Recent questions and answers in 2002

In a $\Delta ABC$, $\tan \frac{A}{2} = \frac{5}{6}, \; \tan \frac{C}{2} = \frac{2}{5}$, then :

answered Jun 2, 2020 by tharunkona111

1 answer

A light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (vertically). If the acceleration of the system is $g/8$, then the ratio of the masses is :

answered Apr 4, 2020 by harshitha1810reddy

1 answer

Wires 1 and 2 carrying currents $i_1$ and $i_2$ respectively are inclined at an angle $\theta$ to each other. What is the force on a small element $dl$ of wire 2 at a distance $r$ from wire 1 (as shown in figure) due to the magnetic field of wire 1 ?<br>

answered Aug 20, 2019 by ankitchaahat

1 answer

One end of massless rope, which passes over a massless and frictionless pulley $P$ is tied to a hook $C$ while the other end is free. Maximum tension that the rope can bear is 360 N. With what value of maximum safe acceleration (in $ms^{-2}$) can a man of 60 kg climb on the rope ? <br>

answered Aug 13, 2019 by sourabhm2001

1 answer

Identify the pair whose dimension are equal :

answered Jul 1, 2019 by meena.clay6

1 answer

For the following reaction in gaseous phase : <br> $CO + \frac{1}{2}O_2 \to CO_2 \; \; \; \; K_c/K_p$ is :

asked Dec 11, 2018 by pady_1

0 answers

The number of real roots of $3^{2x^2 - 7x + 7} =9$ is :

asked Dec 11, 2018 by pady_1

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If $|x| < 1$, then the coefficient of $x^n$ in expansion of $(1 + x + x^2 + x^3 + ...)^2$ is :

asked Dec 11, 2018 by pady_1

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The coefficient of $x^5$ in $(1 + 2x + 3x^2 + ....)^{-3/2}$ is :

asked Dec 11, 2018 by pady_1

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$e^{(x-1) - \frac{1}{2} (x-1)^2 + \frac{(x-1)^3}{3} - \frac{(x-1)^4}{4} + . . . } $ equal to :

asked Dec 11, 2018 by pady_1

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$\displaystyle \lim_{n = 0}^{\infty} \frac{(\log_e x)^n}{n!}$ is equal to

asked Dec 11, 2018 by pady_1

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$\tan^{-1} (\frac{1}{4}) + \tan^{-1} (\frac{2}{9})$ is equal to :

asked Dec 11, 2018 by pady_1

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If $\alpha$ is a root of $25 \cos^2 \theta + 5 \cos \theta - 12 =0$ $\frac{\pi}{2} < \alpha < \pi$, then $\sin 2 \alpha$ is equal to :

asked Dec 11, 2018 by pady_1

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The equation $a \sin x + b \cos x = c$ where $|c| > \sqrt{a^2 + b^2}$ has :

asked Dec 11, 2018 by pady_1

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In a triangle $ABC, \; a = 4, \; b = 3, \; \angle{A} = 60^{\circ}$, then $c$ is the root of the equation :

asked Dec 11, 2018 by pady_1

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If $y = \sin^2 \theta + \mathrm{cosec}^2 \theta, \; \theta \neq 0$, then :

asked Dec 11, 2018 by pady_1

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If $\sin (\alpha + \beta) = 1$, $\sin (\alpha- \beta) = \frac{1}{2}$, then $\tan (\alpha + 2\beta) \tan (2 \alpha +\beta)$ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

If $\tan \theta = -\frac{4}{3} $, then $\sin \theta$ is :

asked Dec 11, 2018 by pady_1

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The value of $\frac{1 - \tan^2 15^{\circ}}{1+ \tan^2 15^{\circ}}$ is :

asked Dec 11, 2018 by pady_1

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The centre of the circle given by $\overrightarrow{r}.(\hat{i} + 2 \hat{j} + 2 \hat{k}) =15 $ and $| \overrightarrow{r} - (\hat{j} + 2 \hat{k})| = 4$ is :

asked Dec 11, 2018 by pady_1

0 answers

If the vectors $\overrightarrow{a} = x \hat{i} + y \hat{j} + z \hat{k} $ and such that $\overrightarrow{a} , \; \overrightarrow{c}$ and $\overrightarrow{b}$ form a right handed system, then $\overrightarrow{c}$ is :

asked Dec 11, 2018 by pady_1

0 answers

The equation of the chord joining two points $(x_1, y_1)$ and $(x_2, y_2)$ on the rectangular hyperbola $xy = c^2$ is :

asked Dec 11, 2018 by pady_1

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The equation of the ellipse whose foci are $(\pm 2, 0)$ and eccentricity is $1/2$ is :

asked Dec 11, 2018 by pady_1

0 answers

The equation of the tangent to the circle $x^2 +y^2 + 4x-4y + 4 =0$ which make equal intercepts on the positive co-ordinate axes, is :

asked Dec 11, 2018 by pady_1

0 answers

The greatest distance of the point $P(10, 7)$ from the circle $x^2 + y^2 - 4x - 2y - 20 = 0$ is :

asked Dec 11, 2018 by pady_1

0 answers

A straight line through the point $(2, 2)$ intersects the lines $\sqrt{3}x + y = 0$ and $\sqrt{3}x - y = 0$ at the points A and B. The equation to the line AB so that the OAB is equilateral, is :

asked Dec 11, 2018 by pady_1

0 answers

Three straight lines $2x+ 11y - 5 = 0, \; 24x + 7y - 20 = 0$ and $4x - 3y - 2 = 0$ :

asked Dec 11, 2018 by pady_1

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Let $f(2) = 4$ and $f'(2) = 4$. Then $\begin{align} \displaystyle\lim_{x \to 2} \frac{xf(2) - 2 f(x)}{x-2} \end{align}$ is given by :

asked Dec 11, 2018 by pady_1

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A fair die is tossed eight times. The probability that a third six is observed on the eight throw, is :

asked Dec 11, 2018 by pady_1

0 answers

A biased coin with probability $p, \; 0 < p < 1$, of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even, is $2/5$, then $p$ equals :

asked Dec 11, 2018 by pady_1

0 answers

If $(\omega \neq 1)$ is a cubic root of unity, then $\begin{vmatrix} 1 & 1+i + \omega^2 & \omega^2 \\ 1-i & -1 & \omega^2 - 1\\ -i & -1+\omega -i & -1 \end{vmatrix}$ equals :

asked Dec 11, 2018 by pady_1

0 answers

The probability of India winning a test match against West-Indies is $1/2$ assuming independence from match to match. The probability that in a match series India's second win occurs at the test is :

asked Dec 11, 2018 by pady_1

0 answers

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

asked Dec 11, 2018 by pady_1

0 answers

$\sin^2 \theta = \frac{4xy}{(x+y)^2}$ is true if and only is :

asked Dec 11, 2018 by pady_1

0 answers

If $\begin{vmatrix} 6 {i} & - 3 {i} & 1 \\ 4 & 3 {i} & -1 \\ 20 &3 & i \end{vmatrix} = x + i y$, then :

asked Dec 11, 2018 by pady_1

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If $\omega$ is an imaginary cube root of unity, then $(1 + \omega - \omega^2 )^7 $ equals :

asked Dec 11, 2018 by pady_1

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If the vectors $\overrightarrow{a}, \overrightarrow{b}$ and $\overrightarrow{c}$ from the sides $BC, CA$ and $AB$ respectively of a triangle $ABC$, then :

asked Dec 11, 2018 by pady_1

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The incentre of the triangle with vertices $(1, \sqrt{3}), \; (0,0)$ and $(2, 0)$ is :

asked Dec 11, 2018 by pady_1

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For $\begin{align} x \in R, \; \displaystyle\lim_{x \to \infty} \begin{pmatrix} \frac{x-3}{x+2} \end{pmatrix}^x \end{align}$ is equal to :

asked Dec 11, 2018 by pady_1

0 answers

In a triangle ABC, $2ca \sin \frac{A - B + C}{2}$ is equal to :

asked Dec 11, 2018 by pady_1

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Let $T_n$ denote the number of triangles which can be formed using the vertices of a regular polygon of $n$ sides. If $T_{n+1} - T_n = 21$ , then $n$ equals :

asked Dec 11, 2018 by pady_1

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The equation of the directrix of the parabola $y^2 + 4y + 4x + 2 =0$ is :

asked Dec 11, 2018 by pady_1

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If A and B are two mutually exclusive events, then :

asked Dec 11, 2018 by pady_1

0 answers

A and B play a game where each is asked to select a number from 1 to 25. If the two number match, both of them win a prize. The probability that they will not win a prize in a single trial, is :

asked Dec 11, 2018 by pady_1

0 answers

The equation of the plane containing the line $\frac{x-x_1}{l} = \frac{y-y_1}{m} = \frac{z- z_1}{n}$ is $a(x-x_1) + b(y-y_1) + c ( z - z_1) = 0$, where :

asked Dec 11, 2018 by pady_1

0 answers

A parallelopiped is formed by planes drawn through the points (2, 3, 5) and (5, 9, 7) parallel to the co-ordinate planes. The length of a diagonal to the parallelopiped is :

asked Dec 11, 2018 by pady_1

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The vector $\hat{i} + x \hat{j} + 3 \hat{k}$ is rotated through an angle $\theta$ and doubled in magnitude, then it becomes $4 \hat{i} + ( 4x - 2) \hat{j} + 2 \hat{k}$. The value of $x$ are :

asked Dec 11, 2018 by pady_1

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Given two vectors are $\hat{i} - \hat{j}$ and $\hat{i} + 2 \hat{j}$ the unit vector coplanar with the two vectors and perpendicular to first is :

asked Dec 11, 2018 by pady_1

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The differential equation of all non-vertical lines in a plane is :

asked Dec 11, 2018 by pady_1

0 answers

The area bounded by the curve $y = 2x - x^2$ and the straight line $y = -x$ is given by :

asked Dec 11, 2018 by pady_1

0 answers

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