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The electric field in a certain region is acting radially outward and is given by E = Ar. A charge contained in a sphere of radius 'a' centered at the origin of the field will be given by:

Two periodic waves of intensities $I_1$ and $I_2$ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is:

The fundamental frequency of a closed organ pipe of a length $20 \text{ cm}$ is equal to the second overtone of an organ pipe open at both ends. The length of the organ pipe open at both ends will be:

An organ pipe filled with a gas at $27^\circ\text{C}$ resonates at $400\text{ Hz}$ in its fundamental mode. If it is filled with the same gas at $90^\circ\text{C}$, the resonance frequency at the same mode will be:

Two identical charged spheres suspended from a common point by two massless strings of lengths l are initially at a distance d (d << l) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of the distance x between the spheres, as:

4d, 5p, 5f and 6p orbitals are arranged in the order of decreasing energy. The correct option is

The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is $20 \text{ cm}$, the length of the open organ pipe is:

The driver of a car travelling at a speed of $30 \text{ m/s}$ towards a hill sounds a horn of frequency $600 \text{ Hz}$. If the velocity of sound in air is $330 \text{ m/s}$, the frequency of reflected sound as heard by the driver is:

Which one of the following statements is true?

Dimensional formula for volume elasticity is

The force between two small charged spheres having charges of $2 \times 10^{-7}$ C and $3 \times 10^{-7}$ C placed 30 cm apart in the air is:

Two identical piano wires kept under the same tension $T$ have a fundamental frequency of $600 \text{ Hz}$. The fractional increase in the tension of one of the wires which will lead to the occurrence of $6 \text{ beats/s}$ when both the wires oscillate together would be:

A wave traveling in the +ve x-direction having maximum displacement along y-direction as $1 \text{ m}$, wavelength $2\pi \text{ m}$ and frequency of $1/\pi \text{ Hz}$, is represented by:

An electric dipole with dipole moment $4 \times 10^{-9}$ C m is aligned at $30^\circ$ with the direction of a uniform electric field of magnitude $5 \times 10^4$ NC$^{-1}$. The magnitude of the torque acting on the dipole is:

Two point charges $q_A = 3 \, \mu\text{C}$ and $q_B = -3 \, \mu\text{C}$ are located $20 \, \text{cm}$ apart in a vacuum. The electric field at the midpoint $O$ of the line $AB$ joining the two charges is:

The equation of a simple harmonic wave is given by $y=3\sin\frac{\pi}{2}(50t-x)$ where $x$ and $y$ are in meters and $t$ is in seconds. The ratio of maximum particle velocity to the wave velocity is:

The wave described by $y = 0.25\sin(10\pi x - 2\pi t)$, where $x$ and $y$ are in metres and $t$ in seconds, is a wave traveling along the:

The bond dissociation energies of $X_2$, $Y_2$ and $XY$ are in the ratio of $1 : 0.5 : 1$. $\Delta H$ for the formation of $XY$ is $-200 \text{ kJ mol}^{-1}$. The bond dissociation energy of $X_2$ will be

The EM wave with the shortest wavelength among the following is:

The symbolic representation of four gates is shown as: Pick out which ones are for AND, NAND, and NOT gates, respectively.