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A pulley of radius 2 m is rotated about its axis by a force $F=(20t-5t^2)$ Newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation made by the pulley before its direction of motion if reversed, is :

asked Dec 11, 2018 by pady_1

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Three perfect gases at absolute temperature $T_1, T_2, T_3$ are mixed. The masses of molecules are $m_1, m_2$ and $m_3$ and the number of molecules are $n_1, n_2$ and $n_3$ respectively. Assuming no loss of energy, the final temperature of the mixture is :

asked Dec 11, 2018 by pady_1

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This question has Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1 : Sky wave signals are used for long distance radio communication. These signals are in general, less stable than ground wave signals. Statement-2: The state of ionosphere varies from hour to hour, day to day and season to season

asked Dec 11, 2018 by pady_1

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Water is flowing continuously from a tap having an internal diameter $8 \times 10^{-3}$m. The water velocity as it leaves the tap is $0.4\; ms^{-1}$. The diameter of the water stream at a distance $2 \times 10^{-1}$ m below the lap is close to :

asked Dec 11, 2018 by pady_1

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A mass M, attached to a horizontal spring, executes S.H.M. with amplitude $A_1$. When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude $A_2$. The ratio of $(\frac{A_1}{A_2})$ is :

asked Dec 11, 2018 by pady_1

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A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats $\gamma$. It is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by :

asked Dec 11, 2018 by pady_1

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A current I flows in an infinitely long wire with cross section in the form of a semicircular ring of radius R. The magnitude of the magnetic induction along its axis is

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Let the $x-z$ plane be the boundary between two transparent media. Medium 1 in $z \geq 0$ has a refractive index of $\sqrt{2}$ and medium 2 with $z < 0$ has a refractive index of $\sqrt{3}$. A ray of light in medium 1 given by the vector $\overrightarrow{A} = 6\sqrt{3} \hat{i} + 8 \sqrt{3} \hat{j} - 10 \hat{k}$ is incident on the plane of separation. The angle of refraction in medium 2 is

asked Dec 11, 2018 by pady_1

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A fully charged capacitor C with initial charge $q_0$ is connected to a coil of self inductance $L$ at $t=0$. The time at which the energy is stored equally between the electric and the magnetic field is :

asked Dec 11, 2018 by pady_1

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An object moving with a speed of 6.25 m/s, is decelerated at a rate given by : $\frac{dv}{dt} = -2.5 \sqrt{v}$ where $v$ is the instantaneous speed. The time taken by the object, to come to rest, would be :

asked Dec 11, 2018 by pady_1

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A boat is moving due east in a region where the earth's magnetic field is $5.0 \times 10^{-5} NA^{-1}m^{-1}$ due north and horiontal. The boat carries a vertical aerial 2m long. If the speed of the boat is $1.50 \;ms^{-1}$, the magnitude of the induced emf in the wire of aerial is :

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Two identical charged spheres suspended from a common point by two massless strings of length $l$ are initially a distance $d(d <<1)$ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charge approach each other with a velocity v. Then as a function of distance x between them,

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Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is :

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Two particles are executing simple harmonic motion of the same amplitude A and frequency $\omega$ along the $x-axis$. Their mean position is separated by distance $X_0(X_0 > A)$. If the maximum separation between them is $(X_0+ A)$, the phase difference between their motion is :

asked Dec 11, 2018 by pady_1

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A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc.

asked Dec 11, 2018 by pady_1

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Work done in increasing the size of a soap bubble from a radius of 3 cm to 5 cm is nearly (Surface tension of soap solution = $ 0.03 Nm^{-1}$) :

asked Dec 11, 2018 by pady_1

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A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is

asked Dec 11, 2018 by pady_1

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A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading : 0 mm Circular scale reading : 52 divisions Given that 1 mm on main scale corresponds to 100 divisions of the circular scale. The diameter of wire from the above date is :

asked Dec 11, 2018 by pady_1

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The transverse displacement $y(x,t)$ of a wave on a string is given by $y (x,t) = e^{-(ax^2 + bx^2 + 2 \sqrt{ab}\; xt)}$. This represents a

asked Dec 11, 2018 by pady_1

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The circle $x^2+ y^2 = 4x + 8y + 5$ intersects the line $3x - 4y = m$ at two points if

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For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is

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An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colour is

asked Dec 11, 2018 by pady_1

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Consider the system of linear equations: $x_1 + 2x_2 + x_3 = 3$ $2x_1 + 3x_2 + x_3 = 3 $ $3x_1 +5 x_2 + 2x_3 = 1$ The system has

asked Dec 11, 2018 by pady_1

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There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out out at random and then transferred to the other. The number of ways in which this can be done is

asked Dec 11, 2018 by pady_1

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Let $f : (-1, 1) \to R$ be a differentiable function with $f(0) = -1$ and $f'(0)=1$. Let $g(x) = [f(2f(x) + 2)]^2$. Then $g'(0)=$

asked Dec 11, 2018 by pady_1

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Let $p(x)$ be a function defined on $R$ such that $p'(x) = p'(1-x)$, for all $x \in [0,1], \; p(0)=1$ and $p(1) =41$. Then $\begin{align} \int_0 ^1p(x) \; dx\end{align}$ equals

asked Dec 11, 2018 by pady_1

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Let $f : R \to R$ be a positive increasing function with $\displaystyle\lim_{x \to \infty} \frac{f(3x)}{f(x)} = 1$ Then $\displaystyle\lim_{x \to \infty} \frac{f(2x)}{f(x)} = $

asked Dec 11, 2018 by pady_1

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A person is to count 4500 currency notes. Let $a_n$ denote the number of notes the counts in the $n^{th} $ minute. If $a_1 = a_2 = .......= a_{10} = 150$ and $a_{10}, a_{11}, ....$ are in A.P. with common difference $-2$, then the time taken by him to count all notes is

asked Dec 11, 2018 by pady_1

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The line L given by $\frac{x}{5}+ \frac{y}{b} = 1$ passes through the poin (13, 32). The line $K$ is parallel to $L$ and has the equation $\frac{x}{c}+\frac{y}{3}=1$. Then the distance between $L$ and $K$ is

asked Dec 11, 2018 by pady_1

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A line AB in three-dimensional space makes angle $45^{\circ}$ and $120^{\circ}$ with the positive $x-axis$ and the positive $y-axis$ respectively. If AB makes an acute $\theta$ with the positive $z-axis$, then $\theta$ equals

asked Dec 11, 2018 by pady_1

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The number of complex number $z$ such that $|z-1| = | z+ 1| = |z-i|$ equals

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If $\alpha$ and $\beta$ are the roots of the equation $x^2 - x + 1 =0$, then $\alpha^{2009} + \beta^{2009}$ =

asked Dec 11, 2018 by pady_1

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For a regular polygon, let $r$ and $R$ be the radii of the inscribed and the circumscribed circles. A false statement among the following is

asked Dec 11, 2018 by pady_1

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Let $f : R \to R$ be a continuous function defined by $f(x) = \frac{1}{e^x + 2e^{-x}}$. Statement-1 : $f(c) = \frac{1}{3}$, for some $c \in R$. Statement-2 : $0 < f(x) \leq \frac{1}{2 \sqrt{2}}$, for all $x \in R$

asked Dec 11, 2018 by pady_1

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Let $A$ be a $ 2 \times 2$ matrix with non-zero entries and let $A^2 =I$, where $I$ is $2 \times 2$ identity matrix. Define $Tr(A)$ = sum of diagonal elements of $A$ and $|A|$ = determinant of matrix A. Assertion : Statement -1: $Tr(A) = 0$ Reason : Statement-2 : $|A| =1$

asked Dec 11, 2018 by pady_1

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Let $S_1 = \displaystyle\sum_{j=1}^{10} j (j - 1)^{10} C_j, S_2 = \displaystyle\sum_{j=1}^{10} j \;^{10} C_j $ and $S_3 = \displaystyle\sum_{j=1}^{10} j^2 \;^{10} C_j $ Statement-1 : $S_3 = 55 \times 2^9$ Statement-2 : $S_1 = 90 \times 2^8$ and $S_2 = 10 \times 2^8$.

asked Dec 11, 2018 by pady_1

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Statement-1: The point $A(3, 1, 6)$ is the mirror image of the point $B (1, 3, 4)$ in the plane $x - y +z =5$. Statement-2 : The plane $x-y +z=5$ bisects the line segment joining $A(3, 1, 6)$ and $B(1, 3, 4)$

asked Dec 11, 2018 by pady_1

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Four numbers are chosen at random (without replacement) from the set $\{1, 2, 3, ..., 20\}$. Statement-1 : The probability that the chosen numbers when arranged in some order will form an AP is $\frac{1}{85}$. Statement-2 : If the four chosen numbers from an AP, then the set of all possible values of common difference is $\{ \pm1, \pm 2, \pm 3, \pm 4, \pm 5 \}$.

asked Dec 11, 2018 by pady_1

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The number of $3 \times 3$ non-singular matrices, with four entries as 1 and all other entries as 0, is

asked Dec 11, 2018 by pady_1

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Let $f : R \to R$ be defined by $f(x) = \begin{cases} k-2x, & \quad \text{if } \text{ x $\leq$ -1}\\ 2x + 3, & \quad \text{if } \text{ x > -1} \end{cases} $. If $f$ has a local minimum at $x=-1$, then a possible value of $k$ is

asked Dec 11, 2018 by pady_1

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Consider the following relations : $R = \{ (x, y) | x, \; y$ are real number and $x = wy$ for some rational number $w \}$; $S = \{ (\frac{m}{n}, \frac{p}{q} ) | m, \; n, \; p $ and $q$ are integers such that $n, \;q \neq 0$ and $qm = pn \}$. Then

asked Dec 11, 2018 by pady_1

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If the vectors $\overrightarrow{a} = \hat{i} - \hat{j} + 2 \hat{k}, \; \overrightarrow{b} = 2 \hat{i} + 4 \hat{j} + \hat{k}$ and $\overrightarrow{c} = \lambda \hat{i} + \hat{j} + \mu \hat{k}$ are mutually orthogonal, then $(\lambda, \mu)$ =

asked Dec 11, 2018 by pady_1

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If two tangets drawn from a point P to the parabola $y^2 = 4x$ are at right angles, then the locus of P is

asked Dec 11, 2018 by pady_1

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The area bounded by the curves $y = \cos x$ and $ y = \sin x$ between the ordinates $x=0$ and $x =\frac{3 \pi}{2}$ is

asked Dec 11, 2018 by pady_1

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Solution of the differential equation $\cos x\; dy = y (\sin x - y) dx, \; 0 < x < \frac{\pi}{2}$ is

asked Dec 11, 2018 by pady_1

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The equation of the tangent to the curve $y = x + \frac{4}{x^2}$, that is parallel to the $x-axis$, is

asked Dec 11, 2018 by pady_1

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Let $\overrightarrow{a} = \hat{j} - \hat{k}$ and $\overrightarrow{c} = \hat{i} - \hat{j} - \hat{k}$. Then vector $\overrightarrow{b}$ satisfying $\overrightarrow{a} \times \overrightarrow{b} + \overrightarrow{c} = \overrightarrow{0}$ and $\overrightarrow{a}.\overrightarrow{b} = 3$ is

asked Dec 11, 2018 by pady_1

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Let S be a non-empty subset of R. Consider the following statement : P : There is a rational number $x \in S$ such that $x > 0$. Which of the following statements is the negation of the statement P ?

asked Dec 11, 2018 by pady_1

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Let $\cos (\alpha + \beta) = \frac{4}{5}$ and let $\sin (\alpha - \beta) = \frac{5}{13}$, where $0 \leq \alpha, \; \beta \leq \frac{\pi}{4}$, then $\tan 2 \alpha = $

asked Dec 11, 2018 by pady_1

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The equation of a wave on a string of linear mass density $0.04\; kg\;m^{-1}$ is given by$ y = 0.02 (m) \sin [ 2 \pi (\frac{t}{0.04 (s)} - \frac{x}{0.50(m)} ) ]$. The tension in the string is

asked Dec 11, 2018 by pady_1

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