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  • Question 1
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    In the relation, P=αβeαz/kθ\displaystyle P=\frac{\alpha }{\beta }e^{{\alpha z}/{k\theta }} PP is pressure, ZZ is distance, KK is Boltzmann constant and θ\displaystyle \theta is the temperature. The dimensions of β\displaystyle \beta will be 

  • Question 2
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    If E,M,JE, M, J and GG respectively denote energy, mass, angular momentum and universal gravitational constant, the quantity, which has the same dimensions as the dimensions of EJ2M5G2\frac{EJ^2}{M^5G^2} is:

  • Question 3
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    Match the following physical quantities with their respective dimensional formula:


    (a) Angular Momentum(e) [ML2T3] \displaystyle \left[ { ML }^{ 2 }{ T }^{ -3 } \right] 
    (b) Impulse(f) [ML2T1] \displaystyle \left[ { ML }^{ 2 }{ T }^{ -1 } \right] 
    (c) Pressure(g) [MLT1] \displaystyle \left[ ML{ T }^{ -1 } \right] 
    (d) Power(h) [ML1T2] \displaystyle \left[ { ML }^{ -1 }{ T }^{ -2 } \right] 

  • Question 4
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    Out of the following pairs, choose the pair in which the physical quantities do not have identical dimension?

  • Question 5
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    Amol has three objects, X, Y and Z. He puts X into a measuring cylinder with 3030 mL of water. Then he puts Y and Z one by one into the same measuring cylinder as shown.
    Which of the objects has/have a volume less than 3030 mL?

  • Question 6
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    Directions For Questions

    These questions consist of two statement, each printed as assertion and reason. While answering these question you are required to cheese any one of the following five responses.

    ...view full instructions

    Assertion: The dimensional formula for relative velocity is same as that of the change in velocity.
    Reason: 
    Relative velocity of P w.r.t. Q is the ratio of velocity of P and that of Q.

  • Question 7
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    The Van der Waal's equation of n'n' moles of a real gas is
    (P+aV2 )(Vb)=nRT\displaystyle \left( P+\frac { a }{ { V }^{ 2 } }  \right) \left( V-b \right) =nRT
    Where PP is pressure, VV is volume, TT is absolute temperature, RR is molar gas constant and a,b,ca, b, c are Van der Waal constants. The dimensional formula for abab is:

  • Question 8
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    A block of mass 1kg is placed on a rough horizontal surface. A spring is attached to the block whose other end is joined to a rigid wall, as shown in the figure. A horizontal force is applied to the block so that it remains at rest while the spring is elongated by x(xμmgk)x(x \geq \dfrac{ \mu mg }{ k } ). Let FmaxF_{max} and FminF_{min} be the maximum and minimum values of force F for which the block remains in equilibrium. For a particular x, FmaxFmin=2Nx, \ F_{max} -F_{min} = 2N. Also shown is the variation of Fmax+Fmin F_{max} + F_{min} versus xx, the elongation of the spring.
    The coefficient of friction between the block and the horizontal surface is :

  • Question 9
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    A beam balance of unequal arm length is used by an unscruplus trader. When an object is weighed on left pan. The weight ii found to be W1{W}_{1}. When the object is weighed on the right plan, the weight is found to be W2{W}_{2}. If W1W2{W}_{1}\neq {W}_{2}, the correct weight of the object is

  • Question 10
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    The dimension of (12 )ε 0E2\left( \frac { 1 }{ 2 }  \right) { \varepsilon  }_{ 0 }{ E }^{ 2 } is (ε 0{ \varepsilon  }_{ 0 }: permittivity of free space, Electric field)

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