Recent questions tagged past papers

A string in a musical instrument is 50 cm long and its fundamental frequency is 270 Hz. If the desired frequency of 1000 Hz is to be produced, the required string length is :

asked Dec 19, 2018 by pady_1

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The equation of wave is : <br> $y = 1.0 \cos 2 \pi (\frac{t}{0.02} - \frac{x}{10})$ where $t$ is in second. The frequency of the wave is :

asked Dec 19, 2018 by pady_1

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In order that heat is conducted from one part of a solid to another part, what is required is ?

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A lead bullet of mass 21g travelling at a speed of $100 \; m/s$ comes to rest in a wooden block. If no heat is taken away by the wood, the rise in temperature of the bullet in the wood nearly is (sp. heat of lead = $30 cal/kg^{\circ}C $) :

asked Dec 19, 2018 by pady_1

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The First Law of thermodynamics states that :

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One litre of helium gas at a pressure of 76 cm-Hg and temperature $27^{\circ}C$ is heated till its pressure and volume are doubled. The final temperature attained by the gas is :

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A real gas can be approximated to an ideal gas at :

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A glass flask of volume $200 \; cm^3$ is completely filled with mercury at $20^{\circ}C$. The amount of mercury that spilt over when the flask is heated to $80^{\circ}C$ is (coefficient of volume expansion for glass $27 \times 10^{-8} /^{\circ}C$, mercury $0.18 \times 10^{-8}/^{\circ}C$) :

asked Dec 19, 2018 by pady_1

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A steel bridge in a town is 200 m long. Where minimum temperature in winter is $10^{\circ}C$ and maximum in summer is $40^{\circ}C$. The change in length of the bridge from winter to summer is [ for steel alpha is $11 \times 10^{-6}/^{\circ}C$] :

asked Dec 19, 2018 by pady_1

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Neglecting gravity, the potential energy of a molecule of a liquid on the surface of the liquid when compared to the potential energy of a molecule inside the liquid is :

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The Poisson's ratio $\sigma$ should satisfy the relation :

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The equation of motion of a particle is given by $\frac{dp}{dt} + m \omega^2 n = 0$, where $p$ is the momentum and $n$ is the position. Then the particle :

asked Dec 19, 2018 by pady_1

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A satellite is revolving near the earth's surface. Its orbital velocity is :

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For an electron circulating around the nucleus, the centripetal force is supplied by :

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The maximum speed with which a car can be driven round a curve of radius 18 m without skidding (when $g = 10\;m/s^2$ and the coefficient of friction between rubber tyres and the roadway is $0.2$ ) is :

asked Dec 19, 2018 by pady_1

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Value of g :

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A stone tied to a string is rotated in a vertical circle. The minimum speed with which the string has to be rotated :

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Dimensions of ohm are same as (h = Planck's constant, e = charge) :

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The position of a particle is given by $\overrightarrow{r} = (\hat{i} + 2 \hat{j} - \hat{k} )$ momentum $\overrightarrow{p} = ( 3 \hat{i} + 4 \hat{j} - 2 \hat{k})$. The angular momentum is perpendicular to :

asked Dec 19, 2018 by pady_1

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If a body is in equilibrium under a set of non-collinear forces, the minimum number of forces has to be :

asked Dec 19, 2018 by pady_1

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A car starts from rest, attains a velocity of $36 \; km/h$ with an acceleration of $0.2 \;m/s^2$, travels $9 \; km$ with this uniform velocity and then comes to halt with a uniform deaceleration of $0.1\; m/s^2$. The total time of travel of the car is :

asked Dec 19, 2018 by pady_1

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A person standing on the edge of a well throws a stone vertically upwards with an initial velocity 5 m/s. The stone goes up, comes down and falls in the well making a sound. If the person hears the sound 3s after throwing, the water is at a depth from ground given by (neglect time of travel for the sound and take $g = 10\;m/s^2$):

asked Dec 19, 2018 by pady_1

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A person throws a bottle into a dustbin at the same heigh as he is 2 m away at an angle of $45^{\circ}$. The velocity of the throw is

asked Dec 19, 2018 by pady_1

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The relation $\overrightarrow{F} = m \overrightarrow{a}$, cannot be deducted from Newton's second law, if :

asked Dec 19, 2018 by pady_1

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A car of mass $400\; kg$ and travelling at $72\; km/h$ crashes into a truck of mass $4000\; kg$ and travelling at $9 \; km/h$, in the same direction. The car bounces back at a speed of $18\; km/h$. The speed of the truck after the impact is :

asked Dec 19, 2018 by pady_1

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A simple pendulum hanging freely and at rest is vertical because in that position :

asked Dec 19, 2018 by pady_1

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An iron block of sides $50\; cm \times 8 \; cm \times 15\; cm $ has to be pushed along the floor. The force required will be minimum when the surface in contact with ground is :

asked Dec 19, 2018 by pady_1

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The solution of $2xy \frac{dy}{dx} = 1 + y^2$, is :

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The order of the differential equation $(\frac{dy}{dx})^{^3} + (\frac{dy}{dx})^{^2} + y^4 = 0$ is :

asked Dec 19, 2018 by pady_1

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$\displaystyle \lim_{n \to \infty} \displaystyle\sum_{r=1}^{n} (\frac{1}{n}) \frac{\sqrt{n+r}}{n-r} $ is equal to :

asked Dec 19, 2018 by pady_1

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The approximate value of $\begin{align} \int_{-3}^3 x^4 \;dx \end{align}$, using trapezoidal rule and taking six equal intervals, is :

asked Dec 19, 2018 by pady_1

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The area bounded by the parabola $x = 4 - y^2$ and the $y$-axis (in sq unit) is:

asked Dec 19, 2018 by pady_1

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$\begin{align} \int_0^{\pi} \cos^3x \;dx \end{align}$ is equal to :

asked Dec 19, 2018 by pady_1

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$\begin{align} \int_0^{\pi/4} (\tan^4 x + \tan^2 x) dx \end{align}$ is equal to :

asked Dec 19, 2018 by pady_1

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$\begin{align} \frac{\sin^3 x + \cos^3 x}{\sin^2x \cos^2 x } dx \end{align}$ is equal to :

asked Dec 19, 2018 by pady_1

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$\begin{align} \int \frac{3dx}{2x^2 - x -1} \end{align}$ is equal to

asked Dec 19, 2018 by pady_1

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$\begin{align} \int \frac{1}{x} \frac{\sqrt{x-1}}{x+1}dx \end{align}$ is equal to :

asked Dec 19, 2018 by pady_1

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$\begin{align} \int \frac{dx}{x(1+\log x)^3} \end{align}$ is equal to :

asked Dec 19, 2018 by pady_1

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The minimum distance from the point $(4, 2)$ to the parabola $y^2 = 8x$ is :

asked Dec 19, 2018 by pady_1

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$\displaystyle\lim_{n \to \infty} \begin{bmatrix}\frac{1}{n+1} + \frac{1}{n+2} + ... +\frac{1}{2n} \end{bmatrix} $ is equal to :

asked Dec 19, 2018 by pady_1

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If $u =x + y$ and $v = x^2 - y^2$, then $\begin {vmatrix} \frac{ \partial u}{ \partial x} & \frac{ \partial u}{ \partial y} \\ \frac{ \partial v}{ \partial x} & \frac{ \partial v}{ \partial y} \end{vmatrix}$ is equal to :

asked Dec 19, 2018 by pady_1

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If $z^2 = \frac{x^{1/2} + y^{1/2}}{x^{1/3} + y^{1/3}}$ then $x \frac{ \partial z}{\partial x} + y \frac{ \partial z}{ \partial y}$ is :

asked Dec 19, 2018 by pady_1

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If $y = sin (7 \sin^{-1} x)$, then $(1-x^2) y_2 - xy_1$ is equal to :

asked Dec 19, 2018 by pady_1

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If $x+y=12$, then the minimum value of $x^2+y^2$ is:

asked Dec 19, 2018 by pady_1

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If the acute angle between the curves $xy=2$ and $y^2 = 4x$ is $\theta$, then $\tan \theta$ is equal to :

asked Dec 19, 2018 by pady_1

1 answer

The equation of the tangent to the curve $y = x^3-2x+7$ at the point $(1,6)$, is :

asked Dec 19, 2018 by pady_1

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A cylindrical vessel of radius $0.5\; m$ is filled with oil at the rate of $0.25\; \pi m^3/min$. The rate, at which the level of oil is increasing, is :

asked Dec 19, 2018 by pady_1

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In a cube the percentage increase in side is 1. The percentage increase in the volume of the cube is :

asked Dec 19, 2018 by pady_1

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If $y = \cot^{-1} \begin{bmatrix} \tan ( \frac{\pi}{2} - x ) \end{bmatrix}$, then $\frac{dy}{dx}$ is equal to :

asked Dec 19, 2018 by pady_1

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If $y=x^x$, then $\frac{dy}{dx}$ is equal to :

asked Dec 19, 2018 by pady_1

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