Recent questions tagged past papers

A beam of unpolarised light of intensity $I_{_0}$ is passed through a polaroid A and then through another polaroid B which is oriented so that its principal plane makes an angle of $45^{\circ}$ relative to that of A. The intensity of the emergent light is:

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Two charges, each equal to q, are kept at $x = -a$ and $x= a$ on the x-axis. A particle of mass m and charge $q_{_0} = \frac{q}{2}$ is placed at the origin. If charge $q_{_0}$ is given a small displacement ( y a) along the y-axis, the net force acting on the particle i proportional to :

asked Dec 11, 2018 by pady_1

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A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. The extension $x_0$ of the spring when it is in equilibrium is: (Here k is spring constant)

asked Dec 11, 2018 by pady_1

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The supply voltage to a room is 120 V. The resistance of the lead wires is 6 $\Omega$. A 60 W bulb is already switched on. What is the decrease of voltage across the bulb, when a 240 W heater is switched on in parallel to the bulb?

asked Dec 11, 2018 by pady_1

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A diode detector is used to detect an amplitude modulated wave of 60% modulation by using a condenser of capacity 250 pico farad in parallel with a load resistance 100 kilo ohm. Find the maximum modulated frequency which could be detected by it.

asked Dec 11, 2018 by pady_1

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In an LCR circuit as shown below both switches are open initially. Now switch $S_1$ is closed, $S_2$ kept open. (q is charge on the capacitor and $\tau = RC$ is capacitive time constant). Which of the following statement is correct?

asked Dec 11, 2018 by pady_1

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The term independent of $x$ is expansion of $\begin{pmatrix} \frac{x+1}{x^{2/3}-x^{1/3} + 1 } - \frac{x-1}{x - x^{1/2}} \end{pmatrix}^{10}$ is

asked Dec 11, 2018 by pady_1

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Distance between two parallel planes $2x + y + 2z = 8$ and $4x + 2y + 4z + 5 = 0$ is

asked Dec 11, 2018 by pady_1

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If the equation $x^2 + 2x + 3 = 0$ and $ax^2 + bx + c = 0, a, b, c \in R$, have a common root, then a : b : c$ is

asked Dec 11, 2018 by pady_1

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The $z$ is a complex number of unit modulus an argument $\theta$, then $arg \begin{pmatrix}\frac{1+z}{1+ \overline{z}} \end{pmatrix}$ equals

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A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is

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If the vectors $\overline{AB} = 3 \hat{i} + 4 \hat{k}$ and $\overline{AC} = 5 \hat{i} - 2 \hat{j} + 4 \hat{k}$ are the sides of a triangles ABC, then the length of the median through A is

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Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of $A \times B$ having 3 or more elements is

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If the lines $\frac{x-2}{1} = \frac{y-3}{1} = \frac{z-4}{-k}$ and $\frac{x-1}{k} = \frac{y-4}{2} = \frac{z-5}{1}$ are coplanar, then $k$ can have

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If $y = \sec(\tan^{-1}x)$, then $\frac{dy}{dx} $ at $x=1$ is equal to

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The numbers of values of k, for which the system of equations $( k + 1) x + 8y = 4k $ kx + (k + 3)y = 3k - 1$ has no solution, is

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If $P = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix}$ is the adjoint of a $3 \times 3$ matrix A and $|A| = 4$, then $\alpha$ is equal to

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Statement -I : The value of the integral $\begin{align} \int_{\pi/6}^{\pi/3} \frac{dx}{1+\sqrt{\tan x} } \end{align}$ is equal to $\frac{\pi}{6}$. Statement-II : $\begin{align} \int_a^b f(x) dx = \int_a^b f(a+b-x) dx \end{align}$

asked Dec 11, 2018 by pady_1

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At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers $x$ is given by $\frac{dP}{dx} = 100 - 12\sqrt{x}$. If the firm employs 25 more workers, then the new level of production of items is

asked Dec 11, 2018 by pady_1

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Let $T_n$ be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If $T_{n+1} - T_n = 10$, then the value of $n$ is

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$\displaystyle{\lim_{x \to 0} \frac{(1 - \cos 2x) ( 3 + \cos x)}{ x \tan 4 x}}$ is equal to

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The real number $k$ for which the equation, $2x^3 + 3x+ k = 0$ has two distinct real roots in $[0, 1]$

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The expression $\frac{\tan A}{1 - \cot A} + \frac{\cot A}{1 - \tan A} $ can be written as

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The area (in square units) bounded by the curves $y = \sqrt{x}, 2y - x + 3 = 0$, x-axis, and lying in the first quadrant is

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Consider : Statement -I : $(P \wedge \sim q ) \wedge ( \sim p \wedge q )$ is a fallacy. Statement-II : $(p \to q) \leftrightarrow ( \sim q \to \sim p)$ is a tautology.

asked Dec 11, 2018 by pady_1

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The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, ….. , is

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The intercepts on x-axis made by tangents to the curve, $\begin{align} y = \int_0^x |t| dt. x \in R \end{align}$. which are parallel to the line $y = 2x$, are equal to

asked Dec 11, 2018 by pady_1

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The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as (0, 1), (1, 1) and (1, 0) is

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The equation of the circle passing through the foci of the ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$, and having centre at (0, 3) is

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If $\displaystyle\int f (x) dx = \Psi (x)$, then $\displaystyle\int x^5 f (x^3) dx$ is equal to

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If $x, y, z$ are in A.P and $\tan^{-1}x. \tan^{-1}y$ and $\tan^{-1}z$ are also in A.P., then

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All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given ?

asked Dec 11, 2018 by pady_1

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A ray of light along $x + \sqrt{3}y = \sqrt{3}$ gets reflected upon reaching x-axis , the equation of the reflected rays is

asked Dec 11, 2018 by pady_1

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Given : A circle, $2x^2 + 2y^2 = 5 $ and a parabola. $y^2 = 4 \sqrt{5} x$. Statement - I : An equation of a common tangent to these curves is $y = x+\sqrt{5}$. Statement - II : If the line, $y = mx + \frac{\sqrt{5}}{m} (m \neq 0)$is their common tangent, then m satisfies $m^4 - 3m^2 +2 = $

asked Dec 11, 2018 by pady_1

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ABCD is a trapezium such that AB and CD are parallel and $BC \perp CD$. If $\angle{ADB} = \theta, \; BC = p$ and $CD = q$, then AB is equal to

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The circle passing through (1, -2) and touching the axis of $x$ at $(3, 0)$ also passes through the point

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In which of the following pairs of molecules/ions, both the species are not likely to exist?

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An organic compound A upon reacting with $NH_3$ gives B. On heating B gives C. C in presence of KOH reacts with $Br_2$ to give $CH_3CH_2NH_2$. A is

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Energy of an electron is given by $E= -2.178 \times 10^{18} J \bigg(\large\frac{Z^2}{n^2}\bigg)$. Wavelength of light required to excite an electron in an hydrogen atom from level $n = 1$ to $n = 2$ will be

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Compound (A), $C_8H_9Br$, gives a white precipitate when warmed with alcoholic $AgNO_3$. Oxidatiion of (A) gives a acid (B), $C_8H_6O_4$. (B) easily forms anhydride on heating. Identify the compound (A).

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Which of the following exists as covalent crystals in the solid state ?

asked Dec 11, 2018 by pady_1

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Consider the following reaction : $xMnO_4^- + yC_2O_4^{2-} + zH^+ \rightarrow xMn^{2+} + 2yCO_2 + \frac{z}{2}H_2O$ The values of $x, y$ and $z$ in the reaction are, respectively :

asked Dec 11, 2018 by pady_1

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The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was :

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For gaseous state, if most probable speed is denoted by $C^*$, average speed by $\overline{C}$ and mean square speed by C, then for a large number of molecules the ratios of these speeds are :

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Which of the following represents the correct order of increasing first ionisation enthalpy for Ca, Ba, S, Se and Ar ?

asked Dec 11, 2018 by pady_1

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The order of stability of the following carbocations : is

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A gaseous hydrocarbon given upon combustion 0.72 g of water and 3.08 g of $CO_2$. The empirical formula of the hydrocarbon is :

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A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 mL to 375 mL at a constant temperature of $37.0^0C$. Ad it does so, it absorbs 208 J of heat. The values of q and w for the process will be : $(R = 8.314 \; J/mol\; K) \; (\ell n 7.5 = 2.01)$

asked Dec 11, 2018 by pady_1

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Which of the following complex species is not expected to exhibit optical isomerism ?

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Synthesis of each molecule of glucose in photosynthesis involves :

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