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IIT-JEE (ADV)
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IIT-JEE (ADV)
Download app for all tests and notes
Click here for NEET/IIT-JEE and other competitive exam books
Q1. A highly
accurate determination of g has a quoted error of 6 parts in 109. If the dependence of
g on geographical latitude at sea level is given by 
where φ is the latitude and β is a dimensionless
constant with a value of 0.0055, estimate the northward displacement near
latitude which gives a change
in g equal to the quoted error (radius of earth =R=6.4 X106)
where φ is the latitude and β is a dimensionless
constant with a value of 0.0055, estimate the northward displacement near
latitude which gives a change
in g equal to the quoted error (radius of earth =R=6.4 X106)
(a) 6m
(b) 9 m
(c) 7 m
(d) 12m
Q2. Backlash error may occur in which of the
following instruments?
((A)
Slide calipers and screw gauge
((B)
Spherometer and screw gauge
((C)
Slide cappliers and spherometer
((D)
Slide calipers, screw gauge and spherometer
Q3. Choose the correct statements:
(A)
The least count of vernier calipers is
the length of the smallest unit on the main scale
(B) The
least count of vernier calipers is the length of the smallest unit on the
vernier scale
(C) The
vernier constant is the least count of the vernier calipers
(D) Vernier
calipers can’t measure the depth of a cylinder
Q4. The time period of oscillation of simple
pendulum is given by
; The length of the pendulum is measured as l = 10±0.1
; The length of the pendulum is measured as l = 10±0.1
cm and time period as
T = 0.5±0.02s. The percentage
error in measuring ‘g’ is
((A)
9
(B) 5
(C) 8
(D) 7
Q5. Which of the following
quantities is having maximum number of significant figure.
(A) 1.124 x 10-3 v
(B) 9.1 x 104km
(C) 1.0080 v
(D) 0.0145 m
Q6. A resistance R of 100 Ω is to be measured by
using an ammeter and voltmeter. If the
readings of ammeter and voltmeter are 12 mA and 1 V respectively. Which of the following conclusion is
incorrect
(A)
sured value of R is 83
(B) Percentage
error in the measurement of R is 17%
(C) Resistance
of voltmeter is 200
(D) Resistance
of voltmeter is 500 M
Q7. In a vernier calliperse, one main scale
division is x cm and n divisions of the vernier scale coincides with (n-1)
divisions of the main scale. The least count (in cm) of the calliperse is
((A)
((B)
((C) x/n
((D) 
Q8. The
percentage error in calculation of specific resistance, 
where
where
r = radius of wire 0.26 ±0.02 cm l = length of wire156 ±0.1 cm
R = resistance of wire 64 ± 2 ohm will be
((A) 18.57
((B) 10.02
((C) 5.38
((D) 6.42
Q9. The significant digits in 200.40 are
(A) 2
(B) 3
(C) 4
(D) 5
Q10. Backlash
error is present in
(A) Vernier callipers
(B) Screw-Gauge and Vernier callipers
(C) Screw – Gauge
(D) Vernier calipers and Spherometer
Q11.A parallel plate capacitor of capacitance is charged
by a battery of emf 100 V. The battery is now disconnected and temperature of
the plates is equal to atmospheric temperature. The plates are now connected by
a thin wire of negligible heat capacity. Assume 50% of their stored energy
increases their temperature till the capacitor gets completely discharged and
energy equally distributes over the plates. If thermal capacity of each plate
is 0.5 JK–1 and coefficient of linear expansion is ,
percentage increase in the volume of the plates is
(a) 0.001%
(b) 0.002%
(c) 0.003%
(d) 0.004%
Q12. In Vernier calipers, m divisions of main scale coincide
with (m + 1) divisions of vernier scale. If each division of main scale is d
units, the least count of the instrument is
((A)
((B) 
((C)
d/m
((D) 
Q13.
|
in
meter- bridge experiment, Unknown resistance X is given as
 where L is the distance of null point from one end and R is known resistance in other gap. The error in the measurement of x is minimum, when value of L is |
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Q14.
|
When
a wave traverses a medium, the displacement of a particle located at at x time t is given by y= a sin(bt-cx) where a,b and c are constants of the
wave, the dimensions of b/c are the same as
those of
((A) Wave length
((B) Wave velocity
((C) Wave amplitude
((D) Wave frequency
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Q15.
|
If the time
period t of a drop of liquid
of density d radius r, vibrating under surface tension S is given by
 and if a=1,c=-1 then b is
((A) 1
((B) 2
((C) 3
((D) 4
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Q16.
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E,M,J and G denote energy, mass, angular momentum and gravitational
constant respectively. The dimensions of
 are that of
((A) Angle
((B) Length
((C) Mass
((D) Time
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Q17.
|
In
planetary motion the areal velocity of position vector of a planet is
intuitionally felt that it may depend on angular velocity ω and the distance of the planet from the sun . The correct relation is
((A)
((B)
((C)
((D)
 |
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Q18.
|
A
physical quantity P is given by
 . The quantity which brings in the maximum percentage error
in P is, (Fractional error in A,B,C and D are equal)
((A) A
((B) B
((C) C
((D) D |
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Q19.
|
The rate of volume flow of water in
an aquifer (Porous rock through which water flows) is given by
 (where A=area of
cross section, H=Difference in height of the ends, L=horizontal length of
aquifer). The quantity K is called hydraulic conductivity of the aquifer. The
dimensional formula of K is
((A) [L3T-1]
((B) [LT-1]
((C) [LT-2]
((D)[L2T-2]
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Q20.
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The largest mass(m) that can be moved by a flowing river depends
on velocity(v), density ρ of river water and acceleration
due to gravity(g). The correct relation is
((A)
((B)
((C)
((D)
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Q21 a formula is given by
where P = pressure
q =
Temperature
t = Time
‘a’ and ‘b’ are constants. Dimensional
formula of ‘b’ is same as
(A) Formula
(B) Linear momentum
(C) Angular
momentum (D) Torque.
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