NEET and JEE

In the formula X = 3YZ², X and Z have dimensions of capacitance and magnetic induction respectively. What are the dimensions of Y in MKSQ system ?

• $M^{-3}L^{-1}T^3Q^{\text{4}}$

• $M^{-3}L^{-2}T^4Q^{\text{4}}$

• $M^{-2}L^{-2}T^4Q^{\text{4}}$

• $M^{-3}L^{-2}T^3Q^{\text{4}}$

The dimension of  $\left(\frac{1}{2}\right)\epsilon_0E^2\$  is ( $\epsilon_0$  :premittivity of free space,electric field)

•  $MLT^{-1}$  

•  $ML^2T^{-1}$  

•  $ML^{-1}T^{-2}$  

•  $ML^{-2}T^{-2}$  

The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. If the resultant is at 90° with the force of smaller magnitude, what are the, magnitudes of forces 

• 12, 5

• 14, 4 

•  5, 13 

•  10, 8

The respective number of significant figures for the numbers 23.203,0.0003 and 2.1 X  $10^3$  are :

• 4,1,2

• 5,1,2

• 3,1,5

• 4,5,1

A screw gauge gives the following readings when used to measure the diameter of a wire.

Main scale reading : 0 mm

Circular scale reading : 52 divisions

given that 1 mm on main scale corresponds to 100 divisions of the circular scale .find the diameter of the wire

• 0.026 cm

• 0.005 cm

• 0.52 cm

• .0.052 cm

The period of oscillation of a simple pendulum is given by  $T=2\pi\ \sqrt{\frac{l}{g}}$   where l is about 100 cm and is known to have 1mm accuracy. The period is about 2s. The time of 100 oscillations is measured by a stop watch of least count 0.1 s. The percentage error in g is 

• 0.1%

• 2%

• 0.2%

• 8%

The percentage errors in the measurement of mass and speed are 2% and 3% respectively. How much will be the maximum error in the estimation of the kinetic energy obtained by measuring mass and speed

• 11 %

• 8%

• 5%

• 1%

The random error in the arithmetic mean of 100 observations is x; then random error in the arithmetic mean of 400 observations would be

• 4x

• $\frac{1}{4}x$

• 2x

• $\frac{1}{2}x$

Which of the following is the dimensionless quantity:

• force of surface tension

• strain

• stress

• co-efficient of viscosity

Dimensions of velocity gradient are same as that of

• time period

• frequency

• angular acceleration

• acceleration