Units, Dimensions & Errors · JEE Main previous year questions

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2025 22 questions

Q292025 · 8 Apr 2025 · Shift 2
A quantity $Q$ is formulated as $X^{- 2} Y^{+ \frac{3}{2}} Z^{- \frac{2}{5}}$ . $X$ , $Y$ , and $Z$ are independent parameters which have fractional errors of $0.1$ , $0.2$ , and $0.5$ , respectively in measurement. The maximum fractional error of $Q$ is
1. A. $0.6$
2. B. $0.8$
3. C. $0.7$
4. D. $0.1$
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Answer: C
Q272025 · 4 Apr 2025 · Shift 1
In an electromagnetic system, the quantity representing the ratio of electric flux and magnetic flux has dimension of $M^{P} L^{Q} T^{R} A^{S}$ , where value of ' Q ' and ' R ' are
1. A. $(3, - 5)$
2. B. $(- 2, 1)$
3. C. $(- 2, 2)$
4. D. $(1, - 1)$
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Answer: D
Q312025 · 4 Apr 2025 · Shift 2
In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of $[M^{P} L^{Q} T^{R} A^{S}]$ . The value of P and Q are :
1. A. $- 1, 0$
2. B. $0, - 1$
3. C. $- 1, 1$
4. D. $1, - 1$
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Answer: B
Q362025 · 4 Apr 2025 · Shift 2
For the determination of refractive index of glass slab, a travelling microscope is used whose main scale contains 300 equal divisions equals to 15 cm . The vernier scale attached to the microscope has 25 divisions equals to 24 divisions of main scale. The least count (LC) of the travelling microscope is (in cm ) :
1. A.0.002
2. B.0.0025
3. C.0.0005
4. D.0.001
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Answer: A
Q272025 · 3 Apr 2025 · Shift 1
A person measures mass of 3 different particles as $435.42 g$ , $226.3 g$ and $0.125 g$ . According to the rules for arithmetic operations with significant figures, the addition of the masses of 3 particles will be.
1. A. $661.845 g$
2. B. $661.84 g$
3. C. $662 g$
4. D. $661.8 g$
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Answer: D
Q372025 · 3 Apr 2025 · Shift 1
1. A. $n R T ln (\frac{L _{1}}{L _{0}}) + M g (L_{1} - L_{0}) + \frac{3 k}{4} (L_{1}^{4} - L_{0}^{4})$
2. B. $n R T ln (\frac{L _{1}}{L _{0}}) + M g (L_{1} - L_{0}) + \frac{k}{4} (L_{1}^{4} - L_{0}^{4})$
3. C. $n R T ln (\frac{L _{1}^{2}}{L _{0}^{2}}) + \frac{M g}{2} (L_{1} - L_{0}) + \frac{k}{4} (L_{1}^{4} - L_{0}^{4})$
4. D. $3 n R T ln (\frac{L _{1}}{L _{0}}) + 2 M g (L_{1} - L_{0}) + \frac{k}{3} (L_{1}^{3} - L_{0}^{3})$
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Answer: B
Q412025 · 3 Apr 2025 · Shift 1
1. A.A, B and C only
2. B.A, C and D only
3. C.A, B and D only
4. D.A and B only
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Answer: C
Q282025 · 3 Apr 2025 · Shift 2
A particle moves along the $x$ -axis and has its displacement $x$ varying with time $t$ according to the equation: $x = c_{0} (t^{2} - 2) + c (t - 2)^{2}$ where $c_{0}$ and $c$ are constants of appropriate dimensions. Then, which of the following statements is correct?
1. A.the acceleration of the particle is $2 (c + c_{0})$
2. B.the acceleration of the particle is $2 c_{0}$
3. C.the acceleration of the particle is $2 c$
4. D.the initial velocity of the particle is $4 c$
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Answer: A
Q342025 · 3 Apr 2025 · Shift 2
A motor operating on $100 V$ draws a current of $1 A$ . If the efficiency of the motor is $91.6%$ , then the loss of power in units of $cal/s$ is
1. A. $6.2$
2. B. $2$
3. C. $8.4$
4. D. $4$
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Answer: B
Q502025 · 3 Apr 2025 · Shift 2· Numerical answer
A physical quantity C is related to four other quantities $p, q, r$ and $s$ as follows $C = \frac{p q ^{2}}{r ^{3} s}$ The percentage errors in the measurement of $p, q, r$ and $s$ are $1%, 2%, 3%$ and $2%$ , respectively. The percentage error in the measurement of $C$ will be__________\%
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Answer: 15
Q402025 · 2 Apr 2025 · Shift 1
The equation for real gas is given by $(P + \frac{a}{V ^{2}}) (V - b) = RT$ , where $P$ , $V$ , $T$ and $R$ are the pressure, volume, temperature and gas constant, respectively. The dimension of $ab^{- 2}$ is equivalent to that of :
1. A.Compressibility
2. B.Planck's constant
3. C.Energy density
4. D.Strain
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Answer: C
Q292025 · 2 Apr 2025 · Shift 2
If $μ_{0}$ and $ϵ_{0}$ are the permeability and permittivity of free space, respectively, then the dimension of $(\frac{1}{μ _{0} ϵ _{0}})$ is :
1. A. $T^{2} /L$
2. B. $L^{2} / T^{2}$
3. C. $T^{2} / L^{2}$
4. D. $L/ T^{2}$
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Answer: B
Q442025 · 2 Apr 2025 · Shift 2
Given a charge q , current I and permeability of vacuum $μ_{o}$ . Which of the following quantity has the dimension of momentum ?
1. A. $q I / μ_{o}$
2. B. $q^{2} μ_{o} I$
3. C. $q μ_{0} / I$
4. D. $q μ_{o} I$
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Answer: D
Q452025 · 29 Jan 2025 · Shift 2
1. A.Both (A) and (R) are true but (R) is NOT the correct explanation of (A)
2. B.Both (A) and (R) are true and (R) is the correct explanation of (A)
3. C.(A) is false but (R) is true
4. D.(A) is true but (R) is false
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Answer: C
Q462025 · 29 Jan 2025 · Shift 2· Numerical answer
A physical quantity $Q$ is related to four observables $a, b, c, d$ as follows : $Q = \frac{a b ^{4}}{c d}$ where, $a = (60 \pm 3) Pa$ ; $b = (20 \pm 0.1) m$ ; $c = (40 \pm 0.2) Ns m^{- 2}$ and $d = (50 \pm 0.1) m$ , then the percentage error in Q is $\frac{x}{1000}$ , where $x =$ ____ .
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Answer: 7700
Q472025 · 28 Jan 2025 · Shift 1· Numerical answer
In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of $[M^{a} L^{b} T^{c}]$ . If $b = - 3$ , the value of $c$ is ____.
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Answer: 0
Q492025 · 28 Jan 2025 · Shift 1· Numerical answer
A tiny metallic rectangular sheet has length and breadth of $5 mm$ and $2.5 mm$ , respectively. Using a specially designed screw gauge which has pitch of $0.75 mm$ and $15$ divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be $\frac{x}{100}$ where $x$ is ____.
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Answer: 3
Q452025 · 24 Jan 2025 · Shift 1
For an experimental expression $y = \frac{32.3 \times 1125}{27.4}$ , where all the digits are significant. Then to report the value of $y$ we should write
1. A. $y = 1326.186$
2. B. $y = 1326.2$
3. C. $y = 1326.19$
4. D. $y = 1330$
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Answer: D
Q482025 · 24 Jan 2025 · Shift 1· Numerical answer
The least count of a screw gauge is $0.01 mm$ . If the pitch is increased by $75%$ and number of divisions on the circular scale is reduced by $50%$ , the new least count will be ____ $\times 1 0^{- 3} mm$
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Answer: 35
Q412025 · 23 Jan 2025 · Shift 2
The energy of a system is given as $E (t) = α^{3} e^{- β t}$ , where $t$ is the time and $β = 0.3 s^{- 1}$ . The errors in the measurement of $α$ and $t$ are $1.2%$ and $1.6%$ , respectively. At $t = 5 s$ , maximum percentage error in the energy is :
1. A. $6%$
2. B. $11.6%$
3. C. $4%$
4. D. $8.4%$
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Answer: A
Q272025 · 22 Jan 2025 · Shift 1
If $B$ is magnetic field and $μ_{0}$ is permeability of free space, then the dimensions of $(B / μ_{0})$ is
1. A. $MT^{- 2} A^{- 1}$
2. B. $L^{- 1} A$
3. C. $ML^{2} T^{- 2} A^{- 1}$
4. D. $LT^{- 2} A^{- 1}$
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Answer: B
Q392025 · 22 Jan 2025 · Shift 1
Given below are two statements : Statement I: In a vernier callipers, one vernier scale division is always smaller than one main scale division. Statement II : The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions. In the light of the above statements, choose the correct answer from the options given below.
1. A.Both Statement I and Statement II are false
2. B.Statement I is true but Statement II is false
3. C.Both Statement I and Statement II are true
4. D.Statement I is false but Statement II is true
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Answer: B