Units, Dimensions & Errors · JEE Main previous year questions

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2021 12 questions

Q332021 · 1 Sept 2021 · Shift 2
The temperature of an ideal gas in 3-dimensions is $300 K$ . The corresponding de-Broglie wavelength of the electron approximately at $300 K$ , is : [ $m_{e}$ = mass of electron $= 9 \times 1 0^{- 31} kg$ , $h$ = Planck constant $= 6.6 \times 1 0^{- 34} Js$ , $k_{B}$ = Boltzmann constant $= 1.38 \times 1 0^{- 23} J K^{- 1}$ ]
1. A. $6.26 nm$
2. B. $8.46 nm$
3. C. $2.26 nm$
4. D. $3.25 nm$
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Answer: A
Q382021 · 1 Sept 2021 · Shift 2
A student determined Young's Modulus of elasticity using the formula $Y = \frac{M g L ^{3}}{4 b d ^{3} δ}$ . The value of g is taken to be $9.8 m/ s^{2}$ , without any significant error, his observations are as follows. $Physical Quantity Mass (M) Length of bar (L) Breadth of bar (b) Thickness of bar (d) Depression (δ) Least count of the Equipment used for measurement 1 g 1 mm 0.1 mm 0.01 mm 0.01 mm Observed value 2 kg 1 m 4 cm 0.4 cm 5 mm$ Then the fractional error in the measurement of Y is :
1. A.0.0083
2. B.0.0155
3. C.0.155
4. D.0.083
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Answer: B
Q372021 · 27 Jul 2021 · Shift 2
1. A.at x > $x_{4}$ K.E. is constant throughout the region.
2. B.at x < $x_{1}$ , K.E. is smallest and the particle is moving at the slowest speed.
3. C.at x = $x_{2}$ , K.E. is greatest and the particle is moving at the fastest speed.
4. D.at x = $x_{3}$ , K.E. = 4 J.
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Answer: B
Q442021 · 27 Jul 2021 · Shift 2
A physical quantity 'y' is represented by the formula $y = m^{2} r^{- 4} g^{x} l^{- \frac{3}{2}}$ If the percentage errors found in y, m, r, l and g are 18, 1, 0.5, 4 and p respectively, then find the value of x and p.
1. A.5 and $\pm 2$
2. B.4 and $\pm 3$
3. C. $\frac{16}{3}$ and $\pm \frac{3}{2}$
4. D.8 and $\pm 2$
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Answer: C
Q522021 · 25 Jul 2021 · Shift 1· Numerical answer
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Answer: 13
Q602021 · 25 Jul 2021 · Shift 1· Numerical answer
A particle of mass 'm' is moving in time 't' on a trajectory given by $r = 10 α t^{2} \hat{i} + 5 β (t - 5) \hat{j}$ Where $α$ and $β$ are dimensional constants. The angular momentum of the particle becomes the same as it was for t = 0 at time t = ____ seconds.
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Answer: 10
Q422021 · 25 Jul 2021 · Shift 2
The force is given in terms of time t and displacement x by the equation F = A cos Bx + C sin Dt The dimensional formula of $\frac{A D}{B}$ is :
1. A. $[M^{0} L T^{- 1}]$
2. B. $[M L^{2} T^{- 3}]$
3. C. $[M^{1} L^{1} T^{- 2}]$
4. D. $[M^{2} L^{2} T^{- 3}]$
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Answer: B
Q562021 · 18 Mar 2021 · Shift 2· Numerical answer
The radius of a sphere is measured to be $(7.50 \pm 0.85) cm$ . Suppose the percentage error in its volume is x. The value of x, to the nearest integer, is ____.
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Answer: 34
Q462021 · 16 Mar 2021 · Shift 1
One main scale division of a vernier callipers is 'a' cm and $n^{th}$ division of the vernier scale coincide with $(n - 1)^{th}$ division of the main scale. The least count of the callipers in mm is :
1. A. $\frac{10 a}{n}$
2. B. $\frac{10 na}{( n - 1 )}$
3. C. $(\frac{n - 1}{10 n}) a$
4. D. $\frac{10 a}{( n - 1 )}$
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Answer: A
Q392021 · 26 Feb 2021 · Shift 1
In a typical combustion engine the workdone by a gas molecule is given by $W = α^{2} β e^{- \frac{β x ^{2}}{k T}}$ , where x is the displacement, k is the Boltzmann constant and T is the temperature. If $α$ and $β$ are constants, dimensions of $α$ will be :
1. A. $[M^{0} L T^{0}]$
2. B. $[M L T^{- 1}]$
3. C. $[M L T^{- 2}]$
4. D. $[M^{2} L T^{- 2}]$
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Answer: A
Q362021 · 26 Feb 2021 · Shift 2
If 'C' and 'V' represent capacitance and voltage respectively then what are the dimensions of $λ$ where $C / V = λ$ ?
1. A. $[M^{- 3} L^{- 4} I^{3} T^{7}]$
2. B. $[M^{- 2} L^{- 3} I^{2} T^{6}]$
3. C. $[M^{- 2} L^{- 4} I^{3} T^{7}]$
4. D. $[M^{- 1} L^{- 3} I^{- 2} T^{- 7}]$
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Answer: C
Q452021 · 25 Feb 2021 · Shift 2
If e is the electronic charge, c is the speed of light in free space and h is Planck's constant, the quantity $\frac{1}{4 π ε _{0}} \frac{∣ e ∣ ^{2}}{h c}$ has dimensions of :
1. A. $[M L T^{- 1}]$
2. B. $[M L T^{0}]$
3. C. $[M^{0} L^{0} T^{0}]$
4. D. $[L C^{- 1}]$
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Answer: C