x\ +\ \frac{x^2}{2}+c$

b)

$\log\left(1-y\right)\ =\ x\ +\ \frac{x^2}{2}+c$

c)

$\log\left(1+y\right)\ =\ x\ +\ \frac{x^3}{3}+c$

d)

$\log\left(1+y\right)\ =\ 2x\ +\ \frac{x^2}{2}+c$

3.

Solution of

\left(x+y+3\right)\ \frac{dy}{dx}=\ 1

is

a)

$x+y+3\ =\ Ce^y$

b)

$x+y+4\ =\ Ce^y$

c)

$x+y+3\ =\ Ce^{-y}$

d)

$x+y+4\ =\ Ce^{-y}$

4.

If

\left|\overrightarrow{a\ }\ -\ \overrightarrow{b\ }\right|=\ \left|\overrightarrow{a\ }\ +\ \overrightarrow{b\ }\right|

then - angle - between

\overrightarrow{a\ }\ and\ \overrightarrow{b\ }\ is\

a)

$\frac{\pi}{3}$

b)

$\frac{\pi}{6}$

c)

$\frac{\pi}{2}$

d)

0

5.

$If\ x\ =a\left(t+\frac{1}{t}\right)\ and\ y\ =a\left(t-\frac{1}{t}\right)\ then\ \frac{dy}{dx}\ is$

a)

$\frac{y}{x}$

b)

$xy$

c)

$\frac{x}{y}$

d)

1

6.

$If\ y\ =\sin^{-1}x\ +\sin^{-1}\ \sqrt{1\ -x^2},\ then\ \frac{dy}{dx}\ =$

a)

cos x

b)

- sin x

c)

1

d)

0

7.

$\int_{ }^{ }\ \frac{\cos\ x-\sin\ x}{1+\sin\ 2x}dx$

a)

$\frac{1}{\left(\sin\ x\ -\cos\ x\right)}+c$

b)

$-\frac{1}{\left(\sin\ x\ -\cos\ x\right)}+c$

c)

$\frac{1}{\left(\sin\ x\ +\cos\ x\right)}+c$

d)

$-\frac{1}{\left(\sin\ x\ +\cos\ x\right)}+c$

8.

$\int_0^{\frac{\pi}{2}}\ \frac{\cos\ x\ -\ \sin\ x}{1\ +\ \sin\ x\ \cos\ x}dx\ =\$

a)

0

b)

1

c)

$\frac{\pi}{4}$

d)

$\pi$

9.

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

a)

$\tan^{-1}\left(2x-1\right)+C$

b)

$\tan\ ^{-1}\left(2x-1\right)+C$

c)

$\sin^{-1}2x+C$

d)

$\sin^{-1}\left(2x-1\right)+C$

10.

The value x if x(i+j+k) is a unit vector

a)

$\pm\frac{1}{\sqrt{3}}$

b)

$\pm\sqrt{3}$

c)

$\pm3$

d)

$\pm\frac{1}{3}$

12/DE/INTE/DIFF/VECT/24.12.2020

Total questions: 10

Worksheet time: 20mins

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