Recent questions tagged 2015

For plane electromagnetic waves propagating in the z direction , which one of the following combination gives thw correct possible direction for $\overrightarrow{E} $ and $\overrightarrow{B} $ field respectively?

asked Oct 5, 2015 by meena.p

1 answer

For the LCR circuit , shown here , the current is observed to lead the applied voltage. An additional capacitor C', when joined with the capacitor C present in the circuit , makes the power factor of the circuit unity. The capacitor C', must have been connected in :

asked Oct 5, 2015 by meena.p

1 answer

A short bar magnet is placed in the magnetic meridian of the earth with north pole pointing north. Neutral points are found at a distance of $30\;cm$ from the magnet on the East - west line, drawn through the middle point of the magnet. The magnetic moment of the magnet in $Am^2$ is close to :

asked Oct 1, 2015 by meena.p

1 answer

A wire carrying current I is tied between points P and Q and is in the shape of a circular arch of radius R due to a uniform magnetic field B (perpendicular to the place of the paper, shown by xxx) in the vicinity of the wire. If the wire subtends an angle $2 \theta$ at the center of the circle(of which it forms an arch) then the tension in the wire is :

asked Oct 1, 2015 by meena.p

1 answer

Two long straight parallel wires, carrying (adjustable) currents $I_2$ and $I_2$ are kept at a distance d apart. If the force $'F'$ between the two wires is taken as 'positive' when the wires repel each other and negative when the wires attract each other , the graph showing the dependence of $'F'$, on the product $I_1,I_2$ would be :

asked Oct 1, 2015 by meena.p

1 answer

The value of the resistor , $R_s$, needed in the dc voltage regular circuit shown here, equals :

asked Oct 1, 2015 by meena.p

1 answer

In the electric network shown, no current flows through the $4 \Omega$ resistor in the arm $EB$ , the potential difference between the points A and D will be

asked Oct 1, 2015 by meena.p

1 answer

In figure is shown a system of four capacitors connected across a $10\;V$ battery . Charge that will flow from switch S When it is closed is

asked Oct 1, 2015 by meena.p

1 answer

An electric field $ \overrightarrow{E} =(25 \hat i +30 \hat j) NC^{-1}$ exists in a region of space. If the potential at the orgin is taken to be zero then the potential at $x=2\;m,y= 2\;m$ is

asked Oct 1, 2015 by meena.p

1 answer

A wire, of length $L(=20 cm) $ is bent into a semi- circular arc. If the two equal halves , of the arc, were each to be uniformly chraged with charges [ $\pm Q, |Q|=10^{3}\; \in_0$ coulomb where $\in_0$ is the permittivity (in SI units)of free space] the net electric field at the center O of the semi circular arc would be :

asked Oct 1, 2015 by meena.p

1 answer

A source of sound emits waves at frequency $f_0$ . It is moving towards an observer with fixed speed $v_s (v_s < v$, where v is the speed $v_0$, One of the following twp graphs (A and B) will give the correct variation of the frequency f heard by the observer as $v_0$ is changed . The variation f with $v_0$ is given correctly by :

asked Oct 1, 2015 by meena.p

1 answer

A pendulum with time period of 1s is losing energy due to damping. At certain time its energy is $45\;J$. If after completing 15 oscillation , its energy has become $15\;J$ its damping constant (in $s^{-1})$ is

asked Sep 30, 2015 by meena.p

1 answer

Using equipartition of energy , the specific heat $(in Jkg^{-1}K^{-})$ of aluminium at room temperature can be estimated to be (atomic weight of aluminium = 27 )

asked Sep 30, 2015 by meena.p

1 answer

An experiment takes 10 minutes to raise the temperature of water in a container from $0^{\circ}C$ to $100^{\circ}$ and another 55 minutes to convert it totally into steam by a heater supplying heat at a uniform rate . Neglecting the specific heat at a container and taking specific heat of water to be $1\;cal/g^{\circ}C$, the heat of vaporization according to this experiment will come out to be :

asked Sep 30, 2015 by meena.p

1 answer

A beaker contains a fluid of density $\rho kg/m^3$ , specific heat $SJ/kg^{\circ}C$ and viscosity $ n$ The beaker is filled up to height h. To estimate the rate of heat transfer per unit are $(Q/A)$ by convection when beaker is put on a hot plate, a student proposes that it should depend on $n$. $\bigg(\large\frac{S \Delta \theta}{h}\bigg)$ and $\bigg(\large\frac{1}{\rho g}\bigg)$ When $\Delta \theta (in \; ^{\circ}C)$ is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for $(Q/A)$ is :

asked Sep 30, 2015 by meena.p

1 answer

A cylindrical block of wood (density $= 650 \;kg\;m^{-3} )$, of base area $30\;cm^2$ and height $54\;cm$ , floats in a liquid of density $900\;kg\;m^{-3}$. The block is depressed slightly and then released . The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length (nearly)

asked Sep 30, 2015 by meena.p

1 answer

Which of the following most closely depicts the correct variation of the gravitation potential $V_{(r)}$ due to a large planet of radius R and uniform mass density ? (figures are not drawn to scale )

asked Sep 30, 2015 by meena.p

1 answer

A particle of mass $2\;kg$ is on a smooth horizontal table and moves in a circular path of radius $0.6\;m$ The height of the table from the ground is $0.8\;m$ If the angular speed of the particle is $12 rad\;s^{-1}$ the magnitude of its angular momentum about a point on the ground right under the center of the circle is :

asked Sep 30, 2015 by meena.p

1 answer

A uniform thin rod AB of length L has linear mass density $\mu(x) =a +\large\frac{bx}{L}$, Where x is measured from A. If the CM of the rod lies at a distance of $ \bigg( \large\frac{7}{12}$$L\bigg)$ from A, then a and b are related as :

asked Sep 30, 2015 by meena.p

1 answer

A particle is moving in a circle of radius r under the action of a force $F= \alpha r^2$ which is directed towards center of the circle. Total mechanical energy (kinetic energy + potential energy ) of the particle is (take potential energy =0 for r=0):

asked Sep 30, 2015 by meena.p

1 answer

A large number (n) of identical beads, each of mass m and radius r are strung on a thin smooth rigid horizontal rod of length $L (L >> r) $ and are at rest at random positions. The rod is mounted between two rigid support (see fig) . If one of the beat is now given a speed v, the average force experienced by each support after a long time is (assume all collision are elastic ):

asked Sep 30, 2015 by meena.p

1 answer

A vector $\overrightarrow{A}$ is rotated by a small angle $\Delta \theta$ radian $\Delta \theta <1) $ to get a new vector $\overrightarrow{B}$. In that case $|\overrightarrow{B} -\overrightarrow{A}| $ is :

asked Sep 30, 2015 by meena.p

1 answer

If electronic charge e, electron mass m, speed of light in vacuum c and plank's constant h are taken as fundamental quantities , the permeability of vacuum $ \mu_0$ can be expressed in units of

asked Sep 30, 2015 by meena.p

1 answer

The contrapositive of the statement If it is raining, then I will not come, is :

asked Sep 30, 2015 by meena.p

1 answer

If $f(x)=2 \tan^{-1} x + \sin^{-1} \bigg(\large\frac{2x}{1+x^2}\bigg),$$x >1$ then $f(5) $ is equal to

asked Sep 30, 2015 by meena.p

1 answer

In a $\Delta ABC, \frac{a}{b}$$=2+\sqrt 3$ and $\angle C=60^{\circ}$. Then the ordered pair $\angle A, \angle B) $ is equal to :

asked Sep 30, 2015 by meena.p

1 answer

A factory is operating in two shifts, day and night, with 70 and 30 workers respectively. If per day mean wage of the day shift workers is Rs.54 and per day mean wage of all the workers is Rs.60, then per day mean wage of the night shift workers (in Rs) is :

asked Sep 30, 2015 by meena.p

1 answer

Let X be a set containing 10 elements and $P(X)$ be its power set. If A and B are picked up at random from $P(X)$, with replacement , then the probability that A and B have equal number of elements, is :

asked Sep 30, 2015 by meena.p

1 answer

Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two unit vectors such that $|\overrightarrow{a}+\overrightarrow{b}|=\sqrt 3 $. If $\overrightarrow{c}=\overrightarrow{a}+2 \overrightarrow{b}+3(\overrightarrow{a} \times \overrightarrow{b})$, then $2 |\overrightarrow{c}|$ is equal to :

asked Sep 30, 2015 by meena.p

1 answer

If the shortest distance between the lines $\large\frac{x-1}{\alpha } = \frac{y+1}{-1}= \frac{z}{1} $$, (\alpha \neq -1) $ and $x+y+z+1=0=2x-y+z+3 $ is $ \large\frac{1}{\sqrt 3} $, then a value of $\alpha $ is

asked Sep 30, 2015 by meena.p

1 answer

If the points $(1, 1, \lambda)$ and $(23, 0, 1)$ are equidistant from the plane, $3x+4y-12z+13=0,$ then $\lambda$ satisfies the equation :

asked Sep 30, 2015 by meena.p

1 answer

An ellipse passes through the foci of the hyperbola, $9x^2-4y^2=36$ and its major and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities of the two conics is $\large\frac{1}{2}$, then which of the following points does not lie on the ellipse ?

asked Sep 30, 2015 by meena.p

1 answer

If the tangent to the conic, $y-6=x^2$ at $(2, 10)$ touches the circle, $x^2+y^2+8x-2y=k$(for some fixed k) at a point $(\alpha, \beta)$ then $(\alpha, \beta)$ is :

asked Sep 30, 2015 by meena.p

1 answer

If $y+3x=0$ is the equation of a chord of the circle, $ x^2+y^2-30=0$, then the equation of the circle with this chord as diameter is :

asked Sep 30, 2015 by meena.p

1 answer

Let L be the line passing through the point $P(1, 2)$ such that its intercepted segment between the co-ordinate axes is bisected at P. If $L_1$ is the line perpendicular to L and passing through the point $(-2, 1),$ then the point of intersection of L and L1 is :

asked Sep 30, 2015 by meena.p

1 answer

The points $\bigg(0,\large\frac{8}{3}\bigg),$$(1,3)$ and $(82,30)$ :

asked Sep 30, 2015 by meena.p

1 answer

If y(x) is the solution of the differential equation $(x+2) \large\frac{dy}{dx}$$=x^2+4x-9, x \neq -2 $ and $y(0)=0,$ then $y(-4)$ is equal to :

asked Sep 30, 2015 by meena.p

1 answer

The area (in square units) of the region bounded by the curves $y+2x^2=0$ and $y+3x^2=1$, is equal to :

asked Sep 30, 2015 by meena.p

1 answer

For $x >0$ , let $f(x)= \int \limits_1^x \large\frac{log t}{1+t}$$dt$. Then $f(x)+f\bigg(\large\frac{1}{x}\bigg)$ is equal to:

asked Sep 30, 2015 by meena.p

1 answer

The integral $\int \large\frac{dx}{(x+1)^{3/4} (x-2)^{5/4}}$ is equal to

asked Sep 29, 2015 by meena.p

1 answer

Let the tangents drawn to the circle, $x^2+y^2=16$ from the point $P(0, h)$ meet the x-axis at points A and B. If the area of $DAPB$ is minimum, then h is equal to :

asked Sep 29, 2015 by meena.p

1 answer

If Rolles theorem holds for the function $f (x)=2x^3+bx^2+cx, x \in [-1, 1],$ at the point $x= \large\frac{1}{2}$, then $2b+c$ equals :

asked Sep 29, 2015 by meena.p

1 answer

The distance, from the origin, of the normal to the curve, $x= 2 \cos t +2 t \sin t; y=2 \sin t- 2t \cos t 2t $ at $t= \large\frac{\pi}{4}$ is :

asked Sep 29, 2015 by meena.p

1 answer

$\lim \limits _{x \to 0} \large\frac{e^{x^2}-\cos x}{\sin ^2 x}$ is equal to

asked Sep 29, 2015 by meena.p

1 answer

The value of $ \sum _{r=16} ^{30} (r+2)(r-3)$ s equal to

asked Sep 29, 2015 by meena.p

1 answer

If the coefficients of the three successive terms in the binomial expansion of $(1+x)^n$ are in the ratio $1 : 7 : 42$, then the first of these terms in the expansion is :

asked Sep 29, 2015 by meena.p

1 answer

Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is :

asked Sep 29, 2015 by meena.p

1 answer

The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is :

asked Sep 29, 2015 by meena.p

1 answer

If $A=\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}$ then which one of the following statements is not correct ?

asked Sep 29, 2015 by meena.p

1 answer

The least value of the product xyz for which the determinant $\begin{bmatrix}x & 1 & 1\\1 & y & 1\\1 & 1 & z\end{bmatrix}$ is non-negative , is :

asked Sep 29, 2015 by meena.p

1 answer

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