Free Printable units and measurement,vectors,kinematics for iit jee

1.

In the formula X = 3YZ², X and Z have dimensions of capacitance and magnetic induction respectively. What are the dimensions of Y in MKSQ system ?

a)

$M^{-3}L^{-1}T^3Q^{\text{4}}$

b)

$M^{-3}L^{-2}T^4Q^{\text{4}}$

c)

$M^{-2}L^{-2}T^4Q^{\text{4}}$

d)

$M^{-3}L^{-2}T^3Q^{\text{4}}$

2.

The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. If the resultant is at 90° with the force of smaller magnitude, what are the, magnitudes of forces

a)

12, 5

b)

14, 4

c)

5, 13

d)

10, 8

3.

A screw gauge gives the following readings when used to measure the diameter of a wire.

Main scale reading : 0 mm

Circular scale reading : 52 divisions

given that 1 mm on main scale corresponds to 100 divisions of the circular scale .find the diameter of the wire

a)

0.026 cm

b)

0.005 cm

c)

0.52 cm

d)

.0.052 cm

4.

The period of oscillation of a simple pendulum is given by $T=2\pi\ \sqrt{\frac{l}{g}}$ where l is about 100 cm and is known to have 1mm accuracy. The period is about 2s. The time of 100 oscillations is measured by a stop watch of least count 0.1 s. The percentage error in g is

a)

0.1%

b)

2%

c)

0.2%

d)

8%

5.

The percentage errors in the measurement of mass and speed are 2% and 3% respectively. How much will be the maximum error in the estimation of the kinetic energy obtained by measuring mass and speed

a)

11 %

b)

8%

c)

5%

d)

1%

6.

The random error in the arithmetic mean of 100 observations is x; then random error in the arithmetic mean of 400 observations would be

a)

4x

b)

$\frac{1}{4}x$

c)

2x

d)

$\frac{1}{2}x$

7.

Which of the following is the dimensionless quantity:

a)

force of surface tension

b)

strain

c)

stress

d)

co-efficient of viscosity

8.

Dimensions of velocity gradient are same as that of

a)

time period

b)

frequency

c)

angular acceleration

d)

acceleration

9.

Suppose the position of an object moving along the x axis varies in time according to the expression x = $ct^3$ with c a constant.Find an expression for the x-component of the velocity as a function of time.

a)

$3ct^2$

b)

$6ct^2$

c)

$9ct^2$

d)

$12ct^2$

10.

A stone is projected from the ground with a velocity of 50 m/s, at an angle of 30°. It crosses the wall after 3 sec. How far beyond the wall the stone will strike the ground(in m)? (g=10 $ms^{-2}$ )

a)

$125\sqrt{3}$

b)

$50\sqrt{2}$

c)

$50\sqrt{3}$

d)

$70$

11.

If the vectors ai + j + k, i + bj + k and i + j + ck (a ≠ b ≠ c ≠ 1) are coplanar, then the value of [1] / [1 − a] + [1] / [1 − b] + [1] / [1 − c] = (a) .

(note that i, j,k are the unit vectors in x,y and z directions)

12.

If b and c are any two non-collinear unit vectors and a is any vector, then (a . b) b + (a . c) c + [a . (b × c) / |b × c|] (b × c) = (a) .

13.

A body is freely falling under the action of gravity. It covers half the total distance in the last second of its fall. If it falls for n second, then value of n is

a)

$2$

b)

$2+\sqrt{2}$

c)

$3$

d)

$2-\sqrt{2}$

14.

Let a = 2i + j − 2k and b = i + j. If c is a vector such that a . c = |c|, |c − a| = 2√2 and the angle between (a × b) and c is 30 degrees, then |(a × b) × c| = (a) .

(note that i,j,k are unit vectors in x,y,z directions)

Answer in decimal.

15.

The greatest possible acceleration or deceleration a train may have is a and its maximum speed is v. Find the maximum time in which the train can get from one station to the next if the total distance is s.

a)

a

b)

b

c)

c

d)

d

16.

a. [(b + c) × (a + b + c)] is equal to (a) .

a,b and c are vectors.

17.

A particle is set in motion at t=0 such that velocity varies as v=v0(1−t/2) where v0 is a positive constant. Find the distance, displacement covered by the particle in first 3 sec.

a)

a

b)

b

c)

c

d)

d

18.

Let a, b and c be vectors with magnitudes 3, 4 and 5 respectively and a + b + c = 0, then the values of a . b + b . c + c . a is (a) .

19.

The magnitudes of mutually perpendicular forces a, b and c are 2, 10 and 11, respectively. Then the magnitude of its resultant is

a)

13

b)

14

c)

15

d)

16

20.

a)

4

b)

9

c)

8

d)

6

21.

If k = sin (π/18) sin (5π/18) sin (7π/18), then what is the numerical value of k?

a)

1/2

b)

1/4

c)

1/8

d)

1/16

22.

Differentiate:

$y=\frac{1}{\log_{ }\cos\ x}$

a)

$\frac{\tan x}{\log\ x\ \cos\ x}$

b)

$\left[\frac{\left(\tan\ x\right)}{\left(\log\ \cos\ x\right)^{ }}\right]^2$

c)

$\frac{\left(\sec\ x\right)}{\left(\log\ \cos\ x\right)^2}$

d)

$\frac{\tan\ x}{\left(\log\ \cos\ x\right)^2}$

23.

Integrate:

\int\left[\frac{\left(\sin^8x-\cos^8x\right)}{1-2\sin^2x\cos^2x}\right]dx

a)

$-\frac{\sin2x}{2}$

b)

$-\frac{\sin2x}{2}+C$

c)

$\frac{\sin2x}{2}+C$

d)

$-\frac{\sin x}{2}+C$

24.

What is the value of the function $\left(x-1\right)\left(x-2\right)^2$ at its maxima?

a)

1/27

b)

2/27

c)

3/27

d)

4/27

25.

A man crosses a river in a boat. If he crosses the river in minimum time he takes 10 min with a drift of 120 m. If he crosses the river taking shortest path, he takes 12.5 min.

The width of river is

a)

300 m

b)

200 m

c)

150 m

d)

250 m

units and measurement,vectors,kinematics for iit jee

Total questions: 25

Worksheet time: 50mins

Similar Resources on Wayground