Free Printable BASICS FOR GRADE XII

1.

Identify the vector quantities

a)

Force

b)

Work

c)

Momentum

d)

velocity

e)

Charge

2.

If A =5 N and B = 2 N, is vector sum of A and B IS always 7 N

a)

TRUE

b)

FALSE

3.

If A = 5 N and B = 5 N, for what angle, vector sum of A and B to be 5 N

a)

zero

b)

90

c)

120

d)

180

e)

60

4.

If A = B = 10 N are two equal vectors, vector sum of A and B for angle between them is zero, is.............

a)

0

b)

10 N

c)

20 N

d)

14.14 N

e)

5.0 N

5.

If A = B = 10 N are two equal vectors, vector sum of A and B for angle between them is 60 degrees, is.............

a)

0 N

b)

17.3 N

c)

1.73 N

d)

14.14 N

e)

1.414 N

6.

If A = B = 10 N are two equal vectors, vector sum of A and B for angle between them is 90 degrees, is.............

a)

1.414 N

b)

1.73 N

c)

17.3 N

d)

14.14 N

e)

20 N

7.

If A = B = 10N are two equal vectors, vector sum of A and B for angle between them is 120 degrees, is.............

a)

0 N

b)

10 N

c)

20 N

d)

15 N

e)

14.14 N

8.

If A = B = 10 N are two equal vectors, vector sum of A and B for A and B anti parallel, is.............

a)

0 N

b)

10 N

c)

20 N

d)

15 N

e)

5 N

9.

What is the net force of three equal vectors 10 N each, acting at a point at the same time equally inclined to each other in the same plane?

a)

0 N

b)

30 N

c)

20 N

d)

10 N

e)

15 N

10.

TWO EQUAL VECTORS A AND B ACT AT 40 DEGREES TO EACH OTHER, WHAT IS THE ANGLE OF THE RESULTANT WITH VECTOR A

a)

0

b)

20

c)

10

d)

40

e)

ANY VALUE BETWEEN 0 TO 40 DEGREE

11.

If A = B = 10 N , the resultant force is..........

a)

10 N

b)

17.3 N

c)

1.73 N

d)

14.14 N

e)

1.414 N

12.

If F = 10N, analyse the given diagram and select the correct statement(s)

a)

$F_x=5\ N$

b)

$F_y=5N$

c)

$F_x=5\sqrt{3}N$

d)

$F_y=5\sqrt{3}N$

e)

$F_x=F_y=10N$

13.

If A = B , vector sum of A and B when they are 120 degrees

a)

A parallel to A

b)

B parallel to B

c)

A along the bisector of A & B

d)

2A along the bisector of A & B

14.

If A = B are two equal vectors, vector sum of A and B for angle between them is zero, is.............

a)

0

b)

A

c)

2A

d)

$\sqrt[]{2}$ A

e)

$\frac{A}{2\ }$

15.

If A = B are two equal vectors, vector sum of A and B for angle between them is 60 degrees, is.............

a)

0

b)

$\sqrt[]{3}$ A making 30 degrees with A & B

c)

$\sqrt[]{2}$ A

A making 30 degrees with A & B

d)

A

A making 30 degrees with A & B

e)

2A

A making 30 degrees with A & B

16.

If A = B are two equal vectors, vector sum of A and B for angle between them is 90 degrees, is.............

a)

$\sqrt[]{2}$ A

making 45 degrees with A & B

b)

$\sqrt[]{3}$ A

making 45 degrees with A & B

c)

A

making 45 degrees with A & B

d)

2A

making 45 degrees with A & B

e)

0

17.

If A and B are two vectors acting at a point with $\theta$ the angle between their directions, then the resultant vector, R is

a)

$R\ =A^2+B^2+2AB\ Cos\theta$

b)

$R\ =\ \sqrt[]{A^2+B^2+2AB\ Cos\theta}$

c)

$R\ =\sqrt[]{A^2+B^2-2AB\ Cos\theta}$

d)

$R\ =\ \sqrt[]{A^2+B^2+2AB\ Sin\theta}$

18.

If A & B are two equal vectors the resultant

a)

is always along the line bisecting the angle between A & B

b)

can be more inclined towards B

c)

can be more inclined towards A

d)

can be any angle between A & B

19.

$\overrightarrow{A\ }\ .\ \overrightarrow{B\ }=$

a)

is a vector with magnitude $ABCos\theta$ and direction normal to both A & B

b)

is a vector with magnitude $AB\ Sin\theta$ and direction normal to both A & B

c)

is a scalar with magnitude

$ABCos\theta$

d)

is a scalar with magnitude

$ABSin\theta$

20.

$\overrightarrow{A\ }\ \times\ \overrightarrow{B\ }=$

a)

is a vector with magnitude $ABCos\theta$ and direction normal to both A & B

b)

is a vector with magnitude $AB\ Sin\theta$ and direction normal to both A & B

c)

is a scalar with magnitude

$ABCos\theta$

d)

is a scalar with magnitude

$ABSin\theta$

21.

If $\overrightarrow{A\ }\times\overrightarrow{B\ }\ =\ \overrightarrow{C\ }$

a)

A is always normal to B

b)

C is always normal to A & B

c)

C can be at any angle to A & B

d)

A & B are always parallel to C

22.

$i\ \times j\ =\$

a)

k

b)

-k

c)

0

d)

j

e)

-j

23.

$j\times j\ =\ i\times i=k\times k=$

a)

1

b)

-k

c)

0

d)

j

e)

-j

24.

$j\ .\ j\ =\ i\ .\ i=k\ .\ k=$

a)

1

b)

-k

c)

0

d)

j

e)

-j

25.

$j\ .\ j\ =\ i\ .\ i=k\ .\ k=$

a)

1

b)

-k

c)

0

d)

j

e)

-j

26.

$i\ .\ j\ =\ j\ .\ i=k\ .\ i=$

a)

1

b)

-k

c)

0

d)

j

e)

-j

27.

Select the correct one

a)

i x j = k

j x k = i

k x i = j

b)

i x j = -k

j x k =- i

k x i = -j

c)

i x j = 0

j x k = 0

k x i = 0

d)

i x j = 1

j x k = 1

k x i = 1

28.

If A & B are two vectors in the same plane, then A X B will be

a)

parallel to A & B

b)

perpendicular to A & B directed out of the paper

c)

perpendicular to A & B directed out of the paper

d)

perpendicular to A & B directed into the paper

e)

perpendicular to A & B directed in or out of the paper

29.

If A & B are two vectors in the same plane, then A X B will be

a)

parallel to A & B

b)

perpendicular to A & B directed out of the paper

c)

perpendicular to A & B directed out of the paper

d)

perpendicular to A & B directed into the paper

e)

perpendicular to A & B directed in or out of the paper

30.

The diagonal of a square of side L is

a)

2L

b)

$\sqrt[]{2}\times L$

c)

$\frac{L}{\sqrt[]{2}}$

d)

$\sqrt[]{3}\times L$

e)

$\frac{L}{\sqrt[]{3}}$

31.

For a cube of side L, the distance from one corner to opposite corner is

a)

2L

b)

$\sqrt[]{2}\times L$

c)

$\frac{L}{\sqrt[]{2}}$

d)

$\sqrt[]{3}\times L$

e)

$\frac{L}{\sqrt[]{3}}$

32.

For a cube of side L, the distance from center to any one corner is

a)

$\frac{\sqrt[]{3}}{2}L$

b)

$\sqrt[]{2}\times L$

c)

$\frac{L}{\sqrt[]{2}}$

d)

$\sqrt[]{3}\times L$

e)

$\frac{L}{\sqrt[]{3}}$

33.

For a regular hexagon of side L, the distance from center to any one corner is

a)

$\frac{\sqrt[]{3}}{2}L$

b)

$\sqrt[]{2}\times L$

c)

L

d)

$\sqrt[]{3}\times L$

e)

$\frac{L}{\sqrt[]{3}}$

34.

The distance from any vertex to center of a square of side L is

a)

2L

b)

$\sqrt[]{2}\times L$

c)

$\frac{L}{\sqrt[]{2}}$

d)

$\sqrt[]{3}\times L$

e)

$\frac{L}{\sqrt[]{3}}$

35.

For an equilateral triangle of side L, altitude (distance from any one vertex to midpoint of opposite side) of the triangle is

a)

$\frac{L}{2}$

b)

$\frac{\sqrt[]{3}}{2}\times L$

c)

$\frac{L}{\sqrt[]{2}}$

d)

$\frac{\sqrt[]{3}}{4}\times L$

e)

$\frac{L}{\sqrt[]{3}}$

36.

For an equilateral triangle of side L, distance from any one vertex to the centroid of the triangle is

a)

$\frac{L}{2}$

b)

$\frac{\sqrt[]{3}}{2}\times L$

c)

$\frac{L}{\sqrt[]{2}}$

d)

$\frac{\sqrt[]{3}}{4}\times L$

e)

$\frac{L}{\sqrt[]{3}}$

37.

A vector E makes an angle $\theta$ with the X axis then

a)

$E_x=ECos\theta$

b)

$E_x=E\ Sin\theta$

c)

$E_y=E\ Cos\theta$

d)

$E_y=E\ Sin\theta$

38.

if a = j + 7 k and b = i + 4 j + 7 k find A x B

a)

-21i+7j-k

b)

23i+7j-k

c)

-2i+j-7k

d)

-3i+7j-k

39.

If P = 3 i + 2 j - 4 k and Q = -i + 3 j - 2 k, find cross product of P and Q

a)

i+8j+11k

b)

8i+10j+11k

c)

i+10j-1k

d)

-i+2j+3k

40.

How do you know if two vectors are orthogonal?

a)

Their sum is 0.

b)

The dot product is 1.

c)

The angle between them is 0°.

d)

The dot product is 0.

41.

Which of the below is False?

a)

i.i=1

b)

j.j=1

c)

k.k=1

d)

i.j=0

e)

j.k=1

42.

if a is perpendicular to b

a)

a.b=0

b)

a.b=ab

c)

a.b=1

d)

a.b=90

43.

if a and b are parallel

a)

a.b=ab

b)

a.b=0

c)

a.b=1

d)

a.b=90

44.

Find the magnitude of the vector -5i + 12j

a)

13

b)

10.91

c)

7

d)

17

45.

Calculate the dot product of the two vectors
v=1i+4j-3k and
u=1j- 2k

a)

10

b)

11

c)

3

d)

-3

46.

|A X B| =

a)

$ABSin\theta$

b)

$AB\ Cos\theta$

c)

$AB\ \tan\theta$

d)

$\frac{A}{B}\ Sin\theta$

47.

A . B =

a)

$ABSin\theta$

b)

$AB\ Cos\theta$

c)

$AB\ \tan\theta$

d)

$\frac{A}{B}\ Sin\theta$

48.

The dot product of F & S is

a)

$F_xS_{x\ }+\ F_yS_{y\ }+F_zS_z$

b)

$F_xF_{y\ }+S_xS_y+F_zS_z$

c)

$F_xS_x+F_xS_x+F_zS_z$

d)

$F_xS_x-F_yS_y-F_zS_z$

49.

A . (A X B) =

a)

$AABCos\theta$

b)

$AAB\ Sin\theta$

c)

$AB\ Sin\theta$

d)

$AB\ Cos\theta$

e)

zero

50.

B . (A X B) =

a)

$AABCos\theta$

b)

$AAB\ Sin\theta$

c)

$AB\ Sin\theta$

d)

$AB\ Cos\theta$

e)

zero

51.

identify the wrong statement from those given below

a)

A x B is a vector

b)

A . B is a vector

c)

A x B is a scalar

d)

A . B is a scalar

52.

Direction of A x B is

a)

perpendicular to A only

b)

perpendicular to B only

c)

perpendicular to A & B

d)

all options are incorrect

e)

parallel to A & B

53.

|A X B| = A . B , then

a)

angle between A & B is zero

b)

angle between A & B is 90 degrees

c)

angle between A & B is 45 degrees

d)

angle between A & B is 180 degrees

54.

A X B =

a)

a

b)

b

c)

c

d)

d

55.

Angle between A X B & B X A is

a)

zero degrees

b)

90 degrees

c)

180 degrees

d)

60 degrees

e)

None of the options are correct

56.

Identify the wrong option

a)

i . i = 1

b)

j . j =1

c)

k . k =1

d)

i x i =1

57.

identify the wrong option

a)

j x i = k

b)

k x i =j

c)

j x k =i

d)

i x k = -j

e)

k x j = - i

58.

$A\ =\left(5i\ +2j-4jk\right)\ \&\ B\ =\left(2i\ -6j+pk\right)$ .If A and B are perpendicular find value of p

a)

-1/2

b)

1/2

c)

2

d)

-2

59.

Example for a scalar quantity is

a)

work

b)

charge

c)

power

d)

torque

e)

force

60.

If A = 2 i + 3 j and B = i + 6 j , then direction of A x B is

a)

along +ve Z axis

b)

along Y axis

c)

along X axis

d)

In X Y plane

e)

along -ve Z axis

61.

Percentage change in X is =

a)

$\frac{\Delta x}{x_{initial}}\ \times100\%$

b)

$\left(\frac{x_{final}-x_{initial}}{x_{initial}}\right)\times100\%$

c)

$\left(\frac{x_{final}}{x_{initial}}-1\right)100\%$

d)

$\frac{\Delta x}{x_{final}}\ \times100\%$

62.

Mass of a proton is

a)

$9.1\ \times10^{-31}kg$

b)

$1.67\ \times10^{-31}kg$

c)

$1.67\times10^{-27}kg$

d)

$1.6\ \times10^{-19}kg$

63.

Mass of an electron is

a)

$9.1\ \times10^{-31}kg$

b)

$1.67\ \times10^{-31}kg$

c)

$1.67\times10^{-27}kg$

d)

$1.6\ \times10^{-19}kg$

64.

Charge of an electron (magnitude) is

a)

$9.1\ \times10^{-31}C$

b)

$1.67\ \times10^{-31}C$

c)

$1.67\times10^{-27}C$

d)

$1.6\ \times10^{-19}C$

65.

Charge of an proton (magnitude) is

a)

$9.1\ \times10^{-31}C$

b)

$1.67\ \times10^{-31}C$

c)

$1.67\times10^{-27}C$

d)

$1.6\ \times10^{-19}C$

66.

Select all correct statements

a)

mass of alpha particle = 2 x mass of proton

b)

mass of alpha particle = 4 x mass of proton

c)

charge of alpha particle = 2 x charge of proton

d)

mass of proton= 4 x mass of alpha particle

e)

charge of alpha particle = 4 x charge of proton

67.

Select all correct statements

a)

proton is positively charged

b)

neutron is negatively charged

c)

alpha particle is positively charged

d)

electron is negatively charged

68.

Mass of a proton is

a)

1836 x mass of electron

b)

1836 x mass of alpha particle

c)

mass of electron/1836

d)

mass of alpha /1836

69.

Select the correct option(s)

a)

An electron will move towards positive charge

b)

An alpha particle will move towards negative charge

c)

An proton will move towards positive charge

d)

An neutron will move towards positive charge

70.

The magnitude of cross product of p and E at a particular angle is half the maximum value of the cross product p and E, the angle in degrees is

a)

45

b)

30

c)

60

d)

90

e)

120

71.

Time period ( T )

a)

$T\ =\frac{1}{frequency}$

b)

$T\ =\ \frac{2\pi\ r}{speed}$

c)

$T\ =\ \frac{2\pi}{\omega}$

d)

$T\ =\frac{\omega}{2\pi}$

e)

$T\ =\frac{\lambda}{speed}$

72.

Angular speed ( $\omega$ )

a)

$\omega=\frac{\theta}{t}$

b)

$\omega=\frac{2\pi}{T}$

c)

$\omega=2\pi\ \times\ frequency$

d)

$\omega=\frac{speed}{radius}$

e)

$\omega=\frac{radius}{speed}$

73.

centripetal force =

a)

$\frac{v^2}{r}$

b)

$m\ \frac{v^2}{r}$

c)

$mr\omega^2$

d)

$mr^2\omega$

74.

centripetal acceleration =

a)

$\frac{v^2}{r}$

b)

$m\ \frac{v^2}{r}$

c)

$r\omega^2$

d)

$mr^2\omega$

75.

Select correct option(s)

a)

milli (m) = $10^{-3}$

micro = $10^{-6}$

nano = $10^{-9}$

pico = $10^{-12}$

b)

milli (m) = $10^{-3}$

micro = $10^{-6}$

nano = $10^{-9}$

pico = $10^{-15}$

c)

milli (m) = $10^3$

micro = $10^6$

nano = $10^9$

pico = $10^{12}$

d)

milli (m) = $10^3$

micro = $10^6$

nano = $10^9$

pico = $10^{15}$

76.

120 rpm =

a)

$4\pi\ ms^{-2}$

b)

$4\pi\ rad\ \times\ s^{-1}$

c)

$4\ rad\ \times\ s^{-1}$

d)

$4\ m\ s^{-2}$

77.

A wire of length L is bent to form a single circular coil, then (select all correct)

a)

radius = $\frac{L}{2\pi}$

b)

diameter = $\frac{L}{\pi}$

c)

Area = $\frac{L^2}{4\pi}$

d)

circumference = L

78.

A wire of length L is bent to form a single square coil, then (select all correct)

a)

one side = $\frac{L}{4}$

b)

one side = $\frac{L}{\pi}$

c)

Area = $\frac{L^2}{16}$

d)

Area = $\frac{L}{16}$

79.

A wire of length L is used to construct a circular coil, square, rectangle and a triangle. The shape enclosing maximum area is

a)

square

b)

circle

c)

rectangle

d)

triangle

80.

A wire of length L is used to construct a circle, square and an equilateral triangle, then

a)

Area of square = $\frac{L^2}{16}$

b)

Area of circle = $\frac{L^2}{4\pi}$

c)

Area of equilateral triangle = $\frac{L^2}{12\sqrt[]{3}}$

d)

Area of equilateral triangle = $\frac{L^2}{36\sqrt[]{3}}$

81.

Area of an equilateral triangle with side L is

a)

A = $\frac{L^2}{2}$

b)

A = $\frac{\sqrt[]{3}}{4}L^2$

c)

A = $\frac{\sqrt[]{3}}{2}L^2$

d)

A = $\frac{L^2}{2\sqrt[]{3}}$

82.

A particle of mass m moves in a circular path of radius r, then work done by the centripetal force is

a)

W = 0, as force and displacement are parallel

b)

Zero only for one complete circular path and non zero for partial circular paths

c)

W = $\frac{mv^2}{r}\times2\pi r$

d)

W = 0, as force and displacement are perpendicular

83.

Select all correct options

a)

sin (90 + θ) = cosθ

b)

Sin(90 - θ) = cosθ

c)

cos(-θ) = cosθ

d)

sin (-θ) = -sinθ

84.

Select all correct options

a)

$Cos^2\theta\ =\ \frac{1+\cos2\theta}{2}$

b)

Sin2θ = 2sinθ cosθ

c)

Sinθ = $Sin\left(\theta\pm2\pi N\right)$

N =0,1,2,3,....

d)

Cosϑ = $Cos\left(\theta\pm2\pi N\right)$

N =0,1,2,3,....

85.

For one complete cycle (t = 0 to t = T) or (θ = 0 to θ = 2π)

a)

Average value of a sinθ = 0

b)

Average value of a cosθ = 0

c)

Average value of a sinθ = 1

d)

Average value of a cosθ = 1

86.

Select all correct options

a)

Slope of a graph = $\frac{\Delta y}{\Delta x}$

b)

Slope of a graph = tanθ, where θ is the angle between the graph and +ve X axis

c)

Slope of a graph = tanθ, where θ is the angle between the graph and +ve Y axis

d)

Area under any graph = a physical quantity which is the product of the quantities on X and Y axes

87.

Select all correct options

a)

$\frac{1}{\sqrt[]{2}}=0.71$

b)

$\pi^2=10$

c)

$\sqrt[]{2}=\ 1.41$

d)

$\sqrt[]{3}=\ 1.73$

e)

$\sqrt[]{5}=2.24$

88.

Power =

a)

$P\ =\ \frac{dW}{dt}$

b)

P = F . v

c)

P =

$F_xv_x+F_yv_y+F_zv_z$

d)

Power is a vector quantity

BASICS FOR GRADE XII

Total questions: 88

Worksheet time: 2hrs 34mins

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