Recent questions tagged 2010

The frequency of vibration magnetometer of the combination of two bar magnets of magnetic moments $M_1$ and $M_2$ is 6 Hz When like poles are tied and it is 2 Hz when the unlike poles are tied together , then the ratio $M_1 : M_2 $ is :

asked Sep 30, 2013 by meena.p

1 answer

Two coherent sources whose intensity ratio is $64 :1 $ produce interference fringes. The ratio of intensities of maxima and minima is :

asked Sep 30, 2013 by meena.p

1 answer

The distance between field lens and eye lens in Ramsden eyepiece is $4 cm$. Then, the distance of the cross-wires from the eye lens is :

asked Sep 30, 2013 by meena.p

1 answer

A ray of light passes through an equilateral prism such that the angle of incidence is equal to the angle of emergence and each one is equal to $\large\frac{3}{4}$ th the angle of prism. Then angle of deviation is :

asked Sep 30, 2013 by meena.p

2 answers

In an optical fibre, core and cladding were made with materials of refractive indices 1.5 and 1.414 respectively . To observe total internal reflection , what will be the range of incident angle with the axis of optical fibre?

asked Sep 30, 2013 by meena.p

1 answer

A sonometer wire has a length of $114$ cm, between two fixed ends. Where should two bridges be placed so as to divide the wire into three segments (in cm) whose fundamental frequencies are in the ratio 1 : 3 : 4 ?

asked Sep 30, 2013 by meena.p

2 answers

An organ pipe $P_1$, closed at one end and containing a gas of density $\rho _1 $ is vibrating in its first harmonic. Another organ pipe $P_2$, open at both ends and containing a gas of density $\rho_2$ is vibrating in its third harmonic . Both the pipes are in resonance with a given tuning fork. If the compressibility of gases is equal in both pipes, the ratio of the lengths of $P_1$ and $P_2$ is (assume the given gases to be monoatomic):

asked Sep 30, 2013 by meena.p

1 answer

Three rods AB,BC and BD made of the same material and having the same cross- section have been joined as shown in the figure. The ends A,C and D are held at temperatures of $20^{\circ},80^{\circ}$ and $80^{\circ}$ respectively. If each rod is of smme length, then the temperature at the junction B of the three rods is :

asked Sep 30, 2013 by meena.p

1 answer

3 moles of an ideal monatomic gas performs $ABCDA$ cyclic process as shown in figure below. The gas temperatures are $T_A=400\;K,T_B=800\;K,T_C=2400\;K,$ and $ T_D=1200\;K$. the work done by the gas is (approximately) $(R= 8.314\;J/mole K)$:

asked Sep 30, 2013 by meena.p

1 answer

An ideal gas expands isothermally from volume $V_1$ to volume $V_2$. It is then compressed to the original volume $V_1$ adiabatically.If $P_1,P_2$ and W represent the initial pressure, final pressure and the net work done by the gas respectively during the entire process, then:

asked Sep 30, 2013 by meena.p

1 answer

Three rods of equal lengths are joined to form an equilateral triangle ABC. D is the mid-point of AB. The coefficient of linear expansion is $\alpha _1$ for material of rod $AB$ and $\alpha _2$ for material of rods $AC$ and $BC$. If the distance $DC$ remains constant for small changes in temperature, then:

asked Sep 30, 2013 by meena.p

1 answer

A bimetallic strip is formed out of two identical strips, One of copper and the other of brass. The coefficients of linear expansion of the two metals are $ \alpha _C$ and $\alpha_{B}.$ On heating, the temperature of the strips increases by $\Delta T$ and the strip bend to from an arc of radius R. Then R is proportional to :

asked Sep 30, 2013 by meena.p

1 answer

Water from a tap emerges vertically downwards with initial velocity $4\;ms^{-1}$. The cross- sectional area of the tap is A. The flow is steady and pressure is constant throughout the stream of water. The distance h vertically below the tap, where the cross- sectional area of the stream becomes $\bigg(\large\frac{2}{3}\bigg)A,$ is $(g=10\; m/s^2)$:

asked Sep 30, 2013 by meena.p

1 answer

The excess pressure inside a spherical soap bubble of radius 1 cm is balanced by a column of oil $(Sp.gr=0.8),2$ mm high, the surface tension of the bubble is :

asked Sep 30, 2013 by meena.p

1 answer

Match the following:

asked Sep 30, 2013 by meena.p

1 answer

The displacements of two particles of same mass executing $SHM$ are represented by the equations $x_1=4 \sin \bigg[10t+\large\frac{\pi}{6}\bigg]$ and $x_2=5 \; \cos(\omega t)$. The value of $\omega$ for which the energy of both the particles remain same is :

asked Sep 30, 2013 by meena.p

1 answer

A launching vehicle carrying an artificial satellite of mass 'm'is set for launch on the surface of the earth of mass 'M' and radius 'R'. If the satellite is intended to move in a circular orbit of radius 7R, the minimum energy required to be spent by the launching vehicle on the satellite is : (Gravitational constant =G)

asked Sep 30, 2013 by meena.p

1 answer

A fly -wheel of mass 25 kg has a radius of $0.2\;m$. It is making 240 rpm. What is the torque necessary to bring to rest in 20 sec?

asked Sep 30, 2013 by meena.p

1 answer

The moment of inertia of a disc, of mass M and radius R, about an axis which is a tangent and to its diameter is :

asked Sep 30, 2013 by meena.p

1 answer

An object takes n times as much as to slide down a $45^{\circ}$ rough inclined plane as it takes to slide down a perfectly smooth inclined plane of the same inclination. The coefficient of kinetic friction between the object and the rough incline is given by :

asked Sep 30, 2013 by meena.p

1 answer

A ball falls from a height h and rebounds after striking the floor. The coefficient of restitution is $e$. The maximum distance covered before it comes to rest is :

asked Sep 30, 2013 by meena.p

1 answer

A bady of mass $M_1=4 kg$ moves at $ 5 \hat i$ m/s and another body of mass $m_2=2 kg$ moves at $10 \hat i$m/s. The kinetic energy of center of mass is :

asked Sep 30, 2013 by meena.p

1 answer

A bomb moving with velocity $ (40 \hat i+50 \hat j -25 \hat k)$m/sec explode into two pieces of mass ratio 1:4. After explosion the small piece moves away with velocity $(200 \hat i+70 \hat j+15 \hat k)$ m/sec. The velocity of larger piece after explosion is :

asked Sep 30, 2013 by meena.p

1 answer

A ball is falling from a height . When it reaches 10 m height from the ground its velocity is $V_0$. It collides with the ground and loses $50 \%$ of its energy and rises back to height of 10 m. Then the velocity $V_0$ is :

asked Sep 30, 2013 by meena.p

1 answer

An athlete completes one round of a circular track of radius R in 40 sec. What will be his displacement at the end of 2 min 20 seconds?

asked Sep 30, 2013 by meena.p

1 answer

A and B are two vectors f equal magnitude and $\theta$ is the angle between them. The angle between $\overrightarrow A$ or $\overrightarrow B$ with their resultant is :

asked Sep 29, 2013 by meena.p

1 answer

If the force is given by $F= at +bt^2$ with t as time. The dimensions of a and b are :

asked Sep 29, 2013 by meena.p

1 answer

A family of curves has the differential equation $xy \large\frac{dy}{dx}$$=2y^2-x^2$. Then the family of curves is :

asked Sep 29, 2013 by meena.p

1 answer

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

asked Sep 29, 2013 by meena.p

1 answer

The values of a function $f(x)$ at different values of x are as follows: $x : \; 0\; 1\; 2\; 3\; 4\; 5\; \qquad f(x):\; 2\; 3 \; 6\; 11\; 18\; 27$ Then the approximate area (in square units) bounded by the curve $y=f(x)$ and X-axis between $x=0$ and 5, using Trapezoidal rule, is :

asked Sep 29, 2013 by meena.p

1 answer

The area ( in square units) of the region enclosed by the two circles $x^2+y^2=1$ and $(x-1)^2+y^2=1$ is :

asked Sep 29, 2013 by meena.p

1 answer

IF $I_n=\int \limits_0^{\frac{\pi}{4}} \tan ^n x dx, $ then $I_2+I_4, I_3+I_5,I_4+I_6,$......... are in :

asked Sep 29, 2013 by meena.p

1 answer

$\int (1- \cos x) cosec^2 x dx =f(x)+c=>f(x)=$

asked Sep 29, 2013 by meena.p

0 answers

If $f_n(x)=\log \;\log\; \log\;......... \log\;x$ ($\log$ is repeated n-times ), then $\int ( x f_1(x)f_2(x).......f_n(x))^{-1}dx=$

asked Sep 29, 2013 by meena.p

1 answer

$\int \large\frac{7x^8+8x^7}{(1+x+x^8)^2}dx$$=f(x)+c => f(x)=$

asked Sep 27, 2013 by meena.p

1 answer

$u= \sin ^{-1} \bigg(\large\frac{x^4+y^4}{x+y}\bigg)$$=> x \large\frac{du}{dx}$$+y \frac{du}{dy}=$

asked Sep 27, 2013 by meena.p

1 answer

A variable triangle ABC is inscribed in a circle of diameter in a circle of diameter x units. At a particular instant, the rate of change in side a is $\large\frac{x}{2}$ times the rate of change in its opposite angle A. Then A=

asked Sep 27, 2013 by meena.p

1 answer

The longest distance of the point $(a,0)$ from the curve $2x^2+y^2=2x$ is :

asked Sep 27, 2013 by meena.p

1 answer

The height of the cone of maximum volume inscribed in a sphere of radius R is :

asked Sep 27, 2013 by meena.p

1 answer

$ y= \sin (m \sin ^{-1} x) =>(1-x^2)y_2-xy_1= $ (Here $y_n$ denotes $\large\frac{d^ny}{dx^n}$)

asked Sep 27, 2013 by meena.p

1 answer

$f(x) = \sin x + \cos x=>f(x)=> f \bigg(\large\frac{\pi}{4}\bigg) $$ f^{(iv)} \bigg (\large\frac{\pi}{4}\bigg)=$

asked Sep 27, 2013 by meena.p

1 answer

$y= \cos ^{-1}\bigg[\large\frac{a^2-x^2}{a^2+x^2}\bigg]+ \sin ^{-1} \bigg[\large\frac{2ax}{a^2+x^2}\bigg]=>\frac{dy}{dx}=$

asked Sep 27, 2013 by meena.p

1 answer

$f(x)=(\cos x) (\cos 2x).........( \cos nx) => f'(x)+ \sum \limits _{r=1} ^ n (r \tan rx) f(x)=$

asked Sep 27, 2013 by meena.p

1 answer

If $f :R \to R$ defined by $f(x)= \left\{ \begin{array}{1 1} \frac{1+3x^2-\cos 2x}{x^2}, & \quad for\; x \neq 0 \\ k & \quad for \; x=0 \end{array}. \right. $ is continuous at x=0, then k=

asked Sep 27, 2013 by meena.p

1 answer

$\lim \limits_{x \to x} \large\frac{\tan x -\sin x}{x^2}=$

asked Sep 27, 2013 by meena.p

1 answer

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

asked Sep 27, 2013 by meena.p

1 answer

A plane meets the coordinate axes at A,B,C so that the centroid of the triangle ABC is (1,2,4). Then the equation of the plane is :

asked Sep 27, 2013 by meena.p

1 answer

If $\alpha, \beta,\gamma$ are the roots of the equation $x^3-6x^2+11x-6=0$ and if $a= \alpha ^2+\beta^2+\gamma^2, \;b= \alpha \beta + \beta \gamma+ \gamma \alpha$ and $ c= (\alpha+\beta)(\beta+\gamma)(\gamma+\alpha),$ then the correct inequality among the following is :

asked Sep 27, 2013 by meena.p

1 answer

The point dividing the join of $(3,-2,1)$ and $(-2,3,11)$ in the ratio $2:3$ is:

asked Sep 27, 2013 by meena.p

1 answer

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

asked Sep 27, 2013 by meena.p

1 answer

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