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Q. No.
Match the LIST-I with LIST-II
List- I List-II
\(\mathrm{(A)}\) Planck's constant \(\mathrm{(I)}\) \([M L^2T^2]\)
\(\mathrm{(B)}\) Stopping potential \(\mathrm{(II)}\) \([T^{-1}]\)
\(\mathrm{(C)}\) Work function \(\mathrm{(III)}\) \([M L^2T^{-1}]\)
\(\mathrm{(D)}\) Threshold frequency \(\mathrm{(IV)}\) \([M L^2 T^{-3}A^{-1}]\)
Choose the correct answer from the options given below:
1. \(\mathrm{A\text-III, B\text-IV, C\text-I, D\text-II}\)
2. \(\mathrm{A\text-I, B\text-II, C\text-III, D\text-IV}\)
3. \(\mathrm{A\text-IV, B\text-III, C\text-I, D\text-II}\)
4. \(\mathrm{A\text-I, B\text-IV, C\text-III, D\text-II}\)
Subtopic:  Dimensions |
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Level 1: 80%+
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Dimensions of universal gravitional constant \((G)\) in terms of Planck's constant \((h)\), distance \((L)\), mass \((M)\) and time \((T)\) are:
1. \([hTLM^{-2}]\)
2. \([hT^{-1}LM^{-2}]\)
3. \([hTL^{2}M^{-2}]\)
4. \([h^{-1}T^{-1}LM^{-2}]\)
Subtopic:  Dimensions |
 80%
Level 1: 80%+
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Match List-I with List-II.
List-I List-II
\(\mathrm{A.}\) Boltzmann constant \(\mathrm{I.}\) \({\left[{M}^{-1} {~L}^3 {~T}^{-2}\right]}\)
\(\mathrm{B.}\) Stefan's constant \(\mathrm{II.}\) \({\left[{M} {~L}^2 {~T}^{-1}\right]} \)
\(\mathrm{C.}\) Planck's constant \(\mathrm{III.}\) \({\left[{M} {~L}^2 {~T}^{-2} {~K}^{-1}\right]}\)
\(\mathrm{D.}\) Gravitational constant \(\mathrm{IV.}\) \( {\left[{M} {~L}^0 {~T}^{-3} {~K}^{-4}\right]}\)
Choose the correct answer from the option given below:
1. \(\mathrm{A\text-I, B\text-II, C\text-III, D\text-IV} \)
2. \(\mathrm{A\text-IV, B\text-III, C\text-II, D\text-I} \)
3. \(\mathrm{A\text-III, B\text-IV, C\text-II, D\text-I} \)
4. \(\mathrm{A\text-II, B\text-I, C\text-IV, D\text-III}\)
Subtopic:  Dimensions |
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Level 1: 80%+
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The potential energy of a particle changes with distance \(x\) from a fixed origin as \(V=\dfrac{A \sqrt{x}}{x+B},\) where \(A\) and \(B\) are constant with appropriate dimensions. The dimensions of \(AB\) are:
1. \({\left[{M}^1{~L}^{5 / 2}{~T}^{-2}\right]} \)
2. \({\left[{M}^{3 / 2}{~L}^{5 / 2} {~T}^{-2}\right]}\)
3. \({\left[{M}^1{~L}^2 {~T}^{-2}\right]}\)
4. \({\left[{M}^1 {~L}^{7 / 2} {~T}^{-2}\right]}\)
Subtopic:  Dimensions |
 68%
Level 2: 60%+
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The dimensional formula of \(\dfrac{1}{2}\varepsilon_0 E^2\) (\(\varepsilon_0\)=permittivity of vacuum and \(E\)=electric field) is \({M}^{a} {~L}^{{b}} {~T}^{{c}} .\) The value of \(2a-b+c\) is:
1. \(0\)
2. \(1\)
3. \(-1\)
4. \(2\)
Subtopic:  Dimensions |
 91%
Level 1: 80%+
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\(L,C\) and \(R\) represents physical quantities inductance, capacitance and resistance respectively. The dimensional formula \( M L ^2 {T}^{-4} {A}^{-2}\) corresponds to:
1. \(\dfrac{R}{\sqrt{L C}}\)
2. \(\dfrac{R}{{L C}}\)
3. \(\dfrac{C}{\sqrt{L R}}\)
4. \(\dfrac{1}{R} \sqrt{\dfrac{L}{C}}~\)
Subtopic:  Dimensions |
 67%
Level 2: 60%+
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Match List-I with List-II.
List-I List-II
\(\mathrm{(A)}\) Meter \((L)\) \(\mathrm{(I)}\) \(\sqrt{\dfrac{h c}{G}}\)
\(\mathrm{(B)}\) Second \((S)\) \(\mathrm{(II)}\) \(\sqrt{\dfrac{G h}{c^5}}\)
\(\mathrm{(C)}\) Kilogram \((M)\) \(\mathrm{(III)}\) \(\sqrt{\dfrac{K^2 L^2 c^3}{G h}}\)
\(\mathrm{(D)}\) Kalvin \((K)\) \(\mathrm{(IV)}\) \(\sqrt{\dfrac{G h}{c^3}}\)
where (Plank's constant), \(G\) (gravitational constant), and \(c\) (speed of light in vacuum) as fundamental units. Choose the correct answer from the given below:
1. \(\mathrm{A\text-II, B\text-IV, C\text-I, D\text-III}\)
2. \(\mathrm{A\text-IV, B\text-II, C\text-I, D\text-III}\)
3. \(\mathrm{A\text-IV, B\text-I, C\text-II, D\text-III}\)
4. \(\mathrm {A\text-III, B\text-I, C\text-II, D\text-IV}\)
Subtopic:  Dimensions |
 88%
Level 1: 80%+
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Consider the equation \(H=\dfrac{x^p \epsilon^q E^r}{t^s}\) 
Where \(H\)=magnetic field ; \(E\)=electric field, \(\epsilon\) = permittivity, \(x\) = distance, \(t\) = time 
The value of \(p, q, r\) and \(s\) respectively are:
1. \(1,1,1,1\)
2. \(-1,1,2,1\)
3. \(1,-1,-2,1\)
4. \(-1,-2,-2,1\)
Subtopic:  Dimensions |
 69%
Level 2: 60%+
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Consider a modified Bernoulli equation. \(\left(P+\dfrac{A}{B t^2}\right)+\rho g(h+B t)+\dfrac{1}{2} \rho V^2=\text {constant}\) If \(t\) has the dimension of time then the dimensions of \(A\) and \(B\) are respectively:
1. \(\left [ML^0T^{-1} \right ]\) and \(\left [M^0LT \right ]\)
2. \(\left [ML^0T^{-1} \right ]\) and \(\left [M^0LT^{-1} \right ]\)
3. \(\left [ML^0T^{-2} \right ]\) and \(\left [M^0LT^{-2} \right ]\)
4. \(\left [ML^0T^{-2} \right ]\) and \(\left [M^0LT^{-1} \right ]\)
Subtopic:  Dimensions |
 74%
Level 2: 60%+
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Match the LIST-I with LIST-II
List-I List-II
A. Spring constant I. \(ML^2T^{-2}K^{-1}\)
B. Thermal conductivity II. \(ML^0T^{-2}\)
C. Boltzmann constant III. \(ML^2T^{-3}A^{-2}\)
D. Inductive reactance IV. \(MLT^{-3}K^{-1}\)
Choose the correct answer from the options given below:
Options: A B C D
1. II I IV III
2. I IV II III
3. III II IV I
4. II IV I III
Subtopic:  Dimensions |
 87%
Level 1: 80%+
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