Recent questions tagged past papers

Photon of frequency $\nu$ has a momentum associated with it. If $c$ is the velocity of light, the momentum is :

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If in a $p-n$ junction diode, a square input signal of 10 V is applied as shown : <br> <br> Then the output signal across $R_L$ will be :

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In gamma ray emission from a nucleus:

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If $M_o$ is the mass of an oxygen isotope $_8O^{17}, M_p$ and $M_n$ are the masses of a proton and a neutron respectively, the nuclear binding energy of the isotope is :

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A current $I$ flows along the length of an infinitely long, straight, thin walled pipe. Then :

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A long straight wire of radius $a$ carries a steady current $i$. The current is uniformly distributed across its cross-section. The ratio of the magnetic field at $\frac{a}{2}$ and $2a$ is :

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An ideal coil of 10 H is connected in series with a resistance of $5 \Omega$ and a battery of $5 V$. 2 s after the connection is made, the current flowing ( in ampere) in the circuit is :

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A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be :

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An electric charge $10^{-3} \mu C$ is placed at the origin (0, 0) of X-Y coordinate system. Two points A and B are situated at $(\sqrt{2}, \sqrt{2})$ and $(2, 0)$ respectively. The potential difference between the points A and B will be :

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In an AC circuit the voltage applied is $E= E_0 \sin \omega t$. The resulting current in the circuit is $I = I_0 \sin (\omega t - \frac{\pi}{2})$. The power consumption in the circuit is given by :

asked Nov 29, 2018 by pady_1

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The displacement of an object attached to a spring and executing simple harmonic motion is given by $x = 2 \times 10^{-2} \cos \pi t \; metre$. The time at which the maximum speed first occurs is :

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If the difference between the roots of the equation $x^2 + ax + 1 = 0$ is less than $\sqrt{5}$, then the set of possible values of $a$ is :

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The area enclosed between the curves $y^2 = x$ and $ y = |x|$ is :

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$\int \frac{dx}{\cos x + \sqrt{3} \sin x}$ equals :

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The solution for $x$ of the equation $\begin{align}\int_{\sqrt{2}}^x \; \; \frac{dt}{t \sqrt{t^2 -1}} = \frac{\pi}{2} \end{align}$ is :

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The function $f : R / \{0\} \to R$ given by $ f(x) = \frac{1}{x} - \frac{2}{e^{2x} -1}$ can be made continuous at $x=0$ by defining $f(0)$ as :

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Let $f: R\to R$ be a function defined by $f(x) = min \{ x + 1, |x| + 1\}$. Then which of the following is true ?

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Let $F(x) = f(x) + f (\frac{1}{x}), f(x) = \int_1^x \frac{ \log t}{1 + t} dt$. Then $F(e)$ equals :

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If one of the lines of $my^2 + (1 - m^2) xy - mx^2 = 0 $ is a bisector of the angle between the lines $xy = 0$, then $m$ is :

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Let P = (-1, 0), Q = (0, 0) and R = (3, 3$\sqrt{3}$) be three points. The equation of the bisector of the angle PQR is :

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Let $A(h, k), B(1, 1)$ and $C(2, 1)$ be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1, then the set of values which $'k'$ can take is given by :

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Let $\overrightarrow{a} = \hat{i} + \hat{j} + \hat{k}, \overrightarrow{b} = \hat{i} - \hat{j} + 2 \hat{k}$ and $\overrightarrow{c} = x \hat{i} + ( x - 2)\hat{j} - \hat{k}$. If the vector $\overrightarrow{c}$ lies in the plane of $\overrightarrow{a}$ and $\overrightarrow{b}$, then $x$ equals :

asked Nov 29, 2018 by pady_1

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If (2, 3, 5) is one end of a diameter of the sphere $x^2 + y^2 + z^2 - 6x - 12 y - 2 z + 20 = 0 $, then the coordinates of the other end of the diameter are :

asked Nov 29, 2018 by pady_1

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The equation of a tangent to the parabola $y^2 = 8x$ is $ y = x + 2$. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is :

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The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is :

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A particle just clears a wall of height b at a distance $a$ and strikes the ground at a distance $c$ from the point of projection. The angle of projection is :

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If $\hat{u}$ and $\hat{v}$ are unit vectors and $\theta$ is the acute angle between them, then $ 2 \hat{u} \times 3 \hat{v}$ is a unit vector for :

asked Nov 29, 2018 by pady_1

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The sum of the series $\frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} - ...$ upto infinity is :

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Let $ A = \begin{bmatrix} 5 & 5 \alpha & \alpha \\\ 0 & \alpha & 5 \alpha \\ 0 & 0 & 5 \end{bmatrix}$ <br> If $|A^2| = 25$, then $|\alpha|$ equals :

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The function $f(x) = \tan^{-1} (\sin x + \cos x) $ is an increasing function in :

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A value of C for which the conclusion of Mean Value Theorem holds for the function $f(x) = \log_e x $ on the interval $[1,3]$ is :

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If a line makes an angle of $\frac{\pi}{4}$ with the positive directions of each of $x-axis$ and $y-axis$, then the angle that the line makes with the positive direction of the $z-axis$ is :

asked Nov 29, 2018 by pady_1

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For the Hyperbola $\frac{x^2}{\cos^2 \alpha} - \frac{y^2}{\sin^2 \alpha} = 1$, which of the following remains constant when $\alpha$ varies?

asked Nov 29, 2018 by pady_1

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If $D = \begin{vmatrix} 1 & 1 & 1 \\ 1 & 1+x & 1 \\ 1 & 1 & 1+y \end{vmatrix}$ for $x \neq 0, y \neq 0$, then $D$ is :

asked Nov 29, 2018 by pady_1

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Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is :

asked Nov 29, 2018 by pady_1

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The resultant of two forces $P \;N$ and $3\; N$ is a force of $7\; N$. If the direction of the $3\; N$ force were reversed, the resultant would be $\sqrt{19} N$. The value of $P$ is :

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If $ | z+4| \leq 3$, then the maximum value of $|z+1|$ is :

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The normal to a curve at $P(x,y)$ meets the $x-axis$ at $G$. If the distance of $G$ from the origin is twice the abscissa of $P$, then the curve is a :

asked Nov 29, 2018 by pady_1

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The sum of the series <br> $^{20}C_0 - ^{20}C_1 + ^{20}C_2 - ^{20}C_3 + . . . .- . . . . + ^{20}C_{10}$ is :

asked Nov 29, 2018 by pady_1

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A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB (=a) subtends an angle of $60^{\circ}$ at the foot of the tower and the angle of elevation of the top of the tower from A or B is $30^{\circ}$. The height of the tower is :

asked Nov 29, 2018 by pady_1

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If $p$ and $q$ are positive real numbers such that $p^2 + q^2 = 1$, then the maximum value of $(p + q)$ is :

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The differential equation of all circles passing through the origin and having their centres on the $x-axis$ is :

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Let $L$ be the line of intersection of the planes $2x + 3y + z = 1$ and $x + 3y + 2z = 2$. If $L$ makes an angle $\alpha$ with the positive $x-axis$, then $\cos \alpha $ equals :

asked Nov 29, 2018 by pady_1

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Consider a family of circles which are passing through the point $(-1, 1)$ and are tangent to $x-axis$. If $(h, k)$ are the coordinates of the centre of the circles, then the set of values of $k$ is given by the interval :

asked Nov 29, 2018 by pady_1

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A pair of fair dice is thrown independently three times. The probabiliy of getting a score of exactly 9 twice is :

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A body weighing 13 kg is suspended by two strings 5 m and 12 m long, their outer ends being fastened to the extremities of a rod 13 m long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are :

asked Nov 29, 2018 by pady_1

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The largest interval lying in $(-\frac{\pi}{2}, \frac{ \pi}{2})$ for which the function $[f(x) = 4 x^{-x^2} + \cos^{-1} (\frac{x}{2} - 1) + \log (\cos x) ]$ is defined, is :

asked Nov 29, 2018 by pady_1

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The set $S : \{1, 2, 3, . . . . ,12\}$ is to be partitioned into three sets $A, B, C$ of equal size. Thus, $A \cup B \cup C = S, A \cap B = B \cap C = A \cap C = \phi$. The number of ways to partition $S$ is :

asked Nov 29, 2018 by pady_1

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In the binomial expansion of $(a-b)^n, n \geq 5$, the sum of $5^{th}$ and $6^{th}$ terms is zero, then $\frac{a}{b}$ equals :

asked Nov 29, 2018 by pady_1

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In $\sin^{-1} (\frac{x}{5}) + \mathrm{cosec}^{-1}(\frac{5}{4}) = \frac{\pi}{2}$, then $a$ value of $x$ is :

asked Nov 29, 2018 by pady_1

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