### JEE Mains Previous Years Questions with Solutions

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1

### AIEEE 2012

Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is
A
6 %
B
zero
C
1 %
D
3 %

## Explanation

We know R = ${V \over I}$

$\therefore$ ${{\Delta R} \over R} = {{\Delta V} \over V} + {{\Delta I} \over I}$

Percentage error in R =

${{\Delta R} \over R} \times 100 = {{\Delta V} \over V} \times 100 + {{\Delta I} \over I} \times 100$

$\therefore$ ${{\Delta R} \over R} \times 100 =$ 3% + 3 % = 6%
2

### 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.
3

### 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.
4

### 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 $\left| {\overrightarrow F } \right| = \left| {q\overrightarrow v \times \overrightarrow B } \right|$

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