Recent questions tagged 2009

In the Young's double slit experiment, the intensities at two points $P_1$ and $P_2$ on the screen are respectively $I_1$ and $I_2$. If $P_1$ is located at the center of a bright fringe and $P_2$ is located at a distance equal to a quarter of fringe width from $P_1$, then $I_1/I_2$ is :

asked Oct 11, 2013 by meena.p

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Two identical piano wires have a fundamental frequency of 600 c/s when kept under the same tension. What fractional increase in the tension of one wire will lead to the occurrence of 6 beats per second when both wires vibrate simultaneously?

asked Oct 11, 2013 by meena.p

1 answer

Two sources A and B are sending notes of frequency $680\;Hz.$ A listener moves from A to B with a constant velocity 'u'. If the speed of sound in air is $340 ms^{-1}$, What must be the value of $'u'$ so that he hears 10 beats per second?

asked Oct 11, 2013 by meena.p

1 answer

Three rods of same dimensions have thermal conductivities 3K,2K and K. They are arranged as shown in the figure below:

asked Oct 11, 2013 by meena.p

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Two cylinders 'A'and 'B' fitted with pistons contain equal number of moles of an ideal mono-atomic gas at $400\;K$. The piston of 'A' is free to move while that of 'B' is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in 'B' is :

asked Oct 11, 2013 by meena.p

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An ideal gas is subjected to a cyclic process involving four thermodynamic states; the amounts of heat (Q) and work (W) involved in each of these stated are :$Q_1=6000\;J,Q_2=-5500; Q_3=-3000\;Q_4=3500\;J: W_1=2500\;J;W_2=-1000\;J;W_3=-1200\;J;W_4=xJ$. The ratio of the net work done by the gas to the total heat absorbed by the gas is $'\eta$. The values of x and $\eta$ respectively are:

asked Oct 11, 2013 by meena.p

1 answer

An ideal gas is subjected to a cyclic process ABCD as depicted in the P-V diagram given below :

asked Oct 11, 2013 by meena.p

1 answer

A piece of metal weights 45 gms in air and 25 gms in a liquid of density $1.5 \times 10^3kg-m^{-3}$ kept at $30^{\circ}C. $ When the temperature of the liquid of density $1.5 \times 10^3\;kg-m^{-3}$ kept at $30^{\circ}C$. When the temperature of the liquid is raised to $40^{\circ}$, the metal piece weight 27 gms. The density of liquid at $40^{\circ}C$ is $1.25 \times 10^3\;kg-m^{-3}.$ The coefficient of linear expansion of metal is :

asked Oct 11, 2013 by meena.p

1 answer

A clock pendulum made of invar has a period of $0.5$ sec at$20^{\circ}$. If the clock is used in a climate where the temperature averages to $30^{\circ}C,$ how much time does the clock lose in each oscillation? (for invar, $\alpha=9 \times 10^{-7}/^{\circ}C,g= constant )$

asked Oct 11, 2013 by meena.p

1 answer

Eight spherical rain drops of the same mass and radius are falling down with a terminal speed of $6\;cm-s^{-1}$. If they coalesce to form one big drop, what will be the terminal speed of bigger drop? (Neglect the buoyancy of the air )

asked Oct 11, 2013 by meena.p

1 answer

A soap bubble of radius r is blown up to from a bubble of radius 2r under isothermal conditions. If T is the surface tension of soap solution, the energy spent in the blowing :

asked Oct 11, 2013 by meena.p

1 answer

If the ratio of lengths, radii and Young's moduli of steel and brass wires shown in the figure are a,b and c respectively, the ratio between the increase in lengths of brass and steel wires would be :

asked Oct 11, 2013 by meena.p

0 answers

The displacement of a particle executing SHM is given by : $y= 5 \sin \bigg(4t+\large\frac{\pi}{3}\bigg).$ If T is the time period and the mass of the particle is $2 gms$, the kinetic energy of the particle when $t= \large\frac{T}{4}$ is given by :

asked Oct 11, 2013 by meena.p

1 answer

A body is projected vertically upwards from the surface of the earth with a velocity equal to half the escape velocity. If R is the radius of the earth , maximum height attained by the body from the surface of the earth is :

asked Oct 11, 2013 by meena.p

1 answer

A particle of mass 4 m explodes into three pieces of masses $m, m $ and $2m$. The equal masses move along X and Y axes with velocities $4 ms^{-1}$ and $6\;ms^{-1}$ respectively. The magnitude of the velocity of the heavier mass is :

asked Oct 11, 2013 by meena.p

1 answer

A body of mass 5 kg makes an elastic collision with another body at rest and continues to move in the original direction after collision direction after collision with a velocity equal to $\large\frac{1}{10}$th of its original velocity. Then the mass of the second body is :

asked Oct 11, 2013 by meena.p

1 answer

A motor of power $P_0$ is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe $n$ times, the power of the motor is insreased to $P_1$. The ratio of $P_1$ to $P_0$ is :

asked Oct 11, 2013 by meena.p

1 answer

A particle is projected up from a point at an angle $\theta$ with the horizontal direction. At any time $'t'$, if p is the linear momentum , y is the vertical displacement ,'x' is horizontal displacement , the graph among the following which does not represent the variation of kinetic 'k' of the particle is:

asked Oct 11, 2013 by meena.p

1 answer

A body is projected vertically upwards at time $t=0$ and it is seen at a height $'H'$ at time $t_1$ and $t_2$ seconds during its flight. The maximum height attained is : (g is acceleration due to gravity)

asked Oct 11, 2013 by meena.p

1 answer

When a wave traverses a medium , the displacement of a particle located at $'x'$ at a time $'t'$ is given by $y=a \sin (bt-cx), where a,b and c are constants of the wave, which of the following is a quantity with dimensions?

asked Oct 11, 2013 by meena.p

1 answer

The differential equation of the family $y=ae^x+bx\; e^x+cx^2\;e^x$ of curves, where $a,b,c$ are arbitrary constants, is :

asked Oct 11, 2013 by meena.p

1 answer

The solution of the differential equation $\large\frac{dy}{dx}$$=\sin (x+y) \tan (x+y)-1$ is :

asked Oct 11, 2013 by meena.p

1 answer

The velocity of a particle which starts from rest is given by the following table :

asked Oct 10, 2013 by meena.p

1 answer

The line $x= \large\frac{\pi}{4}$ divides the area of the region bounded by $y=\sin x, y= \cos x$ and x-axis $\bigg(0 \leq x \leq \large\frac{\pi}{2}\bigg)$ into two regions of areas $A_1$ and $A_2$. Then $A_1 : A_2=$

asked Oct 10, 2013 by meena.p

0 answers

$\int \limits_0^\pi \large\frac{1}{1+\sin x}$$dx$

asked Oct 10, 2013 by meena.p

1 answer

If $I_n=\int \sin ^n x dx $, then $n\; I_n-(n-1)I_{n-2}$=

asked Oct 10, 2013 by meena.p

1 answer

$\int \bigg(\large\frac{2 -\sin 2x}{1-\cos 2x}\bigg)$$e^x dx=$

asked Oct 10, 2013 by meena.p

1 answer

$\int \large\frac{dx}{(x+1)\sqrt {4x+3}}=$

asked Oct 10, 2013 by meena.p

1 answer

$z=\tan (y+ax)+\sqrt {y-ax}=> z_{xx}-a^2z_{yy}=$

asked Oct 10, 2013 by meena.p

1 answer

The maximum value of $\large\frac{\log x}{x}$$,0 < x < \infty$ is :

asked Oct 10, 2013 by meena.p

1 answer

The function $f(x) =x^3+ax^2+bx+x, a^2 \leq 3b$ has:

asked Oct 10, 2013 by meena.p

1 answer

There is an error of $\pm 0.04\;cm$ in the measurement of the diameter of a sphere. When the radius is $10\;cm$, the percentage error in the volume of the sphere is :

asked Oct 10, 2013 by meena.p

1 answer

$y=e^{a \sin ^{-1}x}=>(1-x^2)y_{n+2}-(2n+1)xy_{n+1}=$

asked Oct 10, 2013 by meena.p

1 answer

$\large\frac{d}{dx}$$ \bigg[a \tan ^{-1} + b \log \bigg(\large\frac{x-1}{x+1}\bigg)\bigg]=\frac{1}{x^4-1}$$=>a-2b=$

asked Oct 10, 2013 by meena.p

1 answer

$x= \cos ^{-1} \bigg(\large\frac{1}{\sqrt {1+t^2}}\bigg),$$y= \sin ^{-1} \bigg(\large\frac{t}{\sqrt {1+t^2}}\bigg)=>\frac{dy}{dx}=$

asked Oct 10, 2013 by meena.p

1 answer

$x= \large\frac{1-\sqrt y}{1+\sqrt y}=>\large\frac{dy}{dx}=$

asked Oct 10, 2013 by meena.p

0 answers

If $f:R \to R$ is defined by $f(x) = \left\{ \begin{array}{l l} \frac{2 sin x-\sin 2x}{2x \cos x}, & \quad if \;x \neq 0 \\ a, & \quad if \; x =0 \end{array} \right. $ then the value of $a$ so that f is continuous at 0 is :

asked Oct 10, 2013 by meena.p

1 answer

$\lim \limits _{x \to \infty} \bigg(\large\frac{x+5}{x+2}\bigg)^{x+3}=$

asked Oct 10, 2013 by meena.p

1 answer

The radius of the sphere $x^2+y^2+z^2=12 x +4y+3z$ is :

asked Oct 10, 2013 by meena.p

1 answer

The image of the point $(3,2,1)$ in the plane $2x-y+3z=7$ is :

asked Oct 10, 2013 by meena.p

1 answer

If a line in the space makes angles $\alpha, \beta$ and $\gamma$ with the coordinate axes, then $ \cos 2 \alpha+ \cos 2 \beta+\cos 2 \gamma +\sin ^2 \alpha +\sin ^2 \beta+\sin ^2 \gamma=$

asked Oct 10, 2013 by meena.p

1 answer

The perimeter of the triangle with vertices at $(1,0,0),(0,1,0)$ and $(0,0,1)$ is :

asked Oct 10, 2013 by meena.p

1 answer

The eccentricity of the conic $\large\frac{5}{r}$$=2 + 3 \cos \theta+ 4 \sin \theta$ is :

asked Oct 10, 2013 by meena.p

1 answer

The mid point of the chord $4x-3y=5$ of the hyperbola $2x^2-3y^2=12$ is :

asked Oct 10, 2013 by meena.p

1 answer

If the circle $x^2+y^2=a^2$ intersects the hyperbola $xy=c^2$ in four points $(x_i,y_i),$ for $i=1,2,3$ and $4$, then $y_1+y_2+y_3+y_4=$

asked Oct 10, 2013 by meena.p

1 answer

If the distance between the foci of an ellipse is 6 and the length of the minor axis is 8, then the eccentricity is :

asked Oct 10, 2013 by meena.p

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The number of normals drawn to the parabola $y^2=4x$ from the point (1,0) is :

asked Oct 10, 2013 by meena.p

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The equation of the circle which passes through the origin and cuts orthogonally each of the circles $x^2+y^2-6x+8=0$ and $x^2+y^2-2x-2y=7$ is :

asked Oct 10, 2013 by meena.p

1 answer

The points (3,-4) lies on both the cirlces $x^2+y^2-2x+8y+13=0$ and $x^2+y^2-4x+6y+11=0.$ Then the angle between the circles is :

asked Oct 10, 2013 by meena.p

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The diameter of a circle are along $2x+y-7=0$ and $x+3y-11=0$. Then, the equation of this circle, Which also passes through (5,7) is :

asked Oct 10, 2013 by meena.p

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