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JEE Main Units & Measurements Practice Questions With Solutions

Updated By Diksha Sharma on 07 Jan, 2025 21:16

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JEE Main Physics Units & Measurements Practice Questions

Chemistry Mathematics

Question 1.

The de-Broglie wavelength associated with a particle of mass $m$ and energy $E$ is $h / \sqrt{2 m E}$ . The dimensional formula for Planck's constant is :

[M^{2} L^{2} T^{- 2}]

[{ML}^{- 1} T^{- 2}]

[{ML}^{2} T^{- 1}]

[{MLT}^{- 2}]

Question 2.

The dimensional formula of latent heat is :

[M^{0} {LT}^{- 2}]

[{MLT}^{- 2}]

[M^{0} L^{2} T^{- 2}]

[{ML}^{2} T^{- 2}]

Question 3.

One main scale division of a vernier caliper is equal to $m$ units. If $n^{th}$ division of main scale coincides with $(n + 1)^{th}$ division of vernier scale, the least count of the vernier caliper is :

\frac{1}{(n + 1)}

\frac{m}{(n + 1)}

\frac{n}{(n + 1)}

\frac{m}{n (n + 1)}

Question 4.

If $ϵ_{o}$ is the permittivity of free space and $E$ is the electric field, then $ϵ_{o} E^{2}$ has the dimensions :

[M L^{- 1} T^{- 2}]

[M L^{2} T^{- 2}]

[M^{0} L^{- 2} TA]

[M^{- 1} L^{- 3} T^{4} A^{2}]

Question 5.

There are 100 divisions on the circular scale of a screw gauge of pitch $1 mm$ . With no measuring quantity in between the jaws, the zero of the circular scale lies 5 divisions below the reference line. The diameter of a wire is then measured using this screw gauge. It is found that 4 linear scale divisions are clearly visible while 60 divisions on circular scale coincide with the reference line. The diameter of the wire is :

4.65 mm

4.60 mm

4.55 mm

3.35 mm

Question 6.

Least count of a vernier caliper is $\frac{1}{20 N} cm$ . The value of one division on the main scale is $1 mm$ . Then the number of divisions of main scale that coincide with $N$ divisions of vernier scale is :

(\frac{2 N - 1}{2 N})

(\frac{2 N - 1}{20 N})

(2 N - 1)

(\frac{2 N - 1}{2})

Question 7.

In an expression $a \times 10^{b}$ :

a

is order of magnitude for

b \leq 5

b

is order of magnitude for

a \leq 5

b

is order of magnitude for

a \geq 5

b

is order of magnitude for

5 < a \leq 10

Question 8.

The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to $1 mm$ . The main scale reading is $2 cm$ and second division of vernier scale coincides with a division on main scale. If mass of the sphere is 8.635 $g$ , the density of the sphere is:

2.2 g / {cm}^{3}

2.0 g / {cm}^{3}

1.7 g / {cm}^{3}

2.5 g / {cm}^{3}

Question 9.

In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its $4^{th}$ division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 main scale divisions and zero error in the instrument is $0.04 mm$ then how many main scale divisions are there in $1 cm$ ?

Question 10.

In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division $= 49 MSD; 20$ divisions on main scale in each $cm$

For mark on paper

$MSR = 8.45 cm, VC = 26$

For mark on paper seen through slab

$MSR = 7.12 cm, VC = 41$

For powder particle on the top surface of the glass slab

$MSR = 4.05 cm, VC = 1$

(MSR $=$ Main Scale Reading, VC = Vernier Coincidence)

Refractive index of the glass slab is :

1.52

1.35

1.24

1.42

Question 1.

To find the spring constant $(k)$ of a spring experimentally, a student commits $2 %$ positive error in the measurement of time and $1 %$ negative error in measurement of mass. The percentage error in determining value of $k$ is :

Question 2.

Match List I with List II

	LIST I		LIST II
A.	Torque	I.	$[M^{1} L^{1} T^{- 2} A^{- 2}]$
B.	Magnetic field	II.	$[L^{2} A^{1}]$
C.	Magnetic moment	III.	$[M^{1} T^{- 2} A^{- 1}]$
D.	Permeability of free space	IV.	$[M^{1} L^{2} T^{- 2}]$

Choose the correct answer from the options given below:

A-I, B-III, C-II, D-IV

A-IV, B-II, C-III, D-I

A-III, B-I, C-II, D-IV

A-IV, B-III, C-II, D-I

Question 3.

While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is $1 mm$ and circular scale reading is equal to 42 divisions. Pitch of screw gauge is $1 mm$ and it has 100 divisions on circular scale. The diameter of the wire is $\frac{x}{50} mm$ . The value of $x$ is :

142

Question 4.

What is the dimensional formula of $a b^{- 1}$ in the equation $(P + \frac{a}{V^{2}}) (V - b) = RT$ , where letters have their usual meaning.

[M^{6} L^{7} T^{4}]

[M^{- 1} L^{5} T^{3}]

[M^{0} L^{3} T^{- 2}]

[{ML}^{2} T^{- 2}]

Question 5.

A vernier callipers has 20 divisions on the vernier scale, which coincides with $19^{th}$ division on the main scale. The least count of the instrument is $0.1 mm$ . One main scale division is equal to ________ mm.

0.5

Question 6.

Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as $4.62 s, 4.632 s, 4.6 s$ and $4.64 s$ . The arithmetic mean of these readings in correct significant figure is :

5 s

4.6 s

4.62 s

4.623 s

Question 7.

Applying the principle of homogeneity of dimensions, determine which one is correct,where $T$ is time period, $G$ is gravitational constant, $M$ is mass, $r$ is radius of orbit.

T^{2} = \frac{4 π^{2} r}{G M^{2}}

T^{2} = 4 π^{2} r^{3}

T^{2} = \frac{4 π^{2} r^{3}}{G M}

T^{2} = \frac{4 π^{2} r^{2}}{G M}

Question 8.

The equation of stationary wave is :

$y = 2 a \sin (\frac{2 π nt}{λ}) \cos (\frac{2 π x}{λ}) .$

Which of the following is NOT correct :

The dimensions of

nt

is [L]

The dimensions of

n

[{LT}^{- 1}]

The dimensions of

x

is [L]

The dimensions of

n / λ

is [T]

Question 9.

Match List - I with List - II.

List I (Number)	List II (Significant figure)
(A) 1001	(I) 3
(B) 010.1	(II) 4
(C) 100.100	(III) 5
(D) 0.0010010	(IV) 6

Choose the correct answer from the options given below :

(A)-(II), (B)-(I), (C)-(IV), (D)-(III)

(A)-(IV), (B)-(III), (C)-(I), (D)-(II)

(A)-(I), (B)-(II), (C)-(III), (D)-(IV)

(A)-(III), (B)-(IV), (C)-(II), (D)-(I)

Question 10.

10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is :

\frac{5}{11}

\frac{10}{11}

\frac{50}{11}

\frac{1}{2}

JEE Main Units & Measurements Practice Questions With Solutions

JEE Main Physics Units & Measurements Practice Questions

Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.

Question 1.

Question 2.

Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.

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