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A wire has a mass 0.3 $\pm$ 0.003 g, radius 0.5 $\pm$ 0.005 mm and length 6 $\pm$ 0.06 cm. The maximum percentage error in the measurement of its density is
1. 1
2. 2
3. 3
4. 4

A physical parameter a can be determined by measuring the parameters b, c, d and e using the relation $a=b^{\alpha }{c}^{\beta }/d^{\gamma }{e}^{\delta }$. If the maximum errors in the measurement of b, c, d and e are $b_1\%, c_1\%, d_1\% and e_1\%$, then the maximum error in the value of a determined by the experiment is
1. $(b_1+c_1+d_1+e_1)\%$
2. $(b_1+c_1-d_1-e_1)\%$
3. $(\alpha b_1+\beta c_1-\gamma d_1-\delta e_1)\%$
4. $(\alpha b_1+\beta c_1+\gamma d_1+\delta e_1)\%$

Assertion: When we change the unit of measurement of a quantity, its numerical value changes.
Reason: Smaller the unit of measurement smaller is its numerical value.

Assertion: Specific gravity of a fluid is a dimensionless quantity.
Reason: It is the ratio of density of fluid to the density of water.

Assertion: The quantity $\left(1/\sqrt{{\mu }_0{\epsilon }_0}\right)$ is dimensionally equal to velocity and numerically equal to velocity of light.
Reason: ${\mu }_0$ is permeability of free space and ${\epsilon }_0$ is the permittivity of free space.

The speed of light (c), gravitational constant (G) and Planck's constant (h) are taken as fundamental units in a system. The dimensions of time in this new system should be
1. $G^{1/2}{h}^{1/2}{c}^{-5/2}$
2. $G^{-1/2}{h}^{1/2}{c}^{1/2}$
3. $G^{1/2}{h}^{1/2}{c}^{-3/2}$
4. $G^{1/2}{h}^{1/2}{c}^{1/2}$

Dimensions of electrical resistance are:
1. $\left[M{L}^2{T}^{-3}{A}^{-1}\right]$
2. $\left[M{L}^2{T}^{-3}{A}^{-2}\right]$
3. $\left[M{L}^3{T}^{-3}{A}^{-2}\right]$
4, $\left[M{L}^{-1}{L}^3{T}^3{A}^2\right]$

The length and breadth of a metal sheet are 3.124 m and 3.002 m respectively, the area of this sheet up to four correct significant figure is
1. 9.3782 $m^2$
2. 9.37 $m^2$
3. 9.378248 $m^2$
4. 9.378 $m^2$

If force (F), velocity (V) and time (T) are taken fundamental units, then the dimensions of mass are
1. $\left[FV{T}^{-1}\right]$
2. $\left[FV{T}^{-2}\right]$
3. $\left[F{V}^{-1}{T}^{-1}\right]$
4. $\left[F{V}^{-1}T\right]$

If the dimensions of a physical quantity are given by $M^a{L}^b{T}^c$, then the physical quantity will be
1. pressure if a=1, b=-1 and c=-2
2. velocity  if a=1, b=0 and c=-1
3. acceleration if a=1, b=1 and c=-2
4. force if a=0, b=-1 and c=-2

The velocity v of a particle at time t is given by $v=at+\frac{b}{t+c}$, where a, b and c are constants. The dimensions of a, b and c are respectively:
1. $\left[L{T}^{-2}\right], \left[L\right] and \left[T\right]$
2. $\left[L^2\right], \left[T\right] and \left[L{T}^2\right]$
3. $\left[L{T}^2\right], \left[LT\right] and \left[L\right]$
4. $\left[L\right], \left[LT\right] and \left[T^2\right]$

If the error in the measurement of radius of a sphere is 2%, then the error in the determination of volume of the sphere will be
1. 4%
2. 6%
3. 8%
4. 2%

Assertion: The number 1.202 has four significant figures and the number 0.0024 has two significant figures.
Reason: All the non zero digits are significant.

Match the physical quantities given in Column I with dimensions expressed in terms of mass (M), length (L), Time (T), and charge (Q) given in Column II.
            Column I                        Column II
i. Angular momentum             p.   $\left[M{L}^2{T}^{-2}\right]$
ii. Latent heat                         q.   $\left[M{L}^2{Q}^{-2}\right]$
iii. Torque                                r.   $\left[M{L}^2{T}^{-1}\right]$
iv. Capacitance                       s.  $\left[M{L}^3{T}^{-1}{Q}^{-2}\right]$
v. Inductance                          t.   $\left[M^{-1}{L}^{-2}{T}^2{Q}^2\right]$
vi. Resistivity                          u.   $\left[L^2{T}^{-2}\right]$
Now mark the correct choice from given codes:
Codes
1. i-p, ii-q, iii-s, iv-t, v-u, vi-r
2. i-r, ii-u, iii-p, iv-t, v-s, vi-s
3. i-s, ii-t, iii-u, iv-p, v-q, vi-r
4. i-u, ii-r, iii-p, iv-q, v-s, vi-t

A person measures two quantities as A=1.0 m $\pm$ 0.2 m, B=2.0 m $\pm$ 0.2 m. We should report correct value for $\sqrt{AB}$ as
1. 1.4 m $\pm$ 0.4 m
2. 1.41 m $\pm$ 0.15 m
3. 1.4 m $\pm$ 0.3 m
4. 1.4 m $\pm$ 0.2 m

Number of particles is given by $n= -D\frac{n_2-n_1}{x_2-x_1}$ crossing a unit area perpendicular to X-axis in unit time, where $n_1 and n_2$ are number of particles per unit volume for the value of x meant to $x_2 and x_1$. Find dimensions of D called as diffusion constant.
1. $M^{0}L{T}^2$
2. $M^0{L}^2{T}^{-4}$
3. $M^{0}L{T}^{-3}$
4. $M^0{L}^2{T}^{-1}$

The length of a cylinder is measured with a meter rod having least count 0.1 cm. Its diameter with Vernier calipers having least count 0.01 cm. Given that length is 5.0 cm. and radius is 2.0 cm. The percentage error in the calculated value of the volume will be
1. 1%
2. 2%
3. 3%
4. 4%

If $u_1 and u_2$are the units selected in two systems of measurement and $n_1 and n_2$ their numerical values, then
1. $n_1{u}_1= n_2{u}_2$
2. $n_1{u}_1+ n_2{u}_2= 0$
3. $n_1{u}_2= n_1{u}_2$
4. $\left(n_1+u_1\right)+= \left(n_2+u_2\right)$

If there is a positive error of 50% in the measurement of the velocity of a body, then the error in the measurement of kinetic energy is
1. 25%
2. 50%
3. 100%
4. 125%