The dimensions of physical quantity X in the equation Force $=\frac{X}{\text{Density}}$ is given by 

(1) $M^1{L}^4{T}^{-2}$

(2) $M^2{L}^{-2}{T}^{-1}$

(3) $M^2{L}^{-2}{T}^{-2}$

(4) $M^1{L}^{-2}{T}^{-1}$

Two quantities A and B have different dimensions. Which mathematical operation given below is physically meaningful 

(1) A/B

(2) A + B

(3) A – B

(4) None

A force F is given by F = at + bt², where t is time. What are the dimensions of a and b 

(1) $ML{T}^{-3}$ and $M{L}^2{T}^{-4}$

(2) $ML{T}^{-3}$ and $ML{T}^{-4}$

(3) $ML{T}^{-1}$ and $ML{T}^0$

(4) $ML{T}^{-4}$ and $ML{T}^1$

The decimal equivalent of 1/20 upto three significant figures is

(1) 0.0500

(2) 0.05000

(3) 0.0050

(4) 5.0 × 10^-2

Accuracy of measurement is determined by

(1) Absolute error

(2) Percentage error

(3) Both

(4) None of these

The number of significant figures in all the given numbers 25.12, 2009, 4.156 and $1.217\times {10}^{-4}$ is 

1. 1

2. 2

3. 3

4. 4

Assertion: Out of three measurements l = 0.7 m; l = 0.70 m and l = 0.700 m, the last one is most accurate.

Reason: In every measurement, only the last significant digit is not accurately known.

Choose any one of the following four responses :

(1) If both assertion and reason are true and the reason is the correct explanation of the assertion.

(2) If both assertion and reason are true but the reason is not the correct explanation of the assertion.

(3) If the assertion is true but the reason is false.

(4) If the assertion and reason both are false.

Assertion: Avogadro number is the number of atoms in one gram mole.

Reason: Avogadro number is a dimensionless constant.

If radius of the sphere is (5.3 ± 0.1)cm. Then percentage error in its volume will be 

(1) $3+6.01\times \frac{100}{5.3}$

(2) $\frac{1}{3}\times 0.01\times \frac{100}{5.3}$

(3) $\left(\frac{{\displaystyle 3\times 0.1}}{{\displaystyle 5.3}}\right)\times 100$

(4) $\frac{0.1}{5.3}\times 100$

The pressure on a square plate is measured by measuring the force on the plate and the length of the sides of the plate. If the maximum error in the measurement of force and length are respectively 4% and 2%, The maximum error in the measurement of pressure is 

(1) 1%

(2) 2%

(3) 6%

(4) 8%