Recent questions tagged 2016

Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to $A$ and $T$, respectively. At time $t=0$ one particle has displacement $A$ while the other one has displacement $\large\frac{−A}{2}$ and they are moving towards each other. If they cross each other at time t, then t is :

asked May 18, 2017 by meena.p

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The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is :

asked May 18, 2017 by meena.p

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$200\; g$ water is heated from $40^{\circ}C$ to $60^{\circ}C$. Ignoring the slight expansion of water, the change in its internal energy is close to(Given specific heat of water$=4184\; J/kg/K)$ :

asked May 18, 2017 by meena.p

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Consider a water jar of radius $R$ that has water filled up to height $H$ and is kept on a stand of height h (see figure). Through a hole of radius $r (r << R)$ at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure.If the radius of the cross-section of water stream when it hits the ground is $x$. Then :

asked May 18, 2017 by meena.p

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Figure shows elliptical path abcd of a planet around the sun $S$ such that the area of triangle csa is $\large\frac{1}{4}$ the area of the ellipse. (See figure) With db as the semimajor axis, and ca as the semiminor axis. If $t_1$ is the time taken for planet to go over path abc and $t_2$ for path taken over cda then :

asked May 18, 2017 by meena.p

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A cubical block of side $30\;cm$ is moving with velocity $2 \;ms^{−1}$ on a smooth horizontal surface. The surface has a bump at a point $O$ as shown in figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is :

asked May 18, 2017 by meena.p

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A car of weight $W$ is on an inclined road that rises by $100\; m$ over a distance of $1\; km$ and applies a constant frictional force $\large\frac{W}{20}$ on the car. While moving uphill on the road at a speed of $10 ms^{−1},$ the car needs power $P$. If it needs power $\frac{P}{2}$ while moving downhill at speed $v$ then value of v is :

asked May 18, 2017 by meena.p

1 answer

A rocket is fired vertically from the earth with an acceleration of $2g,$ where $g$ is the gravitational acceleration. On an inclined plane inside the rocket, making an angle $\theta$. With the horizontal , a point object of mass $m$ is kept. The minimum coefficient of friction $\mu_{min}$ between the mass and the inclined surface such that he mass does not move is :

asked May 18, 2017 by meena.p

1 answer

Which of the following option correctly describes the variation of the speed v and acceleration ‘a’ of a point mass falling vertically in a viscous medium that applies a force $F =−kv,$ where ‘k’ is a constant, on the body ? (Graphs are schematic and not drawn to scale)

asked May 18, 2017 by meena.p

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In the following ‘I’ refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity :

asked May 18, 2017 by meena.p

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The Boolean Expression $(p \wedge \sim q) \vee q \vee (\sim p \wedge q)$\ is quivalent to :

asked Mar 22, 2017 by meena.p

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A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is $30^{\circ}$. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is $60^{\circ}$. Then the time taken (in minutes) by him, from B to reach the pillar, is :

asked Mar 22, 2017 by meena.p

1 answer

If $0 \leq x < 2 \pi$, then the number of real values of $x$, which satisfy the equation $\cos x + \cos 2x = \cos 3x + \cos 4x = 0,$ is :

asked Mar 22, 2017 by meena.p

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Let two fair six-faced dice A and B be thrown simultaneously. If $E_1$ is the event that die $A$ shows up four, $E_2$ is the event that die B shows up two and $E_3$ is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?

asked Mar 21, 2017 by meena.p

1 answer

If the standard deviation of the numbers $2, 3, a$ and $11$ is $3.5,$ then which of the following is true?

asked Mar 21, 2017 by meena.p

1 answer

Let $\overrightarrow{a}, \overrightarrow{b}$ and $\overrightarrow{c}$be three unit vectors such that $\overrightarrow{a} \times (\overrightarrow{b} \times \overrightarrow{c}) = \large\frac{3}{2}(\overrightarrow{b}+\overrightarrow{c})$. If $\overrightarrow{b}$ If $\overrightarrow{b}$ is not parallel to $\overrightarrow{c}$ , then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is :

asked Mar 21, 2017 by meena.p

1 answer

If the line, $\large\frac{x-3}{2} =\frac{y+2}{-1}=\frac{z-4}{3}$ lies in the plane,$lx + my - z = 9,$ then $l^2+m^2$ is equal to :

asked Mar 21, 2017 by meena.p

1 answer

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half the distance between its foci, is:

asked Mar 21, 2017 by meena.p

1 answer

Let P be the point on the parabola, $y^2= 8x$ which is at a minimum distance from the centre $C$ of the circle, $x^2+(y + 6)^2= 1.$ Then the equation of the circle, passing through C and having its centre at P is:

asked Mar 21, 2017 by meena.p

1 answer

If one of the diameters of the circle, given by the equation, $x^2 + y^2-4x+6y -12 = 0,$ is a chord of a circle S, whose centre is at $(-3, 2),$ then the radius of S is:

asked Mar 21, 2017 by meena.p

1 answer

The centres of those circles which touch the circle, $x^2+y^2- 8x -8y-4 = 0,$ externally and also touch the x-axis, lie on:

asked Mar 21, 2017 by meena.p

1 answer

Two sides of a rhombus are along the lines, $x = y + 1 = 0$ and $7x - y - 5 = 0$. If its diagonals intersect at $(-1, -2)$, then which one of the following is a vertex of this rhombus?

asked Mar 21, 2017 by meena.p

1 answer

If a curve $y = f(x)$ passes through the point $(1, -1)$ and satisfies the differential equation,$y(1 + xy) dx = x dy,$ then $f\bigg(\large\frac{-1}{2}\bigg)$ is equal to :

asked Mar 20, 2017 by meena.p

1 answer

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

asked Mar 20, 2017 by meena.p

1 answer

$\lim_\limits{n \to \infty} \bigg( \large\frac{(n-1)(n+2)....3n}{n^{2n}}\bigg)^{1/n}$ is eaual to

asked Mar 20, 2017 by meena.p

1 answer

The integral $\int \large\frac{2x^{12} +5x^{9}}{(x^2+x^3+1)^3}$$dx$ is equal to

asked Mar 17, 2017 by meena.p

1 answer

A wire of length $2$ units is cut into two parts which are bent respectively to form a square of side = x units and a circle of radius = r units. If the sum of the areas of the square and the circle so formed is minimum, then:

asked Mar 16, 2017 by meena.p

1 answer

Consider $f(x) = \tan ^{-1} \bigg( \sqrt{\Large\frac{1+ \sin x}{1- \sin x}}\bigg),$$x \in \bigg(0, \large\frac{\pi}{2} \bigg)$ A normal to $y = f(x)$ at $x =\large\frac{\pi}{6}$ also passes through the point:

asked Mar 16, 2017 by meena.p

1 answer

For $x \in R ,f(x) = | \log 2 - \sin x | $ and $g(x) =f(f(x))$, then

asked Mar 16, 2017 by meena.p

1 answer

Let $p = \lim \limits_{x \to 0+} (1+ \tan ^2 \sqrt x )^{1/2x}$ then long p is equal to

asked Mar 16, 2017 by meena.p

1 answer

If the sum of the first ten terms of the series $\bigg(1 \large\frac{3}{5}\bigg) \normalsize +\bigg(2 \large\frac{2}{5} \bigg)^2 \normalsize +\bigg(3 \large\frac{1}{5}\bigg)^2 \normalsize +4^2 +\bigg(4 \large\frac{4}{5} \bigg)^2 \normalsize +.....is\;\large\frac{16}{5}$$\;m$ then m is equal to

asked Mar 16, 2017 by meena.p

1 answer

If the $2^{nd},5^{th}$ and $9^{th}$ terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is:

asked Mar 16, 2017 by meena.p

1 answer

If the number of terms in the expansion of $\bigg(1- \large\frac{2}{x}+\frac{4}{x^2}\bigg)^n,x \neq 0,$ is 28, then the sum of the coefficients of all the terms in this expansion, is

asked Mar 15, 2017 by meena.p

1 answer

If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is:

asked Mar 15, 2017 by meena.p

1 answer

The system of linear equations <br> $x + \lambda y - z = 0 \\\lambda x - y - z = 0 \\x + y - \lambda z = 0$ has a non-trivial solution for:

asked Mar 15, 2017 by meena.p

1 answer

If $A =\begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix}$ and $A \;adj A = AA^T$, then $5a+b$ is equal to

asked Mar 15, 2017 by meena.p

1 answer

The sum of all real values of x satisfying the equation $(x^2-5x+5)^{x^2+4x-60}=1$ is :

asked Mar 15, 2017 by meena.p

1 answer

A value of $\theta$ for which $ \large\frac{2+3 i \sin \theta}{1- 2 i \sin \theta}$ is purely imaginary , is

asked Mar 15, 2017 by meena.p

1 answer

If $f(x) +2y \bigg(\large\frac{1}{x}\bigg)$$=3x,x \neq 0$ and $S=\{x \in R:f(x)=f(-x)\}$ then S:

asked Mar 15, 2017 by meena.p

1 answer

The hottest region of Bunsen flame shown in the figure below is :

asked Mar 14, 2017 by meena.p

1 answer

Which of the following is an anionic detergent ?

asked Mar 14, 2017 by meena.p

1 answer

Thiol group is present in :

asked Mar 14, 2017 by meena.p

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Which of the following statements about low density polythene is FALSE ?

asked Mar 14, 2017 by meena.p

1 answer

In the Hofmann bromamide degradation reaction, the number of moles of $NaOH$ and $Br_2$ used per mole of amine produced are :

asked Mar 14, 2017 by meena.p

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The reaction of propene with $HOCl(Cl_2 + H_2O)$ proceeds through the intermediate :

asked Mar 14, 2017 by meena.p

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2-chloro-2-methylpentane on reaction with sodium methoxide in methanol yields :

asked Mar 14, 2017 by meena.p

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The absolute configuration of

asked Mar 14, 2017 by meena.p

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The product of the reaction given below is :

asked Mar 14, 2017 by meena.p

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The distillation technique most suited for separating glycerol from spent - lye in the soap industry is :

asked Mar 14, 2017 by meena.p

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The concentration of fluoride, lead, nitrate and iron in a water sample from an underground lake was found to be $1000\;ppb, 40\;ppb, 100\; ppm$ and $0.2\;ppm$, respectively. This water is unsuitable for drinking due to high concentration of :

asked Mar 14, 2017 by meena.p

1 answer

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