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Answers posted by pady_1
Questions
4370
answers
1
best answer
0
votes
In the circuit shown in the figure, the current $'I'$ is
answered
Nov 7, 2013
(c) 4 AMP
0
votes
The ends of an element of zinc are kept at a small temperature difference $ \Delta T$ and a small current (I) is passed through the wire. Then, the heat developed per unit time
answered
Nov 7, 2013
(a) is proportional to $\Delta\;T$ and $I$
0
votes
In the meter bridge experiment, the length AB of the wire is 1 m. The resistors $X$ and $Y$ have values $5 \Omega$ and $2 \Omega$ respectively. When a shunt resistance $S$ is connected to $X$, the balancing point is found to be $0.625\;m$ from A. Then, the resistance of the shunt is
answered
Nov 7, 2013
(b) $ 10 \Omega$
0
votes
Two metal plates of area 'A' from a parallel plate capacitor with air in between the plates. The distance between the plate is 'd'. A metal plate of thickness $\large\frac{d}{2}$ and of the same area A is inserted between the plates to from two capacitors of capacitance $C_1$ and $C_2$ as shown in the figure. If the effective capacitance of the two capacitor is $C'$ and the capacitance of the capacitor initially is $C$, then $\large\frac{C'}{C}$ is
answered
Nov 7, 2013
(b) 2
0
votes
A deflection magnetometer is adjusted and a magnet moment M is placed on it in the usual manner and the observed deflection is $\theta$. The period of oscillation of the needed before setting to the deflection is $T$. When the magnet is removed, the period of oscillation of needle is $T_0$ before settling to $0^{\circ}-0^{\circ}$. If the earth's induced magnetic field is $B_{H},$ the relation between $T$ and $T_0$ is
answered
Nov 7, 2013
$(a)\;T^2-T^2_0 \cos \theta$
0
votes
Fresnel diffraction is produced due to light rays falling on a small obstacle. The intensity of light at a point on a screen beyond an obstacle depends on
answered
Nov 7, 2013
b) the number of half-period zones that superpose at the point
0
votes
A microscope consists of an objective of focal length $1.9\;cm$ and eye piece of focal length $5\; cm$. The two lenses are kept at a distance of $10.5 \;cm.$ If the image is to be formed at the least distance of distinct vision, the distance at which the object is to be placed before the objective is (Least distance of distinct vision is 25 cm)
answered
Nov 7, 2013
(b) 2.7 cm
0
votes
The two surfaces of a concave lens, made of glass of refractive index $1.5 $ have the same radii of curvature R. It is now immersed in a medium of refractive index $1.75$ then the lens,
answered
Nov 7, 2013
(a) becomes a convergent lens of focal length $3.5\;R$
0
votes
A glass flask of volume one liter is filled completely with mercury at $0^{\circ}C$. Then flask is now heated to $100 ^{\circ} C.$ Coefficient of volume expansion of mercury is $1.82 \times 10^{-4} /^{\circ} C$ and coefficient of linear expansion of glass is $0.1 \times 10^{-4}/^{\circ} C$. During this process, amount of mercury which overflows is
answered
Nov 7, 2013
(b) 15.2 cc
0
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The terminal velocity of a liquid drop of radius 'r' falling through air is v. If two such drops are combined to form a bigger drop, the terminal velocity with which the bigger drop falls through air is ( Ignore any buoyant force due to air)
answered
Nov 7, 2013
$ (c)\;\sqrt [3] {4} \;v$
0
votes
A capillary tube of radius 'r' is immersed in water rises to a height of 'h'. Mass of water in the capillary tube is $5 \times 10^{-3}\;kg$. The same capillary tube is now immersed in a liquid whose surface tension is $\sqrt 2$ times the surface tension of water. The angle of contact between the capillary tube and this liquid is $45^{\circ}$. The mass of liquid which rises into the capillary tube now is , (in kg)
answered
Nov 7, 2013
$(a)\;5 \times 10^{-3}$
0
votes
A tension of $20 \;N$ is applied to a copper wire of cross sectional area $0.01\;cm^2$, Young's Modulus of copper is $1.1 \times 10^{11} \;N/m^2$ and Poisson's ratio is $0.32$. The decrease in cross sectional area of the wire is
answered
Nov 7, 2013
$(a)\;1.16 \times 10^{-6}\;cm^2$
0
votes
Two particles A and B of masses 'm' and '2m' are suspended from two mass less springs of force constants $K_1$ and $K_2$. During their oscillation, if their maximum velocities are equal, then ratio of amplitudes of A and B is
answered
Nov 7, 2013
$(b)\;\frac{K_2}{2K_1}$
-1
votes
The gravitational force acting on a particle, due to a solid sphere of uniform density and radius $R$, at a distance of $3R$ from the center of the sphere is $F_1$. A spherical hole of radius $(R/2)$ is now made in the sphere as shown in the figure. The sphere with hole now exerts a force $F_2$ on the same particle. Ratio of $F_1$ to $F_2$ is :
answered
Nov 7, 2013
$(a)\;\large\frac{50}{41}$
0
votes
A uniform circular disc of radius R, lying on a friction less horizontal plane is rotating with an angular velocity $\omega$ about its own axis. Another identical circular disc is gently placed on the top of the first disc coaxially. The loss in rotational kinetic energy due to friction between the two discs, as they acquire common angular velocity is (I is moment of inertia of the disc)
answered
Nov 7, 2013
$(b)\;\frac{1}{4} I \omega^2 $
0
votes
Moment of inertia of a body about an axis is $4\;kgm^2$. The body is initially at rest and a torque of $8\;Nm$ starts acting on it along the same axis. Work done by the torque in $20\;sec.$ in joules, is
answered
Nov 7, 2013
(d) 3200
0
votes
The upper half of an inclined plane with an angle of inclination $\phi$, is smooth while the lower half is rough. A body starting from rest at the top of the inclined plane comes to rest at the bottom of the inclined plane. Then the coefficient of friction for the lower half is
answered
Nov 7, 2013
(a) $2\tan \phi$
0
votes
Two bodies of mass 4 kg and 5 kg are moving along east and north directions with velocities 5 m/s and 3 m/s respectively. Magnitude of the velocity of center of mass of the system is
answered
Nov 7, 2013
$(a)\;\frac{25}{9}\; m/s$
0
votes
A mass of $2.9 $ kg is suspended from a string of length $50\; cm$ and is at rest. Another body of mass $q00 \;g$, which is moving horizontally with a velocity of $150\;m/s$ strikes and sticks to it. Subsequently when the string makes an angle of $60^{\circ}$ with the vertical, the tension in the string is $(g=10 m/s^2)$
answered
Nov 7, 2013
(b) 135 N
0
votes
A ball at rest is dropped from a height of 12 m. It looses $25 \%$ of its Kinetic energy on striking the ground and bounces back to a height 'h'. Then value of 'h' is
answered
Nov 7, 2013
(c) 9m
0
votes
Two wooden blocks of masses M and m are placed on a smooth horizontal surface as shown in figure. If a force P is applied to the system as shown in figure such that the mass m remains stationary with respect to block of mass M, then the magnitude of the force P is
answered
Nov 7, 2013
$(a)\;(M+m) g\;\tan \beta$
0
votes
A particle is projected from the ground with an initial speed of v at an angle of projection $\theta$. The average velocity of the particle between its time of projection and time it reaches highest point of trajectory is
answered
Nov 7, 2013
<div class="clay6-step-odd"><div class="clay6-image" id="pr10"...
0
votes
The work done in moving an object from origin to a point whose positiion vector is $\overrightarrow {r}=3 \hat {i}+ 2 \hat j-5 \hat k$ by a force $\overrightarrow {F}=2 \hat {i}- \hat j- \hat k$ is :
answered
Nov 7, 2013
(b) 9 units
0
votes
If $E,M,J$ and $G$ respectively denote energy , mass, angular momentum and universal gravitational constant, the quantity, which has the same dimensions as the dimension of $\large\frac{EJ^2}{M^5G^2}$
answered
Nov 7, 2013
(b) Angle
0
votes
The solution of the differential equation $\large\frac{dy}{dx}$$-2y \tan 2x =e^x\;sec 2x$ is :
answered
Nov 7, 2013
$(b)\;y \cos 2x=e^x+c$
0
votes
The approximate value of $ \int \limits_1^3 \large\frac{dx}{2+3x}$ using Simpson's Rule and dividing the interval $[1,3]$ into two equal parts is
answered
Nov 7, 2013
$(c)\;\frac{29}{110}$
0
votes
An integrating factor of the equation $(1+y+x^2y) dx +(x+x^3)dy=0$ is
answered
Nov 7, 2013
(d) x
0
votes
$\int \large\frac{dx}{x (\log x -2)(\log x-3)}$$=1+c=>1=$
answered
Nov 7, 2013
$(b)\;\log \bigg|\frac{\log x-3}{\log x-2}\bigg|$
0
votes
If $\int \limits_0^b \large\frac{dx}{1+x^2}$$=\int \limits_b^{\infty} \large \frac{dx}{1+x^2},$ then $b=$
answered
Nov 7, 2013
$(d)\;1$
0
votes
The area (in square units) bounded by the curves $x=-2y^2$ and $x=1-3y^2$ is
answered
Nov 7, 2013
$(c)\;\frac{4}{3}$
0
votes
The focal length of a mirror is given by $\large\frac{2}{f}=\frac{1}{v}-\frac{1}{u}.$ In finding the values of $u$ and $v$, the error are equal and equal to 'p'. Then, the relative error in f is
answered
Nov 7, 2013
$ (b)\;p\bigg(\frac{1}{u}+\frac{1}{v}\bigg)$
0
votes
$u=\log(x^3+y^3+z^3-3xyz)=>(x+y+z)(u_x+u_y+u_z)=$
answered
Nov 7, 2013
(d) 3
0
votes
$\int e^x \bigg(\large\frac{2+\sin 2x}{1+\cos 2x}\bigg)$$dx=$
answered
Nov 7, 2013
$(d)\;e^x \tan x +c$
0
votes
$\int \large \frac{x -\sin x}{1+ \cos x} $$ dx=x \tan \bigg(\large\frac{x}{2}\bigg)$$+p \log \bigg |\sec \bigg(\large\frac{x}{2}\bigg)\bigg |$$+c=>p=$
answered
Nov 7, 2013
(a) -4
0
votes
The relation between pressure $p$ and volume $v$ is given by $pv^{\large\frac{1}{4}}$=Constant. If the percentage decrease in volume is $\large\frac{1}{2}$, then the percentage increase in pressure is
answered
Nov 7, 2013
(c) $\frac{1}{8}$
0
votes
$\cos ^{-1} \bigg(\large\frac{y}{b} \bigg)$$=2 \log \bigg(\large\frac{x}{2}\bigg),$$ x > 0=>x^2 \large\frac{d^2y}{dx^2}$$+x \large\frac{dy}{dx}=$
answered
Nov 7, 2013
(b) -4y
0
votes
$\large\frac{d}{dx}$$ [(x+1)(x^2+1)(x^4+1)(x^8+1)]=(15x^p-16x^q+1)(x-1)^{-2}=>(p,q)=$
answered
Nov 7, 2013
(d) (16,15)
0
votes
$\sqrt {\large\frac{y}{x}}+\sqrt {\large\frac{x}{y}}$$=2=>\large\frac{dy}{dx}=$
answered
Nov 7, 2013
$(c)\;1$
0
votes
$f(x)=\large\frac{1}{1+\Large\frac{1}{x}};$$g(x)=\large\frac{1}{1+\Large\frac{1}{f(x)}}$$=>g'(2)=$
answered
Nov 7, 2013
(b) $\frac{1}{25}$
0
votes
$\lim \limits_{x \to 0} \large\frac{\tan ^3 x -\sin ^3 x}{x^5}=$
answered
Nov 7, 2013
(b) $\frac{3}{2}$
0
votes
A variable plane passes through a fixed point $(1,2,3)$. Then the foot of the perpendicular from the origin to the plane lies on
answered
Nov 7, 2013
(b) a sphere
0
votes
Let $f$ be a non-zero real valued continuous function satisfying $f(x+y)=f(x).f(y)$ for all $x,y \in R.$ If $f(2)=9,$ then $f(6)=$
answered
Nov 7, 2013
(b) $3^6$
0
votes
A plane passing through $(-1,2,3)$ and whose normal makes equal angles with the coordinate axes is
answered
Nov 7, 2013
$(c)\;x+y+z-4=0$
0
votes
The direction ratio's of two lines $AB,AC$ are $1,-1,-1$ and $2,-1,1.$ The direction ratios of the normal to the plane $ABC$ are
answered
Nov 7, 2013
(a) 2,3,-1
0
votes
The perpendicular distance from the point $(1,\pi)$ to the line joining $(1,0^{\circ})$ and $(1, \large\frac{\pi}{2}),$ (in polar coordinates) is
answered
Nov 7, 2013
(d) $\sqrt 2$
0
votes
If the foci of the ellipse $\large\frac{x^2}{25}+\frac{y^2}{16}=1$ and the hyperbola $\large\frac{x^2}{4}-\frac{y^2}{b^2}=1$ coincide, then $b^2=$
answered
Nov 7, 2013
(b) 5
0
votes
If $x=9$ is a chord of contact of the hyperbola $x^2-y^2=9,$ then the equation of the tangent at one of the points of contact is
answered
Nov 7, 2013
$(b)\;3x-2 \sqrt 2 \;y-3=0$
0
votes
The midpoint of a chord of the ellipse $x^2+4y^2-2x+20 y=0$ is $(2,-4)$. The equation of the chord is?
answered
Nov 7, 2013
<div class="clay6-step-odd"><div class="clay6-basic" id="pr10"...
0
votes
A circle of radius 4, drawn on a chord of the parabola $y^2=8x$ as diameter, touches the axis of the parabola. Then the slope of the chord is
answered
Nov 7, 2013
(c) 1
0
votes
If the circle $x^2+y^2+4x-6y+c=0$ bisects the circumference of the circle $x^2+y^2-6x+4y-12=0,$ then $c=$
answered
Nov 7, 2013
(d) -62
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