Recent questions in 2018

Let $f(x) = x^2 + \frac{1}{x^2}$ and $g(x) = x - \frac{1}{x},\; x \in R -\{-1, 0, 1\}$ . If $h(x) = \frac{f(x)}{g(x)}$ , then the local minimum value of $h(x)$ is :

asked Dec 11, 2018 by pady_1

1 answer

A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is

asked Dec 11, 2018 by pady_1

2 answers

If sum of all the solutions of the equation $8 \cos x. (\cos (\frac{\pi}{6} + x) . \cos (\frac{\pi}{6} - x) - \frac{1}{2}) = 1$ in $[0, \pi]$ is $k \pi$ , then $k$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

Let $S = \{x \in R : x \geq 0$ and $2|\sqrt{x} - 3| + \sqrt{x} (\sqrt{x} - 6) + 6 = 0\}$ Then $S$ :

asked Dec 11, 2018 by pady_1

1 answer

If the system of linear equations $x+ ky + 3z=0$ $3x + ky - 2z=0$ $2x + 4y - 3z =0$ has a non-zero solution $(x, y, z)$ , then $\frac{xz}{y^2}$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

If the curves $y^2 = 6x, \; 9x^2 + by^2=16$ intersect each other at right angles, then the value of $b$ is :

asked Dec 11, 2018 by pady_1

1 answer

Tangents are drawn to the hyperbola $4x^2 - y^2 = 36$ at the points P and Q. If these tangents intersect at the point $T(0,3)$ then the area (in sq. units) of $\Delta PTQ$ is :

asked Dec 11, 2018 by pady_1

1 answer

If $\alpha, \; \beta \in C$ are the distinct roots, of the equation $x^2 - x + 1 = 0$ , then $\alpha^{101} + \beta^{107}$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

If $L_1$ is the line of intersection of the planes $2x- 2y+ 3z - 2 =0,\; x- y + z+1=0$ and $L_2$ is the line of intersection of the planes $x+2y -z-3=0, \; 3x - y + 2z - 1=0$ , then the distance of the origin from the plane, containing the lines $L_1$ and $L_2$ , is :

asked Dec 11, 2018 by pady_1

1 answer

If the tangent at (1, 7) to the curve $x^2 = y - 6$ touches the circle $x^2 + y^2 + 16x +12 y + c = 0$ then the value of $c$ is :

asked Dec 11, 2018 by pady_1

1 answer

A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the $n^{th}$ power of $R$ . If the period of rotation of the particle is T, then :

asked Dec 11, 2018 by pady_1

0 answers

Two moles of an ideal monoatomic gas occupies a volume $V$ at $27^{\circ}C$ . The gas expands adiabatically to a volume $2V$ . Calculate (a) the final temperature of the gas and (b) change in its internal energy.

asked Dec 11, 2018 by pady_1

0 answers

All the graph are intendent to represent the same motion. One of them does it incorrectly. Pick it up

asked Dec 11, 2018 by pady_1

0 answers

In an a.c circuit, the instantaneous e.m.f and current are given by $e = 100 \sin 30 t$ $i = 20 \sin (30 t - \frac{\pi}{4})$ In one cycle of a.c the average power consumed by the circuit and the wattless current are, respectively :

asked Dec 11, 2018 by pady_1

0 answers

On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is $1\; K \Omega$ . How much was the resistance on the left slot before interchanging the resistances ?

asked Dec 11, 2018 by pady_1

0 answers

The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1% the maximum error in determining the density is :

asked Dec 11, 2018 by pady_1

0 answers

The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is $B_t$ . When the dipole moment is double by keeping the current constant, the magnetic field at the centre of loop is $B_z$ . The ratio $\frac{B_1}{B_2}$ is:

asked Dec 11, 2018 by pady_1

0 answers

In a collinear collision, a particle with an initial speepd $v_0$ strikes a stationary particle of the same mass. If the final kinetic energy $50\%$ greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is :

asked Dec 11, 2018 by pady_1

0 answers

From a uniform circular disc of radius R and mass 9m, a small disc of radius $\frac{R}{3}$ is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is :

asked Dec 11, 2018 by pady_1

0 answers

A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of $10^{12}/sec$ . What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver = 108 and Avagadro number = $6.02 \times 10^{23} gm\; mole^{-1}$ )

asked Dec 11, 2018 by pady_1

0 answers

The angular width of the central maximum in a single slit diffraction pattern is $60^{\circ}$ . The width of the slit is $1\; \mu m$ . The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young's fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm, what is slit separation distance? (i.e. distance between the centres of each slit.)

asked Dec 11, 2018 by pady_1

0 answers

The EM wave from air enters a medium. The electric fields are $E_1 = E_{01} \hat{x} \cos [ 2 \pi v (\frac{z}{c} - t)]$ in air and $E_2 = E_{02} \hat{x} \cos [k(2z - ct)]$ in medium, where the wave number $k$ and frequency $v$ refer to their values in air. The medium is non-magnetic. If $\in_{r_1}$ and $\in_{r_2}$ refer to relative permittivities of air and medium respectively, which of the following options is correct ?

asked Dec 11, 2018 by pady_1

0 answers

Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities $+\sigma, \; -\sigma$ and $+\sigma$ respectively. The potential of shell B is :

asked Dec 11, 2018 by pady_1

0 answers

In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of the cell are connected across 52 cm of the potentiometer wire. If the cell is shunted by resistance of $5 \Omega$ , a balance is found when the cell is connected across 40 cm of the wire. Find the internal resistance of the cell.

asked Dec 11, 2018 by pady_1

0 answers

Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is :

asked Dec 11, 2018 by pady_1

0 answers

A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is $2.7 \times 10^3 kg/m^3$ and its Young's modulus is $9.27 \times 10^{10}$ Pa. What will be the fundamental frequency of the longitudinal vibrations?

asked Dec 11, 2018 by pady_1

0 answers

A telephonic communication service is working at carrier frequency of 10 GHz. Only 10% of it is utilized for transmission. How many telephonic channels can be transmitted simultaneously if each channel requires a bandwidth of 5 kHz?

asked Dec 11, 2018 by pady_1

0 answers

For an RLC circuit driven with voltage of amplitude $v_m$ and frequency $\omega_o = \frac{1}{\sqrt{LC}}$ the current exhibits resonance. The quality factor, Q is given by :

asked Dec 11, 2018 by pady_1

0 answers

A parallel plate capacitor of capacitance $90\; pF$ is connected to a battery of emf $20V$ . If a dielectric material of dielectric constant $K = \frac{5}{3}$ is inserted between the plates, the magnitude of the induced charge will be :

asked Dec 11, 2018 by pady_1

0 answers

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii $r_e, r_p, r_{\alpha}$ respectively in unifrom magnetic field B. The relation between $r_e, \; r_p, \; r_\alpha$ is :

asked Dec 11, 2018 by pady_1

0 answers

The reading of the ammeter for a silicon diode in the given circuit is :

asked Dec 11, 2018 by pady_1

0 answers

An electron from various excited states of hydrogen atom emit radiation of come to the ground state. Let $\lambda_n\; \lambda_g$ be the de Broglie wavelength of the electron in the $n^{th}$ state and the ground state respectively. Let $\bigwedge_{n}$ be the wavelength of the emitted photon in transition from the $n^{th}$ state to the ground state. For large $n$ (A, B are constants)

asked Dec 11, 2018 by pady_1

0 answers

Unpolarized light of intensity I passes through an ideal polarized A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be $\frac{I}{2}$ . Now another identical polarizer C is placed between A and B. The intersity beyond B is now found to be $\frac{I}{8}$ . The angle between polarizer A and C is :

asked Dec 11, 2018 by pady_1

0 answers

If the series limit frequency of the Lyman series is $v_{_L}$ , then the series limit frequency of the Pfund series is :

asked Dec 11, 2018 by pady_1

0 answers

Two masses $m_ = 5\; kg$ and $m_2 = 10 kg$ connected by an inextensible string over a frictionless pulley are moving as shown in the figure . The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of $m_2$ to stop the motion is :

asked Dec 11, 2018 by pady_1

0 answers

A particle is moving in a circular path of radius a under the action of an attractive potential $U = - \frac{k}{2r^2}$ . Its total energy is :

asked Dec 11, 2018 by pady_1

0 answers

Two batteries with e.m.f 12 V and 13 V are connected in paralled across a load resistor of $10 \Omega$ . The internal resistance of the two batteries are $1 \Omega$ and $2 \Omega$ respectively. The voltage across the load lies between :

asked Dec 11, 2018 by pady_1

0 answers

A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area a floats on the surface of the liquid, covering entire cross section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere $(\frac{dr}{r})$ is

asked Dec 11, 2018 by pady_1

0 answers

The mass of a hydrogen molecule is $3.32 \times 10^{-27} kg$ . If $10^{23}$ hydrogen molecules strike, per second, a fixed wall of area $2\;cm^2$ at an angle of $45^{\circ}$ to the normal, and rebound elastically with a speed of $10^3 m/s$ , then the pressure on the wall is nearly :

asked Dec 11, 2018 by pady_1

0 answers

It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is $p_d$ , while for its similar collision with carbon nucleus at rest, fractional loss of energy is $p_c$ . The values of $p_d$ and $p_c$ are respectively :

asked Dec 11, 2018 by pady_1

0 answers

Ask Questions, Get Answers

Let $f(x) = x^2 + \frac{1}{x^2}$ and $g(x) = x - \frac{1}{x},\; x \in R -\{-1, 0, 1\}$ . If $h(x) = \frac{f(x)}{g(x)}$ , then the local minimum value of $h(x)$ is :

A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is

If sum of all the solutions of the equation $8 \cos x. (\cos (\frac{\pi}{6} + x) . \cos (\frac{\pi}{6} - x) - \frac{1}{2}) = 1$ in $[0, \pi]$ is $k \pi$ , then $k$ is equal to :

Let $S = \{x \in R : x \geq 0$ and $2|\sqrt{x} - 3| + \sqrt{x} (\sqrt{x} - 6) + 6 = 0\}$ Then $S$ :

If the system of linear equations <br> $x+ ky + 3z=0$ <br> $3x + ky - 2z=0$ <br> $2x + 4y - 3z =0$ <br> has a non-zero solution $(x, y, z)$ , then $\frac{xz}{y^2}$ is equal to :

If the curves $y^2 = 6x, \; 9x^2 + by^2=16$ intersect each other at right angles, then the value of $b$ is :

Tangents are drawn to the hyperbola $4x^2 - y^2 = 36$ at the points P and Q. If these tangents intersect at the point $T(0,3)$ then the area (in sq. units) of $\Delta PTQ$ is :

If $\alpha, \; \beta \in C$ are the distinct roots, of the equation $x^2 - x + 1 = 0$ , then $\alpha^{101} + \beta^{107}$ is equal to :

If $L_1$ is the line of intersection of the planes $2x- 2y+ 3z - 2 =0,\; x- y + z+1=0$ and $L_2$ is the line of intersection of the planes $x+2y -z-3=0, \; 3x - y + 2z - 1=0$ , then the distance of the origin from the plane, containing the lines $L_1$ and $L_2$ , is :

If the tangent at (1, 7) to the curve $x^2 = y - 6$ touches the circle $x^2 + y^2 + 16x +12 y + c = 0$ then the value of $c$ is :

A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the $n^{th}$ power of $R$ . If the period of rotation of the particle is T, then :

Two moles of an ideal monoatomic gas occupies a volume $V$ at $27^{\circ}C$ . The gas expands adiabatically to a volume $2V$ . Calculate (a) the final temperature of the gas and (b) change in its internal energy. <br>

All the graph are intendent to represent the same motion. One of them does it incorrectly. Pick it up

In an a.c circuit, the instantaneous e.m.f and current are given by <br> $e = 100 \sin 30 t$ <br> $i = 20 \sin (30 t - \frac{\pi}{4})$ <br> In one cycle of a.c the average power consumed by the circuit and the wattless current are, respectively :

On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is $1\; K \Omega$ . How much was the resistance on the left slot before interchanging the resistances ?

The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1% the maximum error in determining the density is :

The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is $B_t$ . When the dipole moment is double by keeping the current constant, the magnetic field at the centre of loop is $B_z$ . The ratio $\frac{B_1}{B_2}$ is:

In a collinear collision, a particle with an initial speepd $v_0$ strikes a stationary particle of the same mass. If the final kinetic energy $50\%$ greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is :

From a uniform circular disc of radius R and mass 9m, a small disc of radius $\frac{R}{3}$ is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through centre of disc is : <br>

A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of $10^{12}/sec$ . What is the force constant of the bonds connecting one atom with the other? <br> (Mole wt. of silver = 108 and Avagadro number = $6.02 \times 10^{23} gm\; mole^{-1}$ )

Three concentric metal shells A, B and C of respective radii a, b and c (a < b < c) have surface charge densities $+\sigma, \; -\sigma$ and $+\sigma$ respectively. The potential of shell B is :

Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is :<br>

A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is $2.7 \times 10^3 kg/m^3$ and its Young's modulus is $9.27 \times 10^{10}$ Pa. What will be the fundamental frequency of the longitudinal vibrations?

A telephonic communication service is working at carrier frequency of 10 GHz. Only 10% of it is utilized for transmission. How many telephonic channels can be transmitted simultaneously if each channel requires a bandwidth of 5 kHz?

For an RLC circuit driven with voltage of amplitude $v_m$ and frequency $\omega_o = \frac{1}{\sqrt{LC}}$ the current exhibits resonance. The quality factor, Q is given by :

A parallel plate capacitor of capacitance $90\; pF$ is connected to a battery of emf $20V$ . If a dielectric material of dielectric constant $K = \frac{5}{3}$ is inserted between the plates, the magnitude of the induced charge will be :

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii $r_e, r_p, r_{\alpha}$ respectively in unifrom magnetic field B. The relation between $r_e, \; r_p, \; r_\alpha$ is :

The reading of the ammeter for a silicon diode in the given circuit is :

If the series limit frequency of the Lyman series is $v_{_L}$ , then the series limit frequency of the Pfund series is :

Two masses $m_ = 5\; kg$ and $m_2 = 10 kg$ connected by an inextensible string over a frictionless pulley are moving as shown in the figure . The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of $m_2$ to stop the motion is : <br>

A particle is moving in a circular path of radius a under the action of an attractive potential $U = - \frac{k}{2r^2}$ . Its total energy is :

Two batteries with e.m.f 12 V and 13 V are connected in paralled across a load resistor of $10 \Omega$ . The internal resistance of the two batteries are $1 \Omega$ and $2 \Omega$ respectively. The voltage across the load lies between :

The mass of a hydrogen molecule is $3.32 \times 10^{-27} kg$ . If $10^{23}$ hydrogen molecules strike, per second, a fixed wall of area $2\;cm^2$ at an angle of $45^{\circ}$ to the normal, and rebound elastically with a speed of $10^3 m/s$ , then the pressure on the wall is nearly :

It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is $p_d$ , while for its similar collision with carbon nucleus at rest, fractional loss of energy is $p_c$ . The values of $p_d$ and $p_c$ are respectively :