### JEE Mains Previous Years Questions with Solutions

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1

### AIEEE 2010

The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 $\times$ 10–3 are
A
5, 1, 2
B
5, 1, 5
C
5, 5, 2
D
4, 4, 2

## Explanation

23.023 has 5 significant figures.

0.0003 has 1 significant figure.

2.1 $\times$ 10–3 has 2 significant figures.
2

### AIEEE 2008

A body of mass m = 3.513 kg is moving along the x-axis with a speed of 5.00 ms−1. The magnitude of its momentum is recorded as
A
17.6 kg ms-1
B
17.565 kg ms-1
C
17.56 kg ms-1
D
17.57 kg ms-1

## Explanation

Momentum, p = m $\times$ v

= 3.513 $\times$ 5.00 = 17.565 kg m/s

= 17.6 kg m/s

Here number of significant digits in m is 4 and in v is 3, so, p must have minimum (which is 3) significant digit.
3

### AIEEE 2008

The dimension of magnetic field in M, L, T and C (coulomb) is given as
A
MLT-1C-1
B
MT2C-2
C
MT-1C-1
D
MT-2C-1

## Explanation

We know that,
Lorentz force $\left| {\overrightarrow F } \right| = \left| {q\overrightarrow v \times \overrightarrow B } \right|$

$\therefore [B]$ = ${[F] \over {[q][v]}}$ = ${[{ML{T^{ - 2}}]} \over {[C] \times [L{T^{ - 1}}]}}$ = [$M{T^{ - 1}}{C^{ - 1}}$]
4

### AIEEE 2005

Out of the following pair, which one does NOT have identical dimensions is
A
angular momentum and Planck's constant
B
impulse and momentum
C
moment of inertia and moment of a force
D
work and torque

## Explanation

Moment of inertia, I = Mr2

$\therefore$ [I] = [ML2]

Moment of force, $\overrightarrow \tau = \overrightarrow r \times \overrightarrow F$

$\therefore$ $[\overrightarrow \tau ]$ = $[L][ML{T^{ - 2}}]$ = $[ML^{ 2}{T^{ - 2}}]$