Recent questions and answers in 2013

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

answered Apr 24, 2020 by priyanka.clay6

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

answered Apr 24, 2020 by priyanka.clay6

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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

answered Apr 24, 2020 by priyanka.clay6

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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

answered Apr 24, 2020 by priyanka.clay6

1 answer

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

answered Apr 24, 2020 by priyanka.clay6

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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

answered Apr 24, 2020 by priyanka.clay6

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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

answered Apr 24, 2020 by priyanka.clay6

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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

answered Apr 24, 2020 by priyanka.clay6

1 answer

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

answered Apr 24, 2020 by priyanka.clay6

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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

answered Apr 24, 2020 by priyanka.clay6

1 answer

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

answered Apr 24, 2020 by priyanka.clay6

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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 : $\begin{align} \int_a^b f(x) dx = \int_a^b f(a+b-x) dx \end{align}$

answered Apr 24, 2020 by priyanka.clay6

1 answer

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

answered Apr 24, 2020 by priyanka.clay6

1 answer

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

answered Apr 24, 2020 by priyanka.clay6

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

answered Apr 24, 2020 by priyanka.clay6

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

answered Apr 24, 2020 by priyanka.clay6

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

answered Apr 24, 2020 by priyanka.clay6

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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

answered Apr 24, 2020 by priyanka.clay6

1 answer

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.

answered Apr 23, 2020 by priyanka.clay6

1 answer

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

answered Apr 23, 2020 by priyanka.clay6

1 answer

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

answered Apr 21, 2020 by priyanka.clay6

1 answer

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

answered Apr 21, 2020 by priyanka.clay6

1 answer

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

answered Apr 21, 2020 by priyanka.clay6

1 answer

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

answered Apr 21, 2020 by priyanka.clay6

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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

answered Apr 21, 2020 by priyanka.clay6

1 answer

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 ?

answered Apr 21, 2020 by priyanka.clay6

1 answer

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

answered Apr 21, 2020 by priyanka.clay6

1 answer

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 $m^4 - 3m^2 +2 =$

answered Apr 20, 2020 by priyanka.clay6

1 answer

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

answered Apr 20, 2020 by priyanka.clay6

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

answered Apr 20, 2020 by priyanka.clay6

1 answer

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

answered Jul 22, 2019 by bathinapavankumar789

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Two short bar magnets of length 1 cm each have magnetic moments $1.20\; Am^2$ and $1.00\; Am^2$ respectively. They are placed on a horizontal table parallel to each other with their N poles pointing towards the South. They have a common magnetic equator and are separated by a distance of 20.0 cm. The value of the resultant horizontal magnetic induction at the mid - point O of the line joining their centres is close to (Horizontal component of earth’s magnetic induction is $3.6 \times 10^{–5} Wb/m^2$ )

asked Dec 11, 2018 by pady_1

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The magnetic field in a travelling electromagnetic wave has a peak value of 20 nT. The peak value of electric field strength is :

asked Dec 11, 2018 by pady_1

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Diameter of plano-convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in material of lens is $2 \times 10^8$ m/s, the focal length of the lens is :

asked Dec 11, 2018 by pady_1

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The amplitude of a damped oscillator decreases to 0.9 times its original magnitude is 5s. In another 10s it will decrease to $\alpha$ times its original magnitude, where $\alpha$ equals

asked Dec 11, 2018 by pady_1

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This question has Statement I and Statement II. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement – I : A point particle of mass m moving with speed v collides with stationary point particle of mass M. If the maximum energy loss possible is given as $f (\frac{1}{2} mv^2 )$ then $f = (\frac{m}{M+m})$ . Statement – II : Maximum energy loss occurs when the particles get stuck together as a result of the collision.

asked Dec 11, 2018 by pady_1

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The I – V characteristic of an LED is

asked Dec 11, 2018 by pady_1

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If a piece of metal is heated to temperature $\theta$ and then allowed to cool in a room which is at temperature $\theta_0$ the graph between the temperature T of the metal and time t will be closest to :

asked Dec 11, 2018 by pady_1

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A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 2.0 A flows through the smaller loop, then the flux linked with bigger loop is

asked Dec 11, 2018 by pady_1

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A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is:

asked Dec 11, 2018 by pady_1

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An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and cylinder have equal cross sectional area A. When the piston is in equilibrium, the volume of the gas is $V_0$ and its pressure is $P_0$ . The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency:

asked Dec 11, 2018 by pady_1

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A hoop of radius r and mass m rotating with an angular velocity $\omega_0$ is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

asked Dec 11, 2018 by pady_1

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Two capacitors $C_1$ and $C_2$ are charged to 120 V and 200 V respectively. It is found that by connecting them together the potential on each one can be made zero. Then :

asked Dec 11, 2018 by pady_1

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A projectile is given an initial velocity of $(\hat{i} + 2 \hat{j}) m/s$ , where $\hat{i}$ is along the ground and ˆj is along the vertical. If $g = 10 m/s^2$ , the equation of its trajectory is:

asked Dec 11, 2018 by pady_1

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What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 2R?

asked Dec 11, 2018 by pady_1

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This question has statement I and statement II. Of the four choices given after the statements, choose the one that best describes the two statements. Statement- I: Higher the range, greater is the resistance of ammeter. Statement- II: To increase the range of ammeter, additional shunt needs to be used across it.

asked Dec 11, 2018 by pady_1

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A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1 %. What is the fundamental frequency of steel if density and elasticity of steel are $7.7 \times 10^3 \;kg/m^3$ and $2.2 \times 10^{11}N/m^2$ respectively?

asked Dec 11, 2018 by pady_1

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The above p-v diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat extracted from the source in a single cycle is

asked Dec 11, 2018 by pady_1

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Let $[\varepsilon_0]$ denote the dimensional formula of the permittivity of vaccum. If M = mass, L = length, T = time and A = electric current, then :

asked Dec 11, 2018 by pady_1

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The graph between angle of deviation (δ) and angle of incidence (i) for a triangular prism is represented by:

asked Dec 11, 2018 by pady_1

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