Recent questions tagged 2007

A particle executes simple harmonic oscillation with an amplitude a. The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is:

asked Jul 26, 2018 by pady_1

1 answer

The particle executing simple harmonic motion has a ienetic energy $K_0 \cos^2 ωt$. The maximum values of the potential energy and the total energy are respectively:-

asked Jul 26, 2018 by pady_1

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The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is :-

asked Jul 26, 2018 by pady_1

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The frequency of a light wave in a material is $2 \times 10^{14}$ Hz and wavelength is $5000$ Å. The refractive index of material will be:-

asked Jul 26, 2018 by pady_1

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A black body is at $727^{\circ}C$. It emits energy at a rate which is proportional to:

asked Jul 26, 2018 by pady_1

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An engine has an efficiency of $1/6$. When the temperature of sink is reduced by $62^{\circ}C$, its efficiency is doubled. Temperature of the source is-

asked Jul 26, 2018 by pady_1

1 answer

Assuming the sun to have a spherical outer surface of radius $r$, radiating like a black body at temperature $t^{\circ}$C, the power received by a unit surface, (normal to the incident rays) at distance $R$ from the centre of the Sun is <br> Where $\sigma$ is the Stefan's Contant :-

asked Jul 26, 2018 by pady_1

1 answer

Two satellites of earth, $S_1$ and $S_2$, are moving in the same orbit. The mass of $S_1$ is four times the mass of $S_2$. Which one of the following statements is true ?

asked Jul 26, 2018 by pady_1

2 answers

A uniform rod AB of length $l$ and mass $m$ is free to rotate about point $A$. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about $A$ is $\frac{ml^2}{3}$,the initial angular acceleration of the rod will be <br> <img src =" "/>

asked Jul 26, 2018 by pady_1

2 answers

A particle of mass $m$ moves in the XY plane with a velocity v along the straight line $AB$. If the angular momentum of the particle with respect to origin $O$ is $L_A$ when it is at $A$ and $L_B$ when it is at $B$, then : <img src =""/>

asked Jul 26, 2018 by pady_1

1 answer

A mass of $2.0 kg$ is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and released the mass executes a simple harmonic motion. The spring constant is $200N/m$. What should be the minimum amplitude of the motion so that the mass gets detached from the pan (Take $g = 10 m/s^2$) <br> <img src =""/>

asked Jul 26, 2018 by pady_1

1 answer

The position $x$ of a particle with respect to time $t$ along x-axis is given by $x = 9t^2 – t^3$ where $x$ is in metres and $t$ in seconds. What will be the position of this particle when it achieves maximum speed along the + x direction ?

asked Jul 26, 2018 by pady_1

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$\overrightarrow{A}$ and $\overrightarrow{B} $ are two vectors and $\theta$ is the angle between them, if $| \overrightarrow{A} \times \overrightarrow{B} | = \sqrt{3} (\overrightarrow{A}.\overrightarrow{B})$ the value of $\theta$ is:-

asked Jul 26, 2018 by pady_1

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A wheel as angular acceleration of $3.0 rad/sec^2$ and initial angular speed of $2.00 rad/sec$. In a time of $2 sec$ it has rotated through an angle (in radian) of :

asked Jul 26, 2018 by pady_1

1 answer

A vertical spring with force constant K is fixed on a table. A ball of mass m at a height h above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance d. The net work done in the process is:-

asked Jul 26, 2018 by pady_1

1 answer

A block B is pushed momentarily along a horizontal surface with an initial velocity v. If $\mu$ is the coefficient of sliding friction between B and the surface, block B will come to rest after time <img src = ""/>:-

asked Jul 26, 2018 by pady_1

1 answer

A particle staring from the origin (0, 0) moves in a straight line in the (x, y) plane. Its coordinates at a later time are($ \sqrt{3},3$) . The path of the parti makes with the x-axis an angle of:-

asked Jul 26, 2018 by pady_1

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A car moves from X to Y with a uniform speed $v_u$ and returns to Y with a uniform speed $v_d$. The average speed for this round trip is:-

asked Jul 26, 2018 by pady_1

1 answer

A particle moving along x-axis has acceleration $f$, at time $t$, given by $f = f_0 (1 - \frac{t}{T})$, where $f_0$ and $T$ are constants. The particle at t = 0 has zero velocity. In the time interval between $t = 0$ and the instant when $f = 0$, the particle's velocity $(v_x)$ is:

asked Jul 26, 2018 by pady_1

1 answer

Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I, would be:-

asked Jul 26, 2018 by pady_1

1 answer

The solution of $\large\frac{dy}{dx}$$+1=e^{x+y}$ is

asked Oct 28, 2013 by meena.p

1 answer

The solution of $\large\frac{dy}{dx}=\frac{y^2}{xy-x^2}$ is

asked Oct 28, 2013 by meena.p

1 answer

The solution of $(x+y+1)\large\frac{dy}{dx}$$=1$

asked Oct 28, 2013 by meena.p

1 answer

The differential equation obtained by eliminating the arbitrary constant a and b from $xy=ae^x+be^{-x}$ is

asked Oct 28, 2013 by meena.p

1 answer

The area (in square unit ) of the region enclosed by the curves $ y=x^2$ and $y=x^3$ is

asked Oct 28, 2013 by meena.p

1 answer

$\int \limits_0^{2x} \sin ^6 x \cos ^5 x dx $ is equal to

asked Oct 28, 2013 by meena.p

1 answer

If $f(t) =\int \limits _{-t}^t \large\frac{e^{-|x|}}{2}$$dx$, then $\lim \limits_{t \to \infty} f(t) $ is equal to

asked Oct 28, 2013 by meena.p

1 answer

$\int \large \frac{\sin x+ 8 \cos x}{4 \sin x+6 \cos x}$$ dx$ is equal to

asked Oct 28, 2013 by meena.p

1 answer

$\int \tan^{-1} \bigg(\sqrt {\large\frac{1-x}{1+x}}\bigg)$$dx$ is equal to

asked Oct 28, 2013 by meena.p

1 answer

If $ \int \large\frac{e^x-1}{e^x+1}$$dx=f(x)+c$, then f(x) is equal to

asked Oct 28, 2013 by meena.p

0 answers

If $z= \log (\tan x +\tan y)$, then $(\sin 2x) \large\frac{\partial z}{\partial x}$$+(\sin 2y) \large\frac{\partial z}{\partial y}$ is equal to

asked Oct 28, 2013 by meena.p

1 answer

Observe the statement given below: Assertion (A): $f(x)=x e^{-x}$ has the maximum at $x=1$ Reason (R): $ f(1)=0$ and $f(1) <0$ which of following is correct ?

asked Oct 28, 2013 by meena.p

1 answer

The circumference of a circle is measured as 56 cm with an error 0.02 cm. The percentage error in its area is

asked Oct 28, 2013 by meena.p

1 answer

The condition $f(x)=x^3+px^2+qx+r(x \in R)$ to have no extreme value, is

asked Oct 28, 2013 by meena.p

1 answer

The lengths of tangent, subtangent, normal and subnormal for the curve $y=x^2+x-1$ at $(1,1)$ are A,B,C and D respectively then their increasing order is

asked Oct 28, 2013 by meena.p

1 answer

$x=\cos \theta,y= \sin 5 \theta =>(1-x^2)\large\frac{d^2y}{dx^2}$$ - x \large\frac{dy}{dx}$ is equal to

asked Oct 28, 2013 by meena.p

1 answer

$y= \log \bigg \{ \bigg (\large\frac{1+x}{1-x}\bigg )^{1/4}\bigg\}-\frac{1}{2}$$ \tan ^{-1}(x),$ then $\large\frac{dy}{dx}$ is equal to

asked Oct 28, 2013 by meena.p

1 answer

If $2x^2-3xy+y^2+x+2y-8=0$, then $\large\frac{dy}{dx}$ is equal to

asked Oct 26, 2013 by meena.p

1 answer

If $f(x)= \left\{ \begin{array}{1 1} \frac{\sin(1+[x])}{[x]}, & \quad for\;[x] \neq 0 \\ 0, & \quad for\;[x] =0 \end{array} \right. $ where $[x]$ denotes the greatest integer not exceeding x, then $\lim \limits _{x \to 0} f(x)$ is equal to

asked Oct 26, 2013 by meena.p

1 answer

If $f(x)= \left\{ \begin{array}{1 1} x-5, & \quad for\; x \leq 1 \\ 4x^2-9, & \quad for\;1 < x < 2 \\ 3x+4, &\quad for\; x \geq 2 \end{array} \right.$ then $f'(2^{+})$ is equal to

asked Oct 26, 2013 by meena.p

1 answer

$\lim \limits_{x \to 2} \large\frac{e^x-e^{\sin x}}{2(x- \sin x)}$

asked Oct 26, 2013 by meena.p

1 answer

The area (in square unit) of the triangle formed by the points with polar coordinates $(1,0), \bigg(2,\large\frac{ \pi}{3}\bigg)$ and $\bigg(3,\large\frac{2 \pi}{3}\bigg)$ is

asked Oct 26, 2013 by meena.p

1 answer

If the line $lx+my=1$ is normal to the hyperbola

asked Oct 26, 2013 by meena.p

1 answer

The value of k , if (1,2),(k,1) are conjugate points with respect to the ellipse $2x^2+3y^2=6$ is

asked Oct 25, 2013 by meena.p

1 answer

For the parabola $y^2+6y-2x+5=0$(I) The vertex is (-2,-3) (II) The directrix is y+3=0

asked Oct 25, 2013 by meena.p

1 answer

The condition for the coaxial system $x^2+y^2+2 \lambda x +c=0,$ where $\lambda$ is a parameter and c is a constant to have distinct limiting points, is

asked Oct 25, 2013 by meena.p

1 answer

The inverse point of (1,2) with respect to the circle $x^2+y^2-4x-6y+9=0$ is

asked Oct 25, 2013 by meena.p

1 answer

The equation of the circle of radius 3 that lies in the fourth quadrant and touching the lines x=0 and y=0 is

asked Oct 25, 2013 by meena.p

1 answer

The cosine of the angle A of the triangle with vertices $A(1,-1,2), B(6,11,2),C(1,2,6)$ is

asked Oct 25, 2013 by meena.p

1 answer

The ratio in which yz - plane divides the line segment joining $(-3,4,-2)$ and $(2,1,3)$ is

asked Oct 25, 2013 by meena.p

1 answer

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