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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The dimensional formula `[ML^(-1)T^(-2)]` is for the quantityA. ForceB. AccelerationC. PressureD. Work |
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Answer» Correct Answer - C |
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| 2. |
If `m` is the mass, `Q` is the charge and `B` is the magnetic induction, `m//BQ` has the same dimensions as:A. frequencyB. TimeC. VelocityD. Acceleration |
| Answer» Correct Answer - B | |
| 3. |
Given that `m` = mass, `l` = length, `t` = time and `i =` current. The dimensional formula of `ml^(2)//t^(3) i` are the same as that ofA. electric fieldB. electric potentialC. CapacitanceD. inductane |
| Answer» Correct Answer - B | |
| 4. |
If `F` is the force, `mu` is the permeability , `H` is the intensity of magneitc field and `i` is the electric current, tehn `(F)/(mu Hi)` has the dimensions ofA. massB. lengthC. timeD. energy |
| Answer» Correct Answer - B | |
| 5. |
If `L` has the dimensions of length, `V` that of potential and `epsilon_(0)` is the permittivity of free space then quantity `epsilon_(0) LV` has the dimensions ofA. currentB. chargeC. resistanceD. voltage |
| Answer» Correct Answer - B | |
| 6. |
`[("Permeability")/("Permittivity")]` will have the dimesional formula of:A. `[M^(0) L^(0) T^(0) A^(0)`B. `[M^(2) L^(2) T^(4) A^(2)]`C. `[M^(2) L^(4) T^(-6) A^(-4)]`D. `[M^(-2) L^(-4) T^(6) A^(4)]` |
| Answer» Correct Answer - C | |
| 7. |
Which of the following measurement is most precise?A. `5.00mm`B. `5.00cm`C. `5.00m`D. `5.00km` |
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Answer» Correct Answer - A All given measurements are correct upto two decimal places. As here `5.00mm`has the smallest unit and the error in `5.00 mm` is least (commonly taken as 0.01 mm if not specified), hence, `5.00 mm` is most precise. |
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| 8. |
The values of a number of quantities are used in a mathematical formula The quantity that should be most precise and accurate in measurement is the oneA. Having smallest magnitudeB. Having largest magnitudeC. Used in the numeratorD. Used in the denominator |
| Answer» Correct Answer - 1 | |
| 9. |
The order of the magnitude of speed of light in SI unit isA. 16B. 8C. 4D. 7 |
| Answer» Correct Answer - 2 | |
| 10. |
The order of magnitude of the diameter of the earth is (diamtere of the earth is `1.28xx10^(7)m`)A. 5B. 6C. 7D. 8 |
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Answer» Correct Answer - C The order of magnitude of the diameter of the earth is 7. |
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| 11. |
Calculate the length of the arc of a circle of radius 31.0 cm which subtands and angle of `(pi)/(6)` at the centre.A. 11.7 cmB. 14.7 cmC. 16.7 cmD. 15.7 cm |
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Answer» Correct Answer - D Here, `theta=(pi)/(6),r=30cm` As `theta=(l)/(r)impliesl=thetar=(pi)/(6)xx30cm=(3.14)/(6)xx30cm=15.7cm` |
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| 12. |
The dimensional formula for coefficient of kinematic visocity is:A. `[M^(0) L^(-1) T^(-1)]`B. `[M^(0) L^(2) T^(-1)]`C. `[M L^(2) T^(-1)]`D. `[ML^(-1)T^(-1)]` |
| Answer» Correct Answer - B | |
| 13. |
If the size of bacteria is 1 micron, what will be the number of it in 1 m length?A. One hundredB. One croreC. One thousandD. One million |
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Answer» Correct Answer - D 1 micron `=10^(-6)m` `because10^(-6)m` space is occupied by 1 bacteria. `therefore1m` space will be occupied by `10^(6)` bacteria=1 million bacteria |
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| 14. |
If `P` is X-ray unit and `Q` is micron the `P//Q` isA. `10^(-5)`B. `10^(5)`C. `10^(7)`D. `10^(-7)` |
| Answer» Correct Answer - D | |
| 15. |
1 micron = ..... NanometerA. `10^(-6)`B. `10^(-10)`C. `10^(3)`D. `10^(-3)` |
| Answer» Correct Answer - C | |
| 16. |
The ratio between pico and giga isA. `10^(21)`B. `10^(-21)`C. `10^(14)`D. `10^(8)` |
| Answer» Correct Answer - B | |
| 17. |
What is the SI unit of mass density of a substance ? |
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Answer» Mass density =`"Mass"/"Volume"` `therefore` SI unit of mass density =`"SI unit of mass"/"SI unit of volume"` `="kg"/m^3` So, SI unit of mass density is `kg//m^3` |
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| 18. |
in an experiment the angles are required to be using an instrument, `29` divisions of the main scale exactly coincide with the `30` divisions of the vernier scale. If the sallest division of the main scale is half- a degree `(= 0.5^(@)`, then the least count of the instrument is : |
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Answer» Least count `= ("Value of main scale division")/("No.of divisons of vernier scale")` `= (1)/(30) MSD = (1)/(30)xx(1^(0))/(2) = (1^(0))/(60) = 3` min |
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| 19. |
Which of the following statement is incorrect regarding significant figures?A. All the non-zero digits are significantB. All the zeros betwee two non-zero digits are significantC. Greater the number of significant figrues in a measurement, smaller is the percentage error.D. The power of 10 is counted while counting the number of significant figures. |
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Answer» Correct Answer - D The power of 10 is irrelevant tt he determination of significant figures. |
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| 20. |
The best method to reduce random error isA. Taking large number of observationsB. Corrected zero errorC. By following proper technique of experimentD. Both (1) & (3) |
| Answer» Correct Answer - 1 | |
| 21. |
if the randon error in the arithmetic mean of 50 observations is `alpha`, then the random error in the arithmetic mean of 150 observations would beA. `alpha`B. `3alpha`C. `alpha/3`D. `2alpha` |
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Answer» Correct Answer - C |
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| 22. |
In two systems of units the relation between velocity acceleration and force is given by `v_(2) = (v_(1)epsilon^(2))/(tau), a_(2) = a_(1) epsilon tau, F_(2) = (F_(1))/(epsilon tau)`, where `epsilon` and `tau` constants then find in this new system: (a) `(m_(2))/(m_(1))` , (b) `(L_(2))/(L_(1))` |
| Answer» Correct Answer - (a)`1/(epsilon^2tau^2) ; (b)epsilon^2/tau^3` | |
| 23. |
Show that time constant `(tau = RC)` of `R - C` circuit has the dimensions of time.A. Square of timeB. Square of inverse timeC. TimeD. Inverse time |
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Answer» Correct Answer - C |
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| 24. |
In what direction does the buoyant force on an object immersed in a liquid act?A. `Vrhog`B. `(rhog)/V`C. `rhogV^2`D. `sqrt(rhogV)` |
| Answer» Correct Answer - 1 | |
| 25. |
Which of the following does not have dimensions of force?A. WeightB. Rate of change of momentumC. Work per unit lengthD. Work done per unit charge |
| Answer» Correct Answer - 4 | |
| 26. |
The dimensionally correct expression for the resistance R among the following is [P = electric power, l = electric current, t = time, V = volatge and E = electric energy]A. `R=sqrt(Pl)`B. `R=E/(l^2t)`C. `R=V^2P`D. R=Vl |
| Answer» Correct Answer - 2 | |
| 27. |
The dimensionally correct expression for the resistance R among the following is [P = electric power, l = electric current, t = time, V = volatge and E = electric energy]A. `R=sqrt(Pl)`B. `R=E/(l^(2)t)`C. `R=V^(2)P`D. R = Vl |
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Answer» Correct Answer - B |
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| 28. |
A : All physically correct equations are dimensionally correct. R : All dimensionally correct equations are physically correct.A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).C. If Assertion is true statement but Reason is false, then mark (3).D. If both Assertion and Reason are false statements, then mark (4). |
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Answer» Correct Answer - C |
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| 29. |
A dimensionally consistent relation for the volume `V` of a liquid of coefficiet of viscosity `eta` flowing per second through a tube of radius `r` and length `l` and having a pressure difference `p` across its end, isA. `V=(piPr^(4))/(8etal)`B. `V=(pieta)/(8Pr^(4))`C. `V=(8Peta)/(pir^(4))`D. `V=(piPeta)/(8r^(4))` |
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Answer» Correct Answer - A |
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| 30. |
Which of the following relations is dimensionally incorrect?A. `1u=931.5` MeVB. 1u=931.5 MeV`//c^(2)`C. 1u=1.67`xx10^(-27)kg`D. none of these |
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Answer» Correct Answer - B `1u=931.5MeV//c^(2)` |
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| 31. |
To find the distance d over which a signal can be seen clearly in foggy conditions, a railways engineer uses dimensional analysis and assumes that the distance depends on the mass density `rho` of the fog, intensity `("power"//"area")` S of the light from the signal and its frequency f. The engineer finds that d is proportional to `S^(1//n)`. The value of n is.A. 4B. 2C. 3D. 1 |
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Answer» Correct Answer - C Let `dproprho^(x)S^(y)f^(z)` or `d=krho^(x)S^(y)f^(z)` where k is a dimensionless constant and x,y and z are the exponents. Writings dimenions on both sides, we get `[M^(0)LT^(0)]=[ML^(-3)T^(0)]^(x)[ML^(0)T^(-3)]^(y)[M^(0)L^(0)T^(-1)]^(z)` `[M^(0)LT^(0)]=M^(x+y)L^(-3x)T^(-3y-z)]` applying the principle of homogeneity of dimensions, we get ltBrgt `x+y=0` . . . (i) `-3x=1` . . . .(ii) `-3-z=0` . . . (iii) Solving eqns. (i), (ii) and (iii), we get `x=-(1)/(3),y=(1)/(3),z=-1,` as `dpropS^(1//3)` `thereforen=3` |
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| 32. |
A : Out of the measurements A = 20.00 and B = 20.000, B is more accurate. R : Percentage error in B is less than the percentage error in A.A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1).B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).C. If Assertion is true statement but Reason is false, then mark (3).D. If both Assertion and Reason are false statements, then mark (4). |
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Answer» Correct Answer - A |
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| 33. |
In an experiment, the values of refractive indices of glass were found to be `1.54, 1.53, 1.44, 1.54, 1.56` and `1.45` in successive measurements (i) mean value of refreactive index of glass (ii) mean absolute error (iii) relative error and (iv) percentage error are respectively.A. `1.51,0.04,0.03%, 3%`B. `1.51,0.4,0.03%, 3%`C. `15.1,0.04,0.03%, 3%`D. `1.51,0.4,0.3%, 3%` |
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Answer» Correct Answer - A `mu_("mean") = (sum mu)/(6), Delta u_("mean") = (sum(mu_("mean") - mu))/(6)`, relative `%` error in `mu = (Delta mu_("mean"))/(mu_("mean")) xx 100` |
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| 34. |
Two physical quantities A and B have different dimensions. Which mathematical operation given below is physically possible ?A. `sqrt(AB)`B. A(1 + B)C. A - BD. A + B |
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Answer» Correct Answer - A |
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| 35. |
If A and B are two physical quantities having different dimensions then which of the following can denote a new physical quantity?A. A+3BB. 3A-BC. `A^3+(3B)^3`D. `A^(1//3)xx(3B)^3` |
| Answer» Correct Answer - 4 | |
| 36. |
If P,Q,R are physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity?A. `((P-Q))/(R)`B. `PQ-R`C. `(PQ)/(R)`D. `((PR-Q^(2)))/(R)` |
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Answer» Correct Answer - A Physical quantities having different dimesions cannot be added or subtracted. As P,Q and R are physical quantities having different dimensions, therefore tthey can neither be added nor be subtracted Thus, (a) can never be a meaningful quantitity. |
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| 37. |
The physical quantity that has no dimensions is:A. angular velocityB. linear momentumC. angular momentumD. strian |
| Answer» Correct Answer - D | |
| 38. |
If momentum `(p)`, area `(A)` and time`(t) `are taken to be fundamental quantities then energy has the dimensional formulaA. `[pA^(-1) T^(1)]`B. `[p^(2) AT]`C. `pA^(-1//2)T]`D. `[pA^(1//2) T]` |
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Answer» Correct Answer - D `E prop p^(a) A^(b) T^(c)` `E = kp^(a) A^(A) T^(C)` `ML^(2) T^(-2) - [MLT^(-1)]^(a) [L^(2)]^(b) [T]^(c)` `= M^(a) L^(2b+a) T^(a+c)` On solving `E = pA^(1//2) T^(-1)`. |
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| 39. |
A pair of physical quantities having the same dimensional formula areA. Force and WorkB. Work and energyC. Force and TorqueD. Work and Power |
| Answer» Correct Answer - B | |
| 40. |
The dimensionla formula for the product of two physical quantities `P` and `Q` is `[ML^(2) T^(-2)]`. The dimensional formula of `(P)/(Q)` is `[MT^(-2)]`. Then `P` and `Q` respectively areA. Force and velocityB. Momentum and displacementC. Force and displacementD. Work and velocity |
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Answer» Correct Answer - C `PQ = ML^(2) T^(-2)`....(1), `(P)/(Q) = MT^(-2)` ....(2) `(1)xx(2) = p^(2) = M^(2) L^(2) T^(-4)` `implies P = MLT^(-2)` = Force `(1)//(2) = Q^(2) = L^(2)` |
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| 41. |
If pressure P, velocity V and time T are taken as fundamental physical quantities, the dimensional formula of force ifA. `[P^(1) V^(1) T^(1)]`B. `[P^(1) V^(2) T^(1)]`C. `[P^(1) V^(1) T^(2)]`D. `[P^(1) V^(2) T^(2)]` |
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Answer» Correct Answer - D `F prop P^(a) V^(b) T^(c)` |
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| 42. |
In the expression `P =E I^2 m^(-5) G^(-2),` E, m, I and G denote energy, mass, angular momentum and gravitational constant, respectively. Show that P is a dimensionless quantity. |
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Answer» `"Given, expression is "P=EL^(2)m^(-5)G^(-2)` `"where E is energy "[E]=[ML^(2)T^(-2)]` `"m is mass "[m]=[M]` `"L is angular momentum "[L]=[ML^(2)T^(-1)]` `"G is gravitational constant "[G]=[M^(-1)L^(3)T^(-2)]` Substituting dimensions of each term in the given expression, `[P]=[ML^(2)T^(-2)]xx[ML^(2)T^(_1)]^(2)xx[M]^(-5)xx[M^(-1)L^(3)T^(-2)]^(-2)` `=[M^(1+2-5+2)L^(2+4-6)T^(-2-2+4)]=[M^(0)L^(0)T^(0)]` Therefore, P is a dimensionless quantity. |
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| 43. |
A suitable unit for gravitational constant isA. kg-m `sec^(-1)`B. `Nm^(-1)` secC. `Nm^2 kg^(-2)`D. kgm sec |
| Answer» Correct Answer - 3 | |
| 44. |
The dimensions of universal gravitational constant are :-A. `[M^(-2) L^2 T^2]`B. `[M^(-1)L^3T^(-2)]`C. `[ML^(-1)T^(-2)]`D. `[ML^2T^(-2)]` |
| Answer» Correct Answer - 2 | |
| 45. |
The number of significant figures in `6.023xx10^(23) "mole"^(-1)` isA. `4`B. `3`C. `2`D. `23` |
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Answer» Correct Answer - A Use limitation of significant figures. |
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| 46. |
Atto is ..........A. An instrument used to measure gradientB. An instrument used to measure the altitudeC. `10^(18)`D. `10^(-18)` |
| Answer» Correct Answer - D | |
| 47. |
`N m s^(-1)` is the unit ofA. PressureB. PowerC. PotentialD. Pressure graident |
| Answer» Correct Answer - B | |
| 48. |
Which one of the following is not measured in the units of energyA. (couple) `xx` (time)B. moment of inertia `xx ("angular velocity")^(2)`C. force `xx` distanceD. impulse `xx` time |
| Answer» Correct Answer - D | |
| 49. |
Which one of the following represnts the correct dimensions of the coefficient of viscocity?A. `[ML^(-1)T^(2)]`B. `[MLT^(-1)]`C. `[ML^(-1)T^(-1)]`D. `[ML^(-2)T^(-2)]` |
| Answer» Correct Answer - C | |
| 50. |
The total plane angle subtended by a circle at its centre isA. `pi` radB. `2pi` radC. `(2pi)/3` radD. `pi/2` rad |
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Answer» Correct Answer - B |
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