Free Printable Basic maths for physics

1.

Using Binomial approximation, the value of $\sqrt{82}$ is

a)

$9+\frac{1}{16}$

b)

$9+\frac{1}{18}$

c)

$9+\frac{1}{22}$

d)

$9+\frac{1}{14}$

2.

Refer to the equation given below. If x is very small compared to a then y will be approximately equal to
$y=\frac{1}{\left(8a^3-x^3\right)^{\frac{2}{3}}}-\frac{1}{\left(8a^3+x^3\right)^{\frac{2}{3}}}$

a)

$\frac{3x^3}{2a^5}$

b)

$\frac{x^3}{20a^5}$

c)

$\frac{x^3}{24a^5}$

d)

$\frac{2x^3}{3a^5}$

3.

Simplify the following using Binomial approximation
$\lfloor\sqrt{70}\rfloor^{\frac{1}{3}}$

a)

$2.031$

b)

$2.131$

c)

$8.031$

d)

$4.031$

4.

The value of $\frac{1}{\sqrt{200}}$ is same as

a)

$0.75$

b)

$0.65$

c)

$0.7$

d)

$0.07$

5.

The rate of flow of liquid (I) in a tube of radius r and length l due to a pressure difference P is given by $I=\frac{\pi}{8\eta}\ \frac{P}{l}r^4$ Here $\eta$ is called coefficient of viscosity. If Pressure increases by 4%, length decreases by 2%, radius increases by 1.5% and coefficient of viscosity increases by 0.5%, find the percentage change in rate of flow

a)

11.5%

b)

11%

c)

8.5%

d)

8%

6.

The mass and radius of a spherical object are 40 g and 4 cm respectively. if mass reduces by 2 g and radius increases by 4 mm then the percentage change in density is given by

a)

35%

b)

-35%

c)

-25%

d)

25%

7.

The angle subtended by a pole with the horizontal is $\frac{44}{21}$ radian. Its value of the angle in degree is given by

a)

$90^0$

b)

$75^0$

c)

$120^0$

d)

$180^0$

8.

The value of $\frac{5\pi}{3}$ radian in degree is given by

a)

120

b)

180

c)

240

d)

300

9.

The value of $\sin\theta$ is $\frac{2}{3}$ then find the value of $\sec\theta$

a)

$\frac{\sqrt{5}}{3}$

b)

$\frac{2}{\sqrt{5}}$

c)

$\frac{3}{\sqrt{5}}$

d)

$\frac{1}{\sqrt{5}}$

10.

A shadow of a pencil of length 10 cm is formed on the desk as shown in the figure. If the length of the shadow is 6 cm then the angle made the pencil wit the floor is

a)

$60^0$

b)

$37^0$

c)

$53^0$

d)

$45^0$

11.

If $\theta$ is $\frac{2\pi}{3}$ then the value of y given by the relation below is $\ \ y=\frac{\left(4\sin^2\theta-2\cos\theta-\tan^22\theta\right)}{\cot\theta}$

a)

$\sqrt{2}$

b)

$\sqrt{3}$

c)

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

d)

$3$

12.

The correct expression for $\tan\left(a+b\right)$ . Hint: use the knowledge of $\sin\ \left(a+b\right)\ and\ \cos\ \left(a+b\right)$

a)

$\frac{\tan a\ -\tan b}{1+\left(\tan a\right)\left(\tan b\right)}$

b)

$\frac{\tan a\ +\tan b}{1-\left(\tan a\right)\left(\tan b\right)}$

c)

$\frac{\tan a\ \tan b}{1-\left(\tan a\right)\left(\tan b\right)}$

d)

$\frac{\tan a\ +\tan b}{\left(\tan a\right)-\left(\tan b\right)}$

13.

$\tan\ \left(180-\theta\right)$ is

a)

$\tan\theta$

b)

$\cot\theta$

c)

$-\tan\theta$

d)

$-\cot\theta$

14.

The approximate value of $\sin\left(40\right)$

a)

$\frac{1}{5}\left(3+\frac{\pi}{15}\right)$

b)

$\frac{1}{5}\left(3-\frac{2\pi}{45}\right)$

c)

$\frac{1}{5}\left(4+\frac{\pi}{30}\right)$

d)

$\frac{1}{5}\left(3+\frac{\pi}{60}\right)$

15.

Statement 1: The sin and cos of an angle is negative in third quadrant

Statement 2: The tan and sin of an angle are positive in second quadrant

Statement 3: The tan and sin of an angle are negative in fourth quadrant

Choose the correct statement

a)

statement 1, 2 and 3 are correct

b)

statement 1, 2 are correct and 3 is wrong

c)

statement 1, 3 are correct and 2 is wrong

d)

statement 1, 2 and 3 are wrong

16.

Consider $y=\sin x$ . If x increases by $3^0$ then the variation in y $\left(ie\ \Delta y\right)$ for $x=60^0$ is

a)

$\frac{\pi}{120}$

b)

$\frac{\pi}{90}$

c)

$\frac{\pi}{60}$

d)

$\frac{\pi}{50}$

Basic maths for physics

Total questions: 16

Worksheet time: 8mins

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