Recent questions tagged past papers

A liquid of mass $M$ and specific heat $S$ is at temperature $2t$. If another liquid of thermal capacity $1.5$ times at a temperature of $\frac{t}{3}$ is added to it, the resultant temperature will be :

asked Dec 19, 2018 by pady_1

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When heat energy of $1500 \;J$ is suplied to a gas at constant pressure, $2.1 \times 10^5\; N/m^2$, there was an increase in its volume equal to $2.5 \times 10^{-3}m^3$. The increase in its internal energy in joules is :

asked Dec 19, 2018 by pady_1

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For a perfect gas, if $\alpha, \; \beta$ are the volume and pressure coefficients of expansions, then :

asked Dec 19, 2018 by pady_1

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If on heating liquid through $80^{\circ}C$, the mass expelled is $\begin{pmatrix} \frac{1}{100} \end{pmatrix}^{th}$ of mass still remaining, the coefficient of apparent expansion of liquid is :

asked Dec 19, 2018 by pady_1

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In a compensated pendulum two rods of different metals are used with their lengths in ratio of $2:3$. The coefficients of linear expansions for metals in the ratio is :

asked Dec 19, 2018 by pady_1

1 answer

When a cylindrical tube is dipped vertically into a liquid then the angle of contact is $140^{\circ}$, if the tube is dipped, with an inclination of $40^{\circ}$ then angle of contact is :

asked Dec 19, 2018 by pady_1

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The elongation of a steel wire stretched by a force is $e$. If a wire of the same material of double the length, and half the diameter is subjected to double the force, its elongation will be :

asked Dec 19, 2018 by pady_1

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Two simple pendulums of lengths $16 l$ and $l$ are in phase at the mean position at a certain time. If $T$ is the time period of shorter pendulum, the minimum time after which they will be again in phase :

asked Dec 19, 2018 by pady_1

1 answer

The maximum velocity of a particle executing SHM is $v$. If the amplitude is doubled and the time period of oscillation decreased to $\frac{1}{3}$ of its original value, the max velocity becomes :

asked Dec 19, 2018 by pady_1

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If $R$ is the radius of earth, the height, at which the weight of a body becomes $\frac{1}{4}$ of its weight on the surface of earth, is :

asked Dec 19, 2018 by pady_1

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Taking that earth revolves round the sun in a circular orbit of radius $15 \times 10^{10}m$, with a time period of 1 year the time taken by another planet, which is at a distance of $540 \times 10^{10}m$, to revolve round the sun in circular orbit once, will be :

asked Dec 19, 2018 by pady_1

1 answer

The moment of inertia of a thin uniform rod of mass $M$ and length $L$ about an axis perpendicular to the rod, through its center is $I$. The moment of inertia of the rod about axis perpendicular to the rod through its end point is :

asked Dec 19, 2018 by pady_1

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A car is moving on a circular level road of curvature $300\;m$. If the coefficient of friction is 0.3 and acceleration due to gravity $10\;m/s^2$, the maximum speed that car can have is :

asked Dec 19, 2018 by pady_1

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The minimum speed for a particle at the lowest point of a vertical circle of radius $R$, to describe the circle is $v$. If the radius of circle is reduced to one-fourth its value, the corresponding minimum speed will be :

asked Dec 19, 2018 by pady_1

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A body takes $1 \frac{1}{3}$ times as much time to slide down a rough inclined plane as it takes to slide down an indentical but smooth inclined plane. If the angle of inclined plane is $45^{\circ}$, the coefficient of friction is:

asked Dec 19, 2018 by pady_1

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Bullets of $0.03\; kg$ mass each, hit a plate at the rate of $200$ bullets per second, with a velocity of $50\;ms^{-1}$ and reflect back with a velocity of $30\;ms^{-1}$. The average force acting on the plate, in newtons, is :

asked Dec 19, 2018 by pady_1

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A ball A moving with a speed of $99\;ms^{-1}$ collides directly with another identical ball B moving with a speed $v$ in the opposite direction, A comes to rest after the collision. If the coefficients of restitution is 0.8, the speed of B before collision, is :

asked Dec 19, 2018 by pady_1

1 answer

The S.I unit of moment of inertia is :

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The dimensional formula for latent heat is :

asked Dec 19, 2018 by pady_1

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The angle between two vectors $6 \hat{i} + 6 \hat{j} - 3 \hat {k} $ and $7 \hat{i} +4 \hat{j} + 4 \hat{k}$ is given by :

asked Dec 19, 2018 by pady_1

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A car starts from rest and travels with uniform acceleration $\alpha$, for some time and then with uniform retardation $\beta$ and comes to rest. If the total travel time of car is $t$, the maximum velocity attained by it is given by :

asked Dec 19, 2018 by pady_1

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Water drops fall from a tap on the floor 5 m below at regular intervals of time, the first drop striking the floor when the fifth drop begins to fall. The height at which the third drop will be, from ground, at that instant when first drop strikes the ground, will be, (taking $g = 10 \; ms^{-2}$ ) :

asked Dec 19, 2018 by pady_1

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The speed of a projectile at its maximum height is $\frac{\sqrt{3}}{2}$ times its initial speed. If the range of the projectile is $P$ times the maximum height attained by it, then $P$ equals :

asked Dec 19, 2018 by pady_1

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The mass of a balloon with its contents is 1.5 kg. It is descending with an acceleration equal to half that of acceleration due to gravity. If it is to go up with the same acceleration, keeping the volume same, its mass should be decreased by :

asked Dec 19, 2018 by pady_1

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An object initially at rest explodes into 3 fragments A, B and C. The momentum of A is $P \hat{i}$ and that of B is $\sqrt{3}P\hat{j}$ where P is a positive number. The momentum of C will be:

asked Dec 19, 2018 by pady_1

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A stone is projected vertically up to reach maximum height $h$. The ratio of its kinetic energy to its potential energy to its potential energy, at a height $\frac{4}{5}h$, will be :

asked Dec 19, 2018 by pady_1

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Two particles of mass 1 kg and 3 kg have position vectors $2 \hat{i} + 3\hat{j} + 4 \hat{k}$ and $-2 \hat{i} + 3 \hat{j} - 4 \hat{k}$ respectively.

asked Dec 19, 2018 by pady_1

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During an adiabatic process, if the pressure of an ideal gas is proportional to the cube of its temperature the ratio $\gamma = \frac{c_p}{c_v}$ is : <br> (Specific heat at constant volume = $c_v$ <br> specific heat at constant pressure = $c_p$ )

asked Dec 19, 2018 by pady_1

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The area of the triangle formed by the axes and the line $(\cos \alpha - \sin \alpha ) x + (\cos \alpha + \sin \alpha) y =2$, in square units, is :

asked Dec 19, 2018 by pady_1

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The co-ordinate of the image of the origin $O$ with respect to the straight line $x+y+1=0$ is:

asked Dec 19, 2018 by pady_1

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If the points $(1,2)$ and $(3,4)$ were to be on the same side of the line $3x -5y +a =0$, then:

asked Dec 19, 2018 by pady_1

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If the point $[x_1 + t(x_2 - x_1), y_1 + t(y_2-y_1)]$ divides the join of the $(x_1,y_1)$ and $(x_2,y_2)$ internally, then :

asked Dec 19, 2018 by pady_1

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The vertices of a triangle are $(6,6), (0,6)$ and $(6,0)$ the distance between its circumcentre and centroid is :

asked Dec 19, 2018 by pady_1

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A straight rod of length 9 units slides with its ends. A and B always on the $x$ and $y$ axis respectively, then the locus of the centroid of $\Delta OAB$ is :

asked Dec 19, 2018 by pady_1

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If two towers of height $h_1$ and $h_2$ subtend angles $60^{\circ} $ and $30^{\circ}$ respectively at the mid point of the line joining their feet, then $h_1:h_2$ is equal to:

asked Dec 19, 2018 by pady_1

1 answer

In a $\Delta ABC, \; r_1 + r_2 - r_3 - r $ is equal to :

asked Dec 19, 2018 by pady_1

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In a $\Delta ABC, \; \cos A+ \cos B + \cos C$ is equal to :

asked Dec 19, 2018 by pady_1

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If in a $\Delta ABC$, $a,b,c$ are in AP then $\tan \frac{A}{2} \tan \frac{C}{2}$ is equal to :

asked Dec 19, 2018 by pady_1

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If $\cos x = \log_e (2 +\sqrt{3})$, then $x$ is equal to :

asked Dec 19, 2018 by pady_1

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$\cos 2 + \sin 2 $ is equal to :

asked Dec 19, 2018 by pady_1

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If $\tan^{-1} 3 + \tan^{-1} n = \tan^{-1} 8$, then $n$ is equal to :

asked Dec 19, 2018 by pady_1

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If $\tan \theta + \sec \theta = \sqrt{3}$, then the principal value of $\theta + \frac{\pi}{6}$ is equal to :

asked Dec 19, 2018 by pady_1

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If $\tan \theta_1 = k \cot \theta_2$, then $\frac{\cos (\theta_1 - \theta_2)}{\cos (\theta_1 + \theta_2)}$ is equal to :

asked Dec 19, 2018 by pady_1

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If $\sin \alpha + \sin \beta = a, \; \cos \alpha + \cos \beta = b$, then $\sin (\alpha + \beta) \cos^2 (\frac{\alpha - \beta}{2})$ is equal to :

asked Dec 19, 2018 by pady_1

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$\cos 6^{\circ} \sin 24^{\circ} \cos 72^{\circ}$ is equal to :

asked Dec 19, 2018 by pady_1

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$\frac{\sin (-660^{\circ}) \tan (1050^{\circ}) \sec(-420^{\circ} )}{\cos(225^{\circ}) \mathrm{cosec} (315^{\circ}) \cos (510^{\circ})}$ is equal to:

asked Dec 19, 2018 by pady_1

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If $(\sin \alpha + \mathrm{cosec} \;\alpha)^2$ + $(\cos \alpha + \sec \alpha)^2$ = $k + \tan^2 \alpha + \cot^2 \alpha$, then $k$ is equal to :

asked Dec 19, 2018 by pady_1

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If $\frac{\cos A}{\cos B} = n , \; \frac{\sin A}{\sin B} = m$, then $(m^2 - n^2) \sin^2B$ is equal to :

asked Dec 19, 2018 by pady_1

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$\begin{bmatrix} \frac{\sqrt{3} + 2 \cos A}{1- 2 \sin A} \end{bmatrix}^3 + \begin{bmatrix} \frac{1 + 2 \sin A}{\sqrt{3} - 2 \cos A} \end{bmatrix}^3$ is equal to :

asked Dec 19, 2018 by pady_1

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The length of normal to the curve $y = \frac{1}{2} a(e^{x/a} + e^{-x/a})$ is :

asked Dec 19, 2018 by pady_1

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