Units, Dimensions & Errors · JEE Main previous year questions

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2020 16 questions

Q272020 · 6 Sept 2020 · Shift 1
A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of 0.5mm is noticed on the pitch scale. The nature of zero error involved and the least count of the screw gauge, are respectively :
1. A.Positive, $0.1 mm$
2. B.Positive, $0.1 μ m$
3. C.Positive, $10 μ m$
4. D.Negative, $2 μ m$
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Answer: C
Q342020 · 6 Sept 2020 · Shift 1
A clock has a continuously moving second's hand of $0.1 m$ length. The average acceleration of the tip of the hand (in units of $m s^{- 2}$ ) is of the order of :
1. A. $1 0^{- 3}$
2. B. $1 0^{- 1}$
3. C. $1 0^{- 2}$
4. D. $1 0^{- 4}$
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Answer: A
Q482020 · 6 Sept 2020 · Shift 1· Numerical answer
The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is $(\frac{x}{100}) %$ . If the relative errors in measuring the mass and the diameter are $6.0%$ and $1.5%$ respectively, the value of x is ______ .
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Answer: 1050
Q432020 · 6 Sept 2020 · Shift 2
A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings $5.50 mm$ , $5.55 mm$ , $5.45 mm$ , $5.65 mm$ . The average of these four readings is $5.5375 mm$ and the standard deviation of the data is $0.07395 mm$ . The average diameter of the pencil should therefore be recorded as :
1. A. $(5.54 \pm 0.07) mm$
2. B. $(5.5375 \pm 0.0740) mm$
3. C. $(5.5375 \pm 0.0739) mm$
4. D. $(5.538 \pm 0.074) mm$
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Answer: A
Q262020 · 3 Sept 2020 · Shift 1
Using screw gauge of pitch 0.1 cm and 50 divisions on its circular scale, the thickness of an object is measured. It should correctly be recorded as
1. A.2.123 cm
2. B.2.124 cm
3. C.2.125 cm
4. D.2.121 cm
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Answer: B
Q302020 · 3 Sept 2020 · Shift 2
Amount of solar energy received on the earth's surface per unit area per unit time is defined as solar constant. Dimension of solar constant is :
1. A. $ML T^{- 2}$
2. B. $M L^{0} T^{- 3}$
3. C. $M^{2} L^{0} T^{- 1}$
4. D. $M L^{2} T^{- 2}$
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Answer: B
Q342020 · 2 Sept 2020 · Shift 1
The least count of the main scale of a vernier callipers is 1 mm. Its vernier scale is divided into 10 divisions and coincide with 9 divisions of the main scale. When jaws are touching each other, the $7^{th}$ division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale between 3.1 cm and 3.2 cm and $4^{th}$ VSD coincides with a main scale division. The length of the cylinder is : (VSD is vernier scale division)
1. A.3.21 cm
2. B.2.99 cm
3. C.3.07 cm
4. D.3.2 cm
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Answer: C
Q352020 · 2 Sept 2020 · Shift 1
If speed V, area A and force F are chosen as fundamental units, then the dimension of Young’s modulus will be
1. A. $F A^{- 1} V^{0}$
2. B. $F A^{2} V^{- 1}$
3. C. $F A^{2} V^{- 2}$
4. D. $F A^{2} V^{- 3}$
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Answer: A
Q382020 · 2 Sept 2020 · Shift 1
A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RT) of the mixture is :
1. A.11
2. B.20
3. C.15
4. D.13
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Answer: C
Q312020 · 2 Sept 2020 · Shift 2
If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is
1. A. $[P^{2} A T^{- 2}]$
2. B. $[P^{\frac{1}{2}} A T^{- 1}]$
3. C. $[P A^{\frac{1}{2}} T^{- 1}]$
4. D. $[P A^{- 1} T^{- 2}]$
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Answer: C
Q262020 · 9 Jan 2020 · Shift 1
A quantity $f$ is given by $f = \frac{h c ^{5}}{G}$ where $c$ is speed of light, $G$ universal gravitational constant and $h$ is the Planck's constant. Dimension of $f$ is that of :
1. A.Energy
2. B.Momentum
3. C.Area
4. D.Volume
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Answer: A
Q342020 · 9 Jan 2020 · Shift 1
If the screw on a screw-gauge is given six rotations, it moves by 3 mm on the main scale. If there are 50 divisions on the circular scale the least count of the screw gauge is :
1. A.0.001 mm
2. B.0.01 cm
3. C.0.02 mm
4. D.0.001 cm
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Answer: D
Q482020 · 9 Jan 2020 · Shift 1· Numerical answer
The distance x covered by a particle in one dimensional motion varies with time t as $x^{2} = a t^{2} + 2 b t + c$ . If the acceleration of the particle depends on x as $x^{- n}$ , where n is an integer, the value of n is _______.
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Answer: 3
Q312020 · 8 Jan 2020 · Shift 1
The dimension of stopping potential $V_{0}$ in photoelectric effect in units of Planck's constant 'h', speed of light 'c' and Gravitational constant 'G' and ampere A is :
1. A. $h^{1/3} G^{2/3} c^{1/3} A^{- 1}$
2. B. $h^{0} c^{5} G^{- 1} A^{- 1}$
3. C. $h^{2/3} c^{5/3} G^{1/3} A^{- 1}$
4. D. $h^{2} G^{3/2} c^{1/3} A^{- 1}$
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Answer: B
Q372020 · 8 Jan 2020 · Shift 2
A particle of mass m is dropped from a height h above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of $2 g h$ . If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of $\frac{h}{g}$ is :
1. A. $\frac{1}{2}$
2. B. $\frac{1}{2}$
3. C. $\frac{3}{2}$
4. D. $\frac{3}{4}$
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Answer: C
Q392020 · 7 Jan 2020 · Shift 2
The dimension of $\frac{B ^{2}}{2 μ _{0}}$ , where B is magnetic field and $μ_{0}$ is the magnetic permeability of vacuum, is :
1. A. $M L^{2} T^{- 2}$
2. B. $ML T^{- 2}$
3. C. $M L^{- 1} T^{- 2}$
4. D. $M L^{2} T^{- 1}$
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Answer: C