Recent questions tagged 2007

A parallel plate condenser with a dielectric of dielectric constant $K$ between the plates has a capacity $C$ and is charged to a potential $V$ volts. The dielectric slab is slowly removed from between the plates and then reinserted. The network done by the system in this process is:

asked Nov 29, 2018 by pady_1

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The resistance of a wire is $5 \Omega$ at $50^{\circ}C$ and $6 \Omega$ at $100^{\circ} C$. The resistance of the wire at $0^{\circ} C$ will be :

asked Nov 29, 2018 by pady_1

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Two identical conducting wires AOB and COD are placed at right angles to each other. The wire AOB carries an electric current $I_1$ and COD carries a current $I_2$. The magnetic field on a point lying at a distance d from O, in a direction perpendicular to the plane of the wires AOB and COD, will be given by :

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A charged particle moves through a magnetic field perpendicular to its direction. Then :

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If $C_P$ and $C_V$ denote the specific heats of nitrgen per unit mass at constant pressure and constant volume respectively, then :

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A sound absorber attenuates the sound level by 20 dB. The intensity decreases by a factor of :

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One end of a thermally insulated rod is kept at a temperature $T_1$ and the other at $T_2$. The rod is composed of two section of length $l_1$ and $l_2$ and thermal conductivities $K_1$ and $K_2$ respectively. The temperature at the interface of the two sections is

asked Nov 29, 2018 by pady_1

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Two lenses of power -15D and +5D are in contact with each other. The focal length of the combination is :

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A block of mass m is connected to another block of mass M by a spring (massless) of spring constant k. The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force F starts acting on the block of mass M to pull it. Find the force on the block of mass m.

asked Nov 29, 2018 by pady_1

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Which of the following transitions in hydrogen atoms emit photons of highest frequency ?

asked Nov 29, 2018 by pady_1

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The potential at a point $x$ (measured in $\mu m$) due to some charges situated on the $x$-axis is given by : $V(x) = 20/(x^2 - 4)$ volt The electric field $E$ at $x=4 \mu m$ is given by :

asked Nov 29, 2018 by pady_1

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A charged particle with charge q enters a region of constant, uniform and mutually orthogonal fields $\overrightarrow{E}$ and $\overrightarrow{B}$ with a velocity $\overrightarrow{v}$ perpendicular to both $\overrightarrow{E}$ and $\overrightarrow{B}$, and comes out without any change in magnitude or direction of $\overrightarrow{v}$. Then :

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Carbon, silicon and germanium have four valence electrons each. At room temperature which one of the following statements is most appropriate ?

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A Carnot engine, having an efficiency of $\eta = 1/10$ as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is :

asked Nov 29, 2018 by pady_1

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The half-life period of a radioactive element X is same as the mean life time of another radioactive element Y. Initially they have the same number of atoms. Then :

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Charges are placed on the vertices of a square as shown. Let $\overrightarrow{E}$ be the electric field and $V$ the potential at the centre. If the charges on A and B are interchanged with those on D and C respectively, then :

asked Nov 29, 2018 by pady_1

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A point mass oscillates along the $x$-axis according to the law $x=x_0 \cos (\omega t - \pi/4)$. If the acceleration of the particle is written as : $a = A \cos (\omega t + \delta)$, then :

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For the given uniform square lamina ABCD, whose centre is O :

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The velocity of a particle is $\nu = \nu_{_0} + gt = ft^2$. If its position is $x=0$ at $t=0$, then its displacement after unit time $(t=1)$ is :

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Photon of frequency $\nu$ has a momentum associated with it. If $c$ is the velocity of light, the momentum is :

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If in a $p-n$ junction diode, a square input signal of 10 V is applied as shown : Then the output signal across $R_L$ will be :

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In gamma ray emission from a nucleus:

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If $M_o$ is the mass of an oxygen isotope $_8O^{17}, M_p$ and $M_n$ are the masses of a proton and a neutron respectively, the nuclear binding energy of the isotope is :

asked Nov 29, 2018 by pady_1

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A current $I$ flows along the length of an infinitely long, straight, thin walled pipe. Then :

asked Nov 29, 2018 by pady_1

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A long straight wire of radius $a$ carries a steady current $i$. The current is uniformly distributed across its cross-section. The ratio of the magnetic field at $\frac{a}{2}$ and $2a$ is :

asked Nov 29, 2018 by pady_1

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An ideal coil of 10 H is connected in series with a resistance of $5 \Omega$ and a battery of $5 V$. 2 s after the connection is made, the current flowing ( in ampere) in the circuit is :

asked Nov 29, 2018 by pady_1

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A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be :

asked Nov 29, 2018 by pady_1

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An electric charge $10^{-3} \mu C$ is placed at the origin (0, 0) of X-Y coordinate system. Two points A and B are situated at $(\sqrt{2}, \sqrt{2})$ and $(2, 0)$ respectively. The potential difference between the points A and B will be :

asked Nov 29, 2018 by pady_1

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In an AC circuit the voltage applied is $E= E_0 \sin \omega t$. The resulting current in the circuit is $I = I_0 \sin (\omega t - \frac{\pi}{2})$. The power consumption in the circuit is given by :

asked Nov 29, 2018 by pady_1

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The displacement of an object attached to a spring and executing simple harmonic motion is given by $x = 2 \times 10^{-2} \cos \pi t \; metre$. The time at which the maximum speed first occurs is :

asked Nov 29, 2018 by pady_1

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If the difference between the roots of the equation $x^2 + ax + 1 = 0$ is less than $\sqrt{5}$, then the set of possible values of $a$ is :

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The area enclosed between the curves $y^2 = x$ and $ y = |x|$ is :

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$\int \frac{dx}{\cos x + \sqrt{3} \sin x}$ equals :

asked Nov 29, 2018 by pady_1

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The solution for $x$ of the equation $\begin{align}\int_{\sqrt{2}}^x \; \; \frac{dt}{t \sqrt{t^2 -1}} = \frac{\pi}{2} \end{align}$ is :

asked Nov 29, 2018 by pady_1

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The function $f : R / \{0\} \to R$ given by $ f(x) = \frac{1}{x} - \frac{2}{e^{2x} -1}$ can be made continuous at $x=0$ by defining $f(0)$ as :

asked Nov 29, 2018 by pady_1

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Let $f: R\to R$ be a function defined by $f(x) = min \{ x + 1, |x| + 1\}$. Then which of the following is true ?

asked Nov 29, 2018 by pady_1

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Let $F(x) = f(x) + f (\frac{1}{x}), f(x) = \int_1^x \frac{ \log t}{1 + t} dt$. Then $F(e)$ equals :

asked Nov 29, 2018 by pady_1

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If one of the lines of $my^2 + (1 - m^2) xy - mx^2 = 0 $ is a bisector of the angle between the lines $xy = 0$, then $m$ is :

asked Nov 29, 2018 by pady_1

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Let P = (-1, 0), Q = (0, 0) and R = (3, 3$\sqrt{3}$) be three points. The equation of the bisector of the angle PQR is :

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Let $A(h, k), B(1, 1)$ and $C(2, 1)$ be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1, then the set of values which $'k'$ can take is given by :

asked Nov 29, 2018 by pady_1

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Let $\overrightarrow{a} = \hat{i} + \hat{j} + \hat{k}, \overrightarrow{b} = \hat{i} - \hat{j} + 2 \hat{k}$ and $\overrightarrow{c} = x \hat{i} + ( x - 2)\hat{j} - \hat{k}$. If the vector $\overrightarrow{c}$ lies in the plane of $\overrightarrow{a}$ and $\overrightarrow{b}$, then $x$ equals :

asked Nov 29, 2018 by pady_1

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If (2, 3, 5) is one end of a diameter of the sphere $x^2 + y^2 + z^2 - 6x - 12 y - 2 z + 20 = 0 $, then the coordinates of the other end of the diameter are :

asked Nov 29, 2018 by pady_1

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The equation of a tangent to the parabola $y^2 = 8x$ is $ y = x + 2$. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is :

asked Nov 29, 2018 by pady_1

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The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is :

asked Nov 29, 2018 by pady_1

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A particle just clears a wall of height b at a distance $a$ and strikes the ground at a distance $c$ from the point of projection. The angle of projection is :

asked Nov 29, 2018 by pady_1

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If $\hat{u}$ and $\hat{v}$ are unit vectors and $\theta$ is the acute angle between them, then $ 2 \hat{u} \times 3 \hat{v}$ is a unit vector for :

asked Nov 29, 2018 by pady_1

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The sum of the series $\frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} - ...$ upto infinity is :

asked Nov 29, 2018 by pady_1

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Let $ A = \begin{bmatrix} 5 & 5 \alpha & \alpha \\\ 0 & \alpha & 5 \alpha \\ 0 & 0 & 5 \end{bmatrix}$ If $|A^2| = 25$, then $|\alpha|$ equals :

asked Nov 29, 2018 by pady_1

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The function $f(x) = \tan^{-1} (\sin x + \cos x) $ is an increasing function in :

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A value of C for which the conclusion of Mean Value Theorem holds for the function $f(x) = \log_e x $ on the interval $[1,3]$ is :

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