Recent questions tagged past papers

When a current of $5 \;mA$ is passed through a galvanometer having a coil of resistance $15 \; \Omega$, it shows full scale defection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range $0 – 10\; V$ is :

asked Dec 11, 2018 by pady_1

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A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by factor of :

asked Dec 11, 2018 by pady_1

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An observer is moving with half the speed of light towards stationary microwave source emitting waves at frequency $10\;GHz$. What is the frequency of the microwave measured by the observer ? (speed of light = $3 \times 10^8\;ms^{–1}$ )

asked Dec 11, 2018 by pady_1

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A particle is executing simple harmonic motion with a time period T. At time = 0, it is at its position of equilibrium. The kinetic energy-time graph of the particle will look like :

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Which of the following statements is false ?

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In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be :

asked Dec 11, 2018 by pady_1

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In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be :

asked Dec 11, 2018 by pady_1

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A capacitance of $2 \mu F$ is required in an electrical circuit across a potential difference of $1.0\; kV$. A large number of $1 \mu F$ capacitors are available which can withstand a potential difference of not more than $300\; V$. The minimum number of capacitors required to achieve this is :

asked Dec 11, 2018 by pady_1

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A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time ?

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In the above circuit the current in each resistance is :

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Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths $r = \lambda_1/\lambda_2$, is given by :

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A time dependent force F = 6t acts on a particle of mass 1kg. If the particle starts from rest, the work done by the force during the first 1 sec. will be :

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In a coil resistance $100 \Omega$, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is :

asked Dec 11, 2018 by pady_1

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An electric dipole has a fixed dipole moment $\overrightarrow{p}$, which makes angle $\theta$ with respect to x-axis. When subjected to an electric field $\overrightarrow{E_1} = E \hat{i}$, it experiences a torque $\overrightarrow{T_1} = \tau \hat{k}$. When subjected to another electric field $\overrightarrow{E_2} = \sqrt{3} E_1 \hat{j}$ it experiences a torque $\overrightarrow{T_2} = - \overrightarrow{T_1}$. The angle $\theta$ is :

asked Dec 11, 2018 by pady_1

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A magnetic needle of magnetic moment $6.7 \times 10^{-2} \; Am^2$ and moment of inertia $7.5 \times 10^{-6} kg\;m^2$ is performing simple harmonic oscillations in a magnetic field of $0.001\; T$. Time taken for $10$ complete oscillations is :

asked Dec 11, 2018 by pady_1

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A particle A of mass m and initial velocity $v$ collides with a particle B of mass $\frac{m}{2}$ which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths $\lambda_A$ to $\lambda_B$ after the collision is :

asked Dec 11, 2018 by pady_1

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In a Young's double slit experiment, slits are separated by 0.5 mm, and the screen is placed 150 cm away. A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is :

asked Dec 11, 2018 by pady_1

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The temperature of an open room of volume $30 \;m^3$ increased from $17^{\circ}C$ to $27^{\circ}C$ due to the sunshine. The atmospheric pressure in the room remains $1 \times 10^5 \; Pa$. If $n_i$ and $n_f$ are the number of molecules in the room before and after heating, then $n_f – n_i$ will be :

asked Dec 11, 2018 by pady_1

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In amplitude modulation, sinusoidal carrier frequency used is denoted by $\omega_c$ and the signal frequency is denoted by $\omega_m$. The bandwidth $(\Delta \omega_m)$ of the signal is such that $\Delta \omega_m<< \omega_c$. Which of the following frequency is not contained in the modulated wave ?

asked Dec 11, 2018 by pady_1

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A copper ball of mass $100\; gm$ is at a temperature T. It is dropped in a copper calorimeter of mass $100 \;gm$, filled with $170\; gm$ of water at room temperature. Subsequently, the temperature of the system is found to be $75^{\circ} C$. T is given by : (Given : room temperature = $30^{\circ}C$, specific heat of copper = $0.1 \;cal/gm^{\circ}C$)

asked Dec 11, 2018 by pady_1

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$C_p$ and $C_v$ are specific heats at constant pressure and constant volume respectively. It is observed that $C_p - C_v$ = a for hydrogen gas $ C_p - C_v$ = b for nitrogen gas The correct relation between a and b is :

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A slender uniform rod of mass M and length l is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. the angular acceleration of the rod when it makes an angle $\theta$ with the vertical is

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The moment of inertia of a uniform cylinder of length $l$ and radius $R$ about its perpendicular bisector is $I$. What is the ratio $l/R$ such that the moment of inertia is minimum ?

asked Dec 11, 2018 by pady_1

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An electron bean is acceleration by a potential difference $V$ to hit a metallic target to produce X-rays. It produces continuous as well as characteristic X-rays. If $\lambda_{min}$ is the smallest possible wavelength of X-ray in the spectrum, the variation of log $\lambda_{min}$ with $\log\; V$ is correctly represented in :

asked Dec 11, 2018 by pady_1

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The following observations were taken for determining surface tension T of water by capillary method : diameter of capillary, $D = 1.25 \times 10^{–2}$ m rise of water , $h = 1.45 \times 10^{–2} m$. Using $ g = 9.80\; m/s^2$ and the simplified relation $T = \frac{rhg}{2} \times 10^3\; N/m$, the possible error in surface tension is closest to :

asked Dec 11, 2018 by pady_1

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A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At sometime t, the ratio of the number of B to that of A is 0.3. Then, t is given by :

asked Dec 11, 2018 by pady_1

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The integral $\begin{align} \int^{\frac{3\pi}{4}}_{\frac{\pi}{4}} \frac{dx}{1+ \cos x} \end{align}$ is equal to

asked Dec 11, 2018 by pady_1

1 answer

If, for a positive integer n, the quadratic equation, $x(x + 1) + (x + 1)(x + 2) +.....+ (x + \overline{n – 1})(x + n) = 10n$ has two consecutive integral solutions, then n is equal to

asked Dec 11, 2018 by pady_1

1 answer

The radius of a circle, having minimum area, which touches the curve $y = 4 - x^2$ and the lines, $y = |x|$ is

asked Dec 11, 2018 by pady_1

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Let $a, \; b, \; c \in R$. If $f(x) = ax^2 + bx + c$ is such that $a + b + c = 3$ and $f(x+y) = f(x) + f(y) + xy, \forall x, y \in R$, then $ \displaystyle\sum_{n=1}^{10} f(n)$ is equal to

asked Dec 11, 2018 by pady_1

1 answer

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is

asked Dec 11, 2018 by pady_1

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The value of $(^{21} C_1 - ^{10}C_1) + (^{21}C_2 - ^{19}C_2) + (^{21}C_3 -^{10}C_3) + (^{21}C_4 - ^{10}C_4) +...+(^{21}C_{10} - ^{10}C_{10})$ is

asked Dec 11, 2018 by pady_1

1 answer

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is

asked Dec 11, 2018 by pady_1

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It two different numbers are taken from the set $\{0,1,2,3,....., 10\}$; then the probability that their sum as well as absolute difference are both multiple of 4, is

asked Dec 11, 2018 by pady_1

1 answer

The normal to the curve $y(x-2)(x-3) = x+6$ at the point where the curve intersects the y-axis passes through the point :

asked Dec 11, 2018 by pady_1

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Let $\overrightarrow{a} = 2 \hat{i} +\hat{j} - 2 \hat{k}$ and $\overrightarrow{b} = \hat{i} + \hat{j}$. Let $\overrightarrow{c}$ be a vector such that $| \overrightarrow{c} - \overrightarrow{a} | = 3, \; |(\overrightarrow{a} \times \overrightarrow{b} ) \times \overrightarrow{c} |=3$ and the angle between $\overrightarrow{c}$ and $\overrightarrow{a} \times \overrightarrow{b} $ be $30^{\circ}$. The $\overrightarrow{a}.\overrightarrow{c}$ is equal to

asked Dec 11, 2018 by pady_1

1 answer

$\displaystyle\lim_{x \to \frac{\pi}{2}} \frac{\cot x - \cos x}{(\pi - 2 x)^3}$ equals

asked Dec 11, 2018 by pady_1

1 answer

The function $f : R \to \begin{bmatrix}-\frac{1}{2}, \frac{1}{2} \end{bmatrix}$ defined as $f(x) = \frac{x}{1+x^2}$, is :

asked Dec 11, 2018 by pady_1

1 answer

A hyperbola passes through the point $P(\sqrt{2}, \sqrt{3})$ and has foci at $(\pm 2, 0)$. Then the tangent to this hyperbola at $P$ also passes through the point :

asked Dec 11, 2018 by pady_1

1 answer

The eccentriciy of an ellipse whose centre is at the origin is $\frac{1}{2}$. If one of its directrices is $x = -4$, then the equation of the normal to it at $(1, \frac{3}{2})$ is

asked Dec 11, 2018 by pady_1

1 answer

Let $I_n = \int \tan^n x\; dx, \; (n > 1)$. If $I_4 + I_6 = a \tan^5 x + bx^5 + C$, where $C$ is a constant of integration, then the ordered pair $(a, b)$ is equal to

asked Dec 11, 2018 by pady_1

1 answer

The distance of the point $(1, 3, -7)$ from the plane passing through the point $(1, -1, -1)$, having normal perpendicular to both the lines $\frac{x-1}{1} = \frac{y+2}{-2} = \frac{z-4}{3}$ and $\frac{x-2}{2} = \frac{y+1}{-1} = \frac{z+7}{-1}$, is

asked Dec 11, 2018 by pady_1

1 answer

For any three positive real numbers $a, \;b$ and $c,\; 9(25a^2 + b^2 ) + 25(c^2 – 3ac) = 15b(3a + c)$, Then

asked Dec 11, 2018 by pady_1

1 answer

If $A = \begin{bmatrix} 2 & -3 \\ -4 & 1 \end{bmatrix}$, then $adj (3A^2 + 12A)$ is equal to :

asked Dec 11, 2018 by pady_1

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A vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground such that $AP = 2 AB$. If $\angle{BPC} = \beta$, then $\tan \beta$ is equal to

asked Dec 11, 2018 by pady_1

1 answer

If $(2+\sin x) \frac{dy}{dx} +(y+1) \cos x = 0$ and $y(0)=1$, then $y(\frac{\pi}{2})$ is equal to :

asked Dec 11, 2018 by pady_1

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If for $x \in (0, \frac{1}{4})$, the derivative of $\tan^{-1} \begin{pmatrix} \frac{6x \sqrt{x}}{1-9x^3} \end{pmatrix}$ is $\sqrt{x}. g(x)$, then $g(x)$ equals :

asked Dec 11, 2018 by pady_1

1 answer

If the image of the point P(1, -2, 3) in the plane $2x + 3y - 4z + 22 =0$ measured parallel to the line, $\frac{x}{1} = \frac{y}{4} = \frac{z}{5}$ is $Q$, then $PQ$ is equal to :

asked Dec 11, 2018 by pady_1

1 answer

The area (in sq. units) of the region $\{ (x, y) : x \geq 0, \; x + y \leq 3, \; x^2 \leq 4y$ and $ y \leq 1 + \sqrt{x} \}$ is :

asked Dec 11, 2018 by pady_1

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Twenty meters of wires is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is :

asked Dec 11, 2018 by pady_1

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