The percentage error in measuring M, L and T are 1 %, 1.5% and 3% respectively. Then the percentage error in measuring the physical quantity with dimensions [ML^-1 T^-1] is

• 1 %

• 3.5 %

• 5.5 %

• 4.5 %

The displacement of a particle moving along x-axis with respect to time t is x = at + bt² − ct³. The dimensions of c are

• [T^-3]

• [LT^-2]

• [LT^-3]

• [LT³]

The mass and volume of a body are found to be 5.00 ± 0.05 kg and 1.00 ± 0.05 m 3 respectively. Then the maximum possible percentage error in its density is

• 6 %

• 3 %

• 10 %

• 5 %

If F denotes force and t time, then in the equation F = at^-1 + bt², the dimensions of a and b respectively are

• [LT^-4] and [LT^-1]

• [LT^-1] and [LT^-4]

• [MLT^-4] and [MLT^-1]

• [MLT] and [MLT^-4]

A ball dropped from a height of 2 m rebounds to a height of 1.5 m after hitting the ground. Then the percentage of energy lost is

• 25

• 30

• 50

• 100

26.

The quantities RC and $\left(\frac{\mathrm{L}}{\mathrm{R}}\right)$ (where R, L and C stand for resistance, inductance and capacitance respectively) have the dimensions of

• force

• linear momentum

• linear acceleration

• time

The number of significant figures in 0.002305 is

• 6

• 4

• 7

• 2

The percentage errors in the measurement of length and time period of a simple pendulum are 1% and 2% respectively. Then the maximum error in the measurement of acceleration due to gravity is

• 8 %

• 3 %

• 5 %

• 6 %

Dimensional formula of Stefan's constant is

• [MT^-3K^-4]

• [MLT^-2K^-4]

• [ML²T^-2]

• [MT^-2L⁰]

If C is the capacitance and V is the potential, the dimensional formula for CV² is

• [ML²T^-1]

• [ML^-2T^-3]

• [ML²T^-2]

• [ML^-2T^-2]