The dimensional formula for energy is  

The pair of the quantities having same dimensions is 

The dimensional formula for relative refractive index is 

The dimensional formula $\left[M{L}^{-1}{T}^{-2}\right]$ is for the quantity 

The dimensionally correct expression for the resistance R among the following is 

[P=electric power, l= electric current, t=time 

V=voltage and E=electric energy]

Which of the following does not have dimensions of force?

Dimensional analysis cannot be used for:

Which of the following does not have the dimensions of force?

Which of the following is not a unit of time?

Which of the following measurements is most precise?

Which of the following ratios express pressure?

The number of significant figures in 0.06900 is:

The sum of the numbers 436.32, 227.2, and 0.301 in appropriate significant figures is

The mass and volume of a body are 4.237 g and 2.5 ${\mathrm{cm}}^3$, respectively. The density of the material of the body in correct significant figures will be

The numbers 2.745 and 2.735 on rounding off to 3 significant figures will give, respectively, 

The length and breadth of a rectangular sheet are 16.2 cm and 10.1 cm, respectively. The area of the sheet in appropriate significant figures and error would be, respectively,

Which of the following pairs of physical quantities does not have the same dimensional formula?

The measure of two quantities along with the precision of respective measuring instrument is $\mathrm{A}=2.5{\mathrm{ms}}^{-1}\pm 0.5{\mathrm{ms}}^{-1},\mathrm{B}=0.10\mathrm{s}\pm 0.01\mathrm{s}$. The value of AB will be:

You measure two quantities as A = 1.0 m $\pm$ 0.2 m, B = 2.0 m $\pm$ 0.2 m. We should report the correct value for $\sqrt{\mathrm{AB}}$ as

The mean length of an object is 5 cm. Which of the following measurements is most accurate?

The period of oscillation of a simple pendulum is $\mathrm{T} =2\mathrm{\pi }\sqrt{\frac{\mathrm{L}}{\mathrm{g}}}$. Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1 s resolution. The percentage error in g is:

Young's modulus of steel is $1.9\times {10}^{11} \mathrm{N}/{\mathrm{m}}^2$. When expressed in CGS units of $\mathrm{dyen}/{\mathrm{cm}}^2$, it will be equal to $\left(1 \mathrm{N}={10}^5 \mathrm{dyne}, 1 {\mathrm{m}}^2={10}^4 {\mathrm{cm}}^2\right)$:

$$\begin{gathered} \left(1\right) 1.9\times {10}^{10} \\ \left(2\right) 1.9\times {10}^{11} \\ \left(3\right) 1.9\times {10}^{12} \\ \left(4\right) 1.9\times {10}^9 \end{gathered}$$

On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion are not correct?
a. \(y = asin ~2\pi / T\)
b. \(y = a~sin~vt\)
c. \(y = {a \over T} sin ({t \over a})\)
d. \(y = a \sqrt 2 (sin {2 \pi t \over T} - cos {2 \pi \over T})\)

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 - ${\mathrm{Q}}^2)$/R

(e) (R + Q)/P

Photon is a quantum of radiation with energy E = h$\mathrm{\nu }$, where $\mathrm{\nu }$ is the frequency
and h is Planck's constant. The dimensions of h are the same as that of

(a) linear impulse

(b) angular impulse

(c) linear momentum

(d) angular momentum

If Planck's constant (h) and speed of light in a vacuum (c) are taken as two fundamental quantities, which one of the following can, in addition, be taken to express length, mass, and time in terms of the three chosen fundamental quantities?

(a) Mass of electron (${\mathrm{m}}_{\mathrm{e}}$)    (b) Universal gravitational constant (G)

(c) Charge of electron (e)    (d) Mass of proton (${\mathrm{m}}_{\mathrm{p}}$)

Which of the following ratios express pressure?

(a) Force/Area

(b) Energy/Volume

(c) Energy/Area

(d) Force/Volume

Which of the following are not a unit of time?

(a) Second
(b) Parsec
(c) Year
(d) Light year

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:

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

This objective question is based on NCERT Exemplar subjective Question.