The angle of 1' (minute of arc) in radian is nearly equal to:

Time intervals measured by a clock give the following readings : 

1.25 sec, 1.24 sec, 1.27sec, 1.21 sec and 1.28 sec. 

What is the percentage relative error of the observations? 

19. We have different units for the same physical quantity,

(a) To have the different dimensions

(b) To have the same value in the different units

(c) To have a wide range of the measurements

(d) None of the above

This objective question is based on NCERT Exemplar subjective Question.

Each side of a cube is measured to be 7.203 m. What are the total surface area and the volume respectively of the cube to appropriate significant figures?

5.74 g of a substance occupies 1.2 ${\mathrm{cm}}^3$. Its density by keeping the significant figures in view is:

20. The radius of the atom is of the order of 1 $\stackrel{\mathrm{o}}{\mathrm{A}}$ and the radius of a nucleus is of the order of fermi. How many magnitudes higher is the volume of an atom as compared to the volume of the nucleus?

$$\begin{gathered} \left(1\right) {10}^{13} \\ \left(2\right) {10}^{14} \\ \left(3\right) {10}^{15} \\ \left(4\right) {10}^{16} \end{gathered}$$

This objective question is based on NCERT Exemplar subjective Question.

21. The device used for measuring the mass of atoms and molecules:

This objective question is based on NCERT Exemplar subjective question.

22. The unified atomic mass unit in kg is equal to:

$$\begin{gathered} \left(1\right) 1.67\times {10}^{+27} \\ \left(2\right) 3.2\times {10}^{-27} \\ \left(3\right) 1.67\times {10}^{-27} \\ \left(4\right) 9.1\times {10}^{-27} \end{gathered}$$

This objective question is based on NCERT Exemplar subjective Question.

23. A function f($\mathrm{\theta }$) is defined as $\mathrm{f}\left(\mathrm{\theta }\right)=1-\mathrm{\theta }+\frac{{\mathrm{\theta }}^2}{2!}-\frac{{\mathrm{\theta }}^3}{3!}+\frac{{\mathrm{\theta }}^4}{4!}+ ...$
f($\mathrm{\theta }$) is a dimensionless quantity because:

(a) $\mathrm{\theta }$ is dimensionless.

(b) Combination of different powers of $\mathrm{\theta }$ is dimensionless.

(c) It has no relation with $\mathrm{\theta }$.

(d) None of the above

This objective question is based on NCERT Exemplar subjective Question.

24. Length, mass, and time are chosen as base quantities in mechanics because

(a) these are special quantities.

(b) these are independent quantities.

(c) these are independent of other quantities but depend on each other.

(d) these are only the measurable quantities.

This objective question is based on NCERT Exemplar subjective Question.

25. The earth-moon distance is about 60 earth radius. What will be the diameter of the earth (approximately in degrees) as seen from the moon?

(a) 2$°$

(b) 1$°$

(c) 3$°$

(d) 4$°$

This objective question is based on NCERT Exemplar subjective Question.

Which of the following time measuring devices is most precise:

(a) A wall clock
(b) A stopwatch
(c) A digital watch
(d) An atomic clock

This objective question is based on NCERT Exemplar subjective Question

28. The vernier scale of a travelling microscope has 50 divisions which coincide with 49 main scale divisions. If each main scale division is 0.5 mm, the minimum inaccuracy in the measurement of distance:

$$\begin{gathered} \left(1\right) 0.02 \mathrm{mm} \\ \left(2\right) 0.2 \mathrm{mm} \\ \left(3\right) 0.1 \mathrm{cm} \\ \left(4\right) 0.01 \mathrm{mm} \end{gathered}$$

This objective question is based on NCERT Exemplar subjective Question.

37. The volume of a liquid flowing out per second of a pipe of length l and radius r is written by a student as $\mathrm{V}=\frac{\mathrm{\pi }}{8}\frac{{\mathrm{Pr}}^4}{\mathrm{\eta l}}$ where P is the pressure difference between the two ends of the pipe and $\mathrm{\eta }$ is the coefficient of the viscosity of the liquid having dimensional formula $\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-1}\right]$. Then,

This objective question is based on NCERT Exemplar subjective Question.

29. During a total solar eclipse-the moon almost entirely covers the sphere of the sun. The relation between the distances and sizes of the sun and moon is:

$$\begin{gathered} \left(1\right) \frac{{\mathrm{R}}_{\mathrm{s}}}{{\mathrm{R}}_{\mathrm{m}}}=\frac{{\mathrm{R}}_{\mathrm{se}}}{{\mathrm{R}}_{\mathrm{me}}} \\ \left(2\right) \frac{{\mathrm{R}}_{\mathrm{s}}}{{\mathrm{R}}_{\mathrm{m}}}={\left(\frac{{\mathrm{R}}_{\mathrm{se}}}{{\mathrm{R}}_{\mathrm{me}}}\right)}^2 \\ \left(3\right) \frac{{\mathrm{R}}_{\mathrm{s}}}{{\mathrm{R}}_{\mathrm{m}}}=\sqrt{\frac{{\mathrm{R}}_{\mathrm{se}}}{{\mathrm{R}}_{\mathrm{me}}}} \\ \left(4\right) \frac{{\mathrm{R}}_{\mathrm{m}}}{{\mathrm{R}}_{\mathrm{s}}}=\frac{{\mathrm{R}}_{\mathrm{se}}}{{\mathrm{R}}_{\mathrm{me}}} \end{gathered}$$

30. If the unit of force is 100 N, the unit of length is 10 m, and the unit of time is 100 sec, what is the unit of mass in this system of units?

$$\begin{gathered} \left(1\right) 10 \mathrm{kg} \\ \left(2\right) {10}^3 \mathrm{kg} \\ \left(3\right) {10}^{-5} \mathrm{kg} \\ \left(4\right) {10}^{+5} \mathrm{kg} \end{gathered}$$

This objective question is based on NCERT Exemplar subjective Question.

31. A physical quantity that has a unit but no dimensions is:

(a) Plane angle

(b) Strain

(c) Gravitational Constant

(d) Reynold's Number

This objective question is based on NCERT Exemplar subjective Question.

32. What will be the length of the arc of a circle of radius 31.0 cm which subtends an angle of $\mathrm{\pi }/6$ at the centre?

This objective question is based on NCERT Exemplar subjective Question.

33. Calculate the solid angle subtended by the periphery of an area of 1 ${\mathrm{cm}}^2$ at a point situated symmetrically at a distance of 5 cm from the area.

$$\begin{gathered} \left(1\right) 3\times {10}^{-2}\text{ steradian } \\ \left(2\right) 4\times {10}^{-2}\text{ steradian } \\ \left(3\right) 4\times {10}^{-1}\text{ steradian } \\ \left(4\right) 3\times {10}^{-1}\text{ steradian } \end{gathered}$$

34. The displacement of a progressive wave is represented by y = Asin ($\mathrm{\omega }$t —kx), where x is distance and t is time. The dimensional formula of $\mathrm{\omega }$ and k are, respectively;

$$\begin{gathered} \left(1\right) \left[{\mathrm{LT}}^{-1}\right] \& \left[{\mathrm{T}}^{-1}\right] \\ \left(2\right) \left[{\mathrm{L}}^2{\mathrm{T}}^{-1}\right] \& \left[{\mathrm{LT}}^{-1}\right] \\ \left(3\right) \left[{\mathrm{T}}^{-1}\right] \& \left[{\mathrm{L}}^{-1}\right] \\ \left(4\right) \left[{\mathrm{LT}}^{-2}\right] \& \left[{\mathrm{T}}^{-2}\right] \end{gathered}$$

This objective question is based on NCERT Exemplar subjective Question.

35. Time for 20 oscillations of a pendulum is measured as ${\mathrm{t}}_1=39.6\mathrm{s}$; ${\mathrm{t}}_2=39.9\mathrm{s}$ and ${\mathrm{t}}_3=39.5\mathrm{s}$. What is the accuracy of the measurement?

$$\begin{gathered} \left(1\right) \pm 0.2 \sec \\ \left(2\right) \pm 0.02 \sec \\ \left(3\right) \pm 2.0 \sec \\ \left(4\right) \pm 0.3 \sec \end{gathered}$$

This objective question is based on NCERT Exemplar subjective Question.

36. A new system of units is proposed in which the unit of mass is $\mathrm{\alpha }$ kg, unit of length $\mathrm{\beta }$ m and unit of time $\mathrm{\gamma }$ s. How much will 5 J measure in this new system?

This objective question is based on NCERT Exemplar subjective Question.

38. A physical quantity X is related to four measurable quantities a, b, c, and d as follows $\mathrm{X}={\mathrm{a}}^2{\mathrm{b}}^3{\mathrm{c}}^{5/2}{\mathrm{d}}^{-2}$. The percentage error in measuring a, b, c, and d is 1%, 2%, 3%, and 4%, respectively. What is the percentage error in quantity X?

This objective question is based on NCERT Exemplar subjective Question.

39. In the expression $\mathrm{P}={\mathrm{EL}}^2{\mathrm{m}}^{-5}{\mathrm{G}}^{-2}$, E, m, L, and G denote energy, mass, angular momentum, and gravițational constant, respectively. Dimensions of P are:

$$\begin{gathered} \left(1\right) \left[{\mathrm{M}}^1{\mathrm{L}}^2{\mathrm{T}}^{-1}\right] \\ \left(2\right) \left[{\mathrm{M}}^1{\mathrm{L}}^0{\mathrm{T}}^{-2}\right] \\ \left(3\right) \left[{\mathrm{M}}^0{\mathrm{L}}^0{\mathrm{T}}^0\right] \\ \left(4\right) \left[{\mathrm{M}}^2{\mathrm{L}}^0{\mathrm{T}}^1\right] \end{gathered}$$

This objective question is based on NCERT Exemplar subjective Question.

40. If the velocity of light c, Planck's constant h, and gravitational constant G are taken as fundamental quantities, then the dimensions of mass are:

$$\begin{gathered} \left(1\right) \mathrm{m}=\mathrm{k}\sqrt{\frac{\mathrm{h}}{\mathrm{cG}}} \\ \left(2\right) \mathrm{m}=\mathrm{k}\sqrt{\frac{\mathrm{cG}}{\mathrm{h}}} \\ \left(3\right) \mathrm{m}=\mathrm{k}\sqrt{\frac{\mathrm{c}}{\mathrm{hG}}} \\ \left(4\right) \mathrm{m}=\mathrm{k}\sqrt{\frac{\mathrm{ch}}{\mathrm{G}}} \end{gathered}$$

This objective question is based on NCERT Exemplar subjective Question.

41. An artificial satellite is revolving around a planet of mass M and radius R, in a circular orbit of radius r. From Kepler's third law about the period of a satellite around a common central body, the square of the period of revolution T is proportional to the cube of the radius of the orbit r. The time period of a satellite is:

This objective question is based on NCERT Exemplar subjective Question.

42. In the experiment to estimate the size of a molecule of oleic acid film, the thickness of the oleic acid film:

$$\begin{gathered} \left(1\right) \frac{\mathrm{nV}}{20\times 20} \mathrm{cm} \\ \left(2\right) \frac{\mathrm{nV}}{20\times 20\times \mathrm{A}} \mathrm{cm} \\ \left(3\right) \frac{\mathrm{nVA}}{20\times 20} \mathrm{cm} \\ \left(4\right) \frac{\mathrm{nA}}{20\times 20\mathrm{V}} \mathrm{cm} \end{gathered}$$

This objective question is based on NCERT Exemplar subjective question.

How many astronomical units (AU) make 1 parsec?

$$\begin{gathered} \left(1\right) 2\times {10}^{15} \mathrm{AU} \\ \left(2\right) 3\times {10}^8 \mathrm{AU} \\ \left(3\right) 1\times {10}^5 \mathrm{AU} \\ \left(4\right) 2\times {10}^5 \mathrm{AU} \end{gathered}$$

This objective question is based on NCERT Exemplar subjective Question.

Two resistors of resistances ${\mathrm{R}}_1 = \left(100 \pm 3\right)$ ohm and ${\mathrm{R}}_2 = \left(200 \pm 4\right)$ ohm are connected in parallel. The equivalent resistance of the parallel combination is:

The relative error in Z, if Z = $\frac{{\mathrm{A}}^4{\mathrm{B}}^{1/3}}{{\mathrm{CD}}^{3/2}}$ is: