1

IIT-JEE 2005 Screening

MCQ (Single Correct Answer)
Which of the following set have different dimensions?
A
Pressure, Young's modulus, Stress
B
EMF, Potential difference, Electric potential
C
Heat, Work done, Energy
D
Dipole moment, Electric flux, Electric field
2

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)
A wire of length $$l = 6 \pm 0.06$$ cm and $$r = 0.5 \pm 0.005$$ cm and mass $$m = 0.3 \pm 0.003$$ gm. Maximum percentage error in density is
A
4
B
2
C
1
D
6.8
3

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)
Pressure depends on distance as, $$P = {\alpha \over \beta }\exp \left( { - {{\alpha z} \over {k\theta }}} \right)$$, where $$\alpha $$, $$\beta $$ are constants, z in distance, k is Boltzman's constant and $$\theta $$ is temperature. The dimention of $$\beta $$ are
A
[M0L0T0]
B
[M-1L-1T-1]
C
[M0L2T0]
D
[M-1L1T2]

Explanation

The given expression is

$$P = {\alpha \over \beta }\exp \left( { - {{\alpha z} \over {k\theta }}} \right)$$

Now,

$$[z] = [{L^1}]$$

$$[\theta ] = [{K^1}]$$

$$[k] = [{M^1}{L^2}{T^{ - 2}}{K^{ - 1}}]$$

Since the terms which are raised to power in an exponential function are dimensionless, we get

$$[\alpha] = \left[ {{{k\theta } \over z}} \right] = [{M^1}{L^1}{T^{ - 2}}]$$

Also, $$[P] =$$ $$\left[ {{\alpha \over \beta }} \right]$$

$$ \Rightarrow $$ $$\left[ \beta \right] = \left[ {{\alpha \over P}} \right]$$

$$ \Rightarrow $$ $$\left[ \beta \right] = \left[ {{{{M^1}{L^1}{T^{ - 2}}} \over {M{L^{ - 1}}{T^{ - 2}}}}} \right]$$ = $$[{M^0}{L^2}{T^0}]$$

Answer (C)
4

IIT-JEE 2003 Screening

MCQ (Single Correct Answer)

A cube has a side of length 1.2 ✕ 10-2 m. Calculate its volume.

A
1.7 ✕ 10-6 m3
B
1.73 ✕ 10-6 m3
C
1.70 ✕ 10-6 m3
D
1.732 ✕ 10-6 m3

Explanation

We have

V = l3 = (1.2 $$\times$$ 10$$-$$2)3 = 1.728 $$\times$$ 10$$-$$6 m3

Since l has two significant figures, V should also have two significant figures; hence,

V = 1.7 $$\times$$ 10$$-$$6 m3

Answer (A)

Joint Entrance Examination

JEE Advanced JEE Main

Graduate Aptitude Test in Engineering

GATE CSE GATE EE GATE ECE GATE ME GATE CE GATE PI GATE IN

Medical

NEET

CBSE

Class 12