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The effective capacitances of two capacitors are $3 \text{ \mu F}$ and $16 \text{ \mu F}$, when they are connected in series and parallel respectively. The capacitance of two capacitors are:

The equation of a wave is given by $Y = A \sin \omega (\frac{x}{v} - k)$ where $\omega$ is the angular velocity, $x$ is length and $v$ is the linear velocity. The dimension of $k$ is:

Dimensions of resistance in an electrical circuit, in terms of dimension of mass $M$, length $L$, time $T$, and current $I$, would be:

The value of Planck's constant is

The pair having the same dimensions is:

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The potential (V) at any axial point, at 2 m distance (r) from the centre of the dipole of dipole moment vector P of magnitude, $4\times10^{-6}$ C m, is $\pm 9\times10^3$ V. (Take $1/4\pi\varepsilon_0 = 9\times10^9$ SI units) Reason (R): $V = \pm \frac{2P}{4\pi\varepsilon_0 r^2}$, where r is the distance of any axial point situated at 2 m from the centre of the dipole. In the light of the above statements, choose the correct answer from the options given below:

Which one of the following compounds will be most readily dehydrated?

The main scale of a vernier calliper has $n$ divisions/cm. $n$ divisions of the vernier scale coincide with $(n-1)$ divisions of the main scale. The least count of the vernier calliper is:

The angle between the electric lines of force and the equipotential surface is:

Match the following columns and select the correct option. Column-I (a) Pituitary gland (b) Thyroid gland (c) Adrenal gland (d) Pancreas Column-II (i) Grave's disease (ii) Diabetes mellitus (iii) Diabetes insipidus (iv) Addison's disease

A series combination of n₁ capacitors, each of value C₁, is charged by a source of potential difference 4V. When another parallel combination of n₂ capacitors, each of value C₂, is charged by a source of potential difference V, it has the same (total) energy stored in it as the first combination has. The value of C₂ in terms of C₁ is:

The number of protons, neutrons and electrons in $^{175}_{71}\text{Lu}$, respectively, are:

Force $F$ on a particle moving in a straight line varies with distance $d$ as shown in the figure. The work done on the particle during its displacement of $12$ m is:

A particle moves with a velocity $(5\hat i-3\hat j+6\hat k)\text{ ms}^{-1}$ horizontally under the action of a constant force $(10\hat i+10\hat j+20\hat k)\text{ N}$. The instantaneous power supplied to the particle is:

In an experiment four quantities $a$, $b$, $c$ and $d$ are measured with percentage error $1\%$, $2\%$, $3\%$ and $4\%$ respectively. Quantity $P$ is calculated as follows $P = \frac{a^3 b^2}{cd}$. The percentage error in $P$ is

Dimensions of magnetic field intensity is:

A rectangular film of liquid is extended from $(4 \text{ cm} \times 2 \text{ cm})$ to $(5 \text{ cm} \times 4 \text{ cm})$. If the work done is $3 \times 10^{-4} \text{ J}$, then the value of the surface tension of the liquid is:

At what height from the surface of the earth, are the gravitation potential and the value of $g$ are: $-5.4 \times 10^7 \text{ J/kg}$ and $6.0 \text{ ms}^{-2}$ respectively? (Take, the radius of the earth as $6400 \text{ km}$)

The determination of the value of acceleration due to gravity ($g$) by simple pendulum method employs the formula, $g = 4\pi^2 \frac{L}{T^2}$. The expression for the relative error in the value of $g$ is:

A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 s is s₁ and that covered in the first 20 s is s₂, then