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The velocity $v$ of a particle at time $t$ is given by ${v}={at}+\frac{{b}}{{t}+{c}}.$ The dimensions of ${a}$ , ${b}$ , and ${c}$ are respectively:
1. ${\left[{LT}^{-2}\right],[{L}],[{T}]}$
2. ${\left[{L}^2\right],[{T}] \text { and }\left[{LT}^2\right]}$
3. ${\left[{LT}^2\right],[{LT}] \text { and }[{L}]}$
4. ${[{L}],[{LT}], \text { and }\left[{T}^2\right]}$

Q4:

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If the dimensions of a physical quantity are given by

[M^{a} L^{b} T^{c}],

$\left[M^aL^bT^c\right],$ then the physical quantity will be:

1.	pressure if $a=1, ~b=-1,~c=-2$
2.	velocity if $a=1,~b=0,~c=-1$
3.	acceleration if $a=1,~b=1,~c=-2$
4.	force if $a=0, ~b= -1,~c=-2$

Q5:

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The universal gravitational constant is dimensionally represented as:
1. $\left[ML^2T^{-1}\right]$
2. $\left[M^{-2}L^3T^{-2}\right]$
3. $\left[M^{-2}L^2T^{-1}\right]$
4. $\left[M^{-1}L^3T^{-2}\right]$

Q6:

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The force

F

$F$ acting on a body as a function of position

(x)

$(x)$ and time

(t)

$(t)$ is expressed as

F = A \sin (k_{1} x) + B \cos (k_{2} t) .

$F=A \sin \left(k_1 x\right)+B \cos \left(k_2 t\right).$ From the given information, match Column I with Column II.

	Column I		Column II
$(\mathrm A)$	Dimensions of $A$	$(\mathrm P)$	$[M^0L^0T^{-1}]$
$(\mathrm B)$	Dimensions of $k_{1}$	$(\mathrm Q)$	$[M^0L^{-1}T^{-1}]$
$(\mathrm C)$	Dimensions of $k_{2}$	$(\mathrm R)$	$[MLT^{-2}]$
$(\mathrm D)$	Dimensions of $k_{1}k_{2}$	$(\mathrm S)$	$[M^0L^{-1}T^{0}]$

Codes:

1.	$\mathrm {A \rightarrow R, B \rightarrow S, C \rightarrow P, D \rightarrow Q }$
2.	$\mathrm {A \rightarrow P, B \rightarrow Q, C \rightarrow R, D \rightarrow S }$
3.	$\mathrm {A \rightarrow R, B \rightarrow P, C \rightarrow Q, D \rightarrow S }$
4.	$\mathrm {A \rightarrow S, B \rightarrow P, C \rightarrow Q, D \rightarrow R}$

Q7:

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Which, among the pairs of quantities has the same dimensions?

1.	${\large\frac{\text{force}}{\text{volume}}},\text{ surface tension}$
2.	$\text{torque},\text{ pressure}\times\text{volume}$
3.	$\text{specific heat}\times\text{mass},\text{ energy}$
4.	${\large\frac{\text{pressure}}{\text{acceleration}}},\text{ density}$

Q8:

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The dimensional formula of pressure is:

1.	$\left[MLT^{-2}\right]$	2.	$\left[ML^{-1}T^{2}\right]$
3.	$\left[ML^{-1}T^{-2}\right]$	4.	$\left[MLT^{2}\right]$

Q9:

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The dimensional formula for impulse is:

1.	$[MLT^{-2}]$	2.	$[MLT^{-1}]$
3.	$[ML^2T^{-1}]$	4.	$[M^2LT^{-1}]$

Q10:

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