Recent questions tagged 2001

$\begin{align} \int \frac{dx}{\sqrt{x} (x+9)} \end{align}$ is equal to :

asked Dec 11, 2018 by pady_1

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If $u = xy^2 \tan^{-1} (\frac{y}{x})$, then $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y}$ is equal to :

asked Dec 11, 2018 by pady_1

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If $u = e^{x^2 -y^2}$, then :

asked Dec 11, 2018 by pady_1

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The maximum value of $xy$ subject to $x+y =7$ is :

asked Dec 11, 2018 by pady_1

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The area (in square units) of the region bounded by $x^2 = 8y, \; x = 4$ and $x$-axis, is :

asked Dec 11, 2018 by pady_1

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The equation of tangent to the curve $6y = 7 - x^3$ at $(1,1)$ is :

asked Dec 11, 2018 by pady_1

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The minimum value of $(x- \alpha) ( x-\beta)$ is:

asked Dec 11, 2018 by pady_1

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If $f(x) = \frac{x^2}{x+a}$, then $f''(a)$ is equal to :

asked Dec 11, 2018 by pady_1

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If $y_{_k}$ is the $k^{th}$ derivative of $y$ with respect to $'x'$ and $y = \cos (\sin x)$, then $y_{_1} \sin x+y_{_2} \cos x$ is equal to :

asked Dec 11, 2018 by pady_1

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$\frac{d}{dx} \sin^{-1} (3x-4x^3)$ is equal to :

asked Dec 11, 2018 by pady_1

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If $h(x) = x^{x^2}$, then at $x=1$ $\frac{h'(x)}{h(x)}$ is equal to :

asked Dec 11, 2018 by pady_1

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If $f(x) = \frac{x^2 - 10x + 25}{x^2 - 7x + 10}$ and $f$ is continuous at $x=5$, then $f(5)$ is equal to :

asked Dec 11, 2018 by pady_1

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$\displaystyle\lim_{x \to 0} \begin{pmatrix}\frac{x. 10^x - x}{1-\cos x}\end{pmatrix} $ is equal to :

asked Dec 11, 2018 by pady_1

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$\displaystyle\lim_{x \to \infty} \begin{pmatrix}\frac{x+a}{x+b}\end{pmatrix}^{a+b} $ is equal to :

asked Dec 11, 2018 by pady_1

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Evaluate $\begin{align} \int_{-1}^1 f(x) \;dx \end{align}$, where <br> <br>$f(x) = \begin{cases} 1-2x, & x \leq 0 \\ 1+2x, & x \geq 0 \end{cases} $

asked Dec 11, 2018 by pady_1

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Equation of curve in polar co-ordinates is $\frac{l}{r} = 2 \sin^2 \frac{\theta}{2}$, then it represents :

asked Dec 11, 2018 by pady_1

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The equation $16x^2 + y^2 + 8xy - 74x -78 y +212 = 0$ represents :

asked Dec 11, 2018 by pady_1

1 answer

The products of lengths of perpendiculars from any point of hyperbola $x^2 - y^2 =8 $ to its asymptotes; is :

asked Dec 11, 2018 by pady_1

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The eccentricity of ellipse $\frac{x^2}{16} + \frac{y^2}{9}=1$ is:

asked Dec 11, 2018 by pady_1

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If the normal to the parabola $y^2 = 4x$ at $P(1,2)$ meets the parabola again in $Q$, then co-ordinates of $Q$ are :

asked Dec 11, 2018 by pady_1

1 answer

The length of latus rectum of parabola $y^2 + 8x -2y+17=0$ is :

asked Dec 11, 2018 by pady_1

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If the polar of a point on the circle $x^2+y^2=p^2$ with respect to the circle $x^2+y^2=q^2$ touches the circle $x^2+y^2=r^2$, then $p, q, r$ are in:

asked Dec 11, 2018 by pady_1

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The radical axis of circles $x^2 + y^2 + 5x + 4y-5=0$ and $x^2 + y^2 - 3x+ 5y-6=0$ is

asked Dec 11, 2018 by pady_1

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The limiting points of the co-axial system containing the two circles $x^2 +y^2+2x-2y+2=0$ and $25(x^2+y^2) -10x -80 y +65 =0$ are:

asked Dec 11, 2018 by pady_1

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The equation of the normal to the circle $x^2 + y^2 + 6 x + 4y -3=0$ at $(1,-2)$ is:

asked Dec 11, 2018 by pady_1

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A variable plane is at a constant distance $h$ from the origin and meets the co-ordinate axes in A, B, C. Locus of centroid of $\Delta ABC$ is :

asked Dec 11, 2018 by pady_1

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If $P = (0, 1, 2), \; Q = (4, -2,1), O = (0, 0, 0 )$, then $\angle{POQ}$ is equal to :

asked Dec 11, 2018 by pady_1

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If the foot of the perpendicular from $(0, 0, 0)$ to the plane is $(1,2,2)$, then the equation of the plane is :

asked Dec 11, 2018 by pady_1

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If a line makes angle $\frac{\pi}{3}$ and $\frac{\pi}{4}$ with the $x$-axis and $y$-axis respectively, then the angle made by the line with the $z$-axis is :

asked Dec 11, 2018 by pady_1

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The foot of the perpendicular from $(0, 2, 3)$ to the line $\frac{x+3}{5} = \frac{y-1}{2} = \frac{z+4}{3}$ is :

asked Dec 11, 2018 by pady_1

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If the extremities of diagonal of a square $(1, -2, 3), \; (2, -3, 5)$ then the length of its side, is:

asked Dec 11, 2018 by pady_1

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If the slope of one line is twice the slope of other in the pair of straight lines $ax^2 + 2hxy + by^2=0$, then $8h^2$ is equal to :

asked Dec 11, 2018 by pady_1

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If one of the lines of pair of straight lines $ax^2 + 2hxy + by^2 =0$ bisects the angle between the co-ordinates axes, then :

asked Dec 11, 2018 by pady_1

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The orthocentre of triangle formed by the lines $x + 3y = 10$ and $6x^2 + xy - y^2 = 0$ is :

asked Dec 11, 2018 by pady_1

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The incentre of triangle formed by the lines $x+y = 1, \; x=1, \;y=1$ is :

asked Dec 11, 2018 by pady_1

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The number of circles that touch all the straight lines $x+y=4$, $x-y=-2$ and $y=2$ is :

asked Dec 11, 2018 by pady_1

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The lines $2x + 3y = 6, \; 2x + 3y = 8$ cut the $x$-axis at $A$ and $B$ respectively. A line L drawn through the point $(2,2)$ meets the $x$-axis as $C$ in such a way that abscissae of A, B and C are in arithmetic progression. Then the equation of the line L is :

asked Dec 11, 2018 by pady_1

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For all values of $a$ and $b$ the line $(a + 2b) x + (a-b)y + (a+5b) = 0$ passes through the point :

asked Dec 11, 2018 by pady_1

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For a binomial variate $X$, if $n=4$ and $P(X = 4) =6 \; P(X =2)$, then the value of $p$ is

asked Dec 11, 2018 by pady_1

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Find the binomial probability distribution whose mean is 3 and variance is 2.

asked Dec 11, 2018 by pady_1

1 answer

Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number, is :

asked Dec 11, 2018 by pady_1

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The events A and B have probabilities 0.25 and 0.50 respectively. The probability that both A and B occur simultaneously is 0.14, then the probability that neither A nor B occurs, is :

asked Dec 11, 2018 by pady_1

1 answer

The probabiliy that a number selected at random from the set of numbers $(1, 2, 3, ...., 100)$ is a cube, is :

asked Dec 11, 2018 by pady_1

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In a competition A, B, C are participating the probability that A wins is twice that of B, the probability that B wins is twice that of C, then probability that A loses is :

asked Dec 11, 2018 by pady_1

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$\overrightarrow{a} , \; \overrightarrow{b}, \; \overrightarrow{c}, \; \overrightarrow{d}$ are co-planar vectors, then $(\overrightarrow{a} \times \overrightarrow{b}) \times (\overrightarrow{c} \times \overrightarrow{d})$ is equal to :

asked Dec 11, 2018 by pady_1

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$[ \hat{i}-\hat{j}, \; \hat{j} - \hat{k}, \; \hat{k} - \hat{i} ]$ is equal to :

asked Dec 11, 2018 by pady_1

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If $\theta$ is the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ and $|\overrightarrow{a} \times \overrightarrow{b} | = |\overrightarrow{a}. \overrightarrow{b}|$, then $\theta$ is equal to :

asked Dec 11, 2018 by pady_1

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If $\overrightarrow{a}= \hat{i} + \hat{j} + t \hat{k}$, $\overrightarrow{b} = \hat{i} + 2 \hat{j} +3 \hat{k}$, then the values of $'t'$ for which $(\overrightarrow{a} + \overrightarrow{b})$ and $(\overrightarrow{a} - \overrightarrow{b})$ are perpendicular, are :

asked Dec 11, 2018 by pady_1

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ABCD is a parallelogram, with AC, BD as diagonals, then $\overrightarrow{AC} - \overrightarrow{BD}$ is equal to :

asked Dec 11, 2018 by pady_1

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If $\overrightarrow{a} = \hat{i} + 4 \hat{j}, \; \overrightarrow{b} = 2 \hat{i} - 3 \hat{j}, \; \overrightarrow{c} = 5 \hat{i} + 9 \hat{j}$, then $\overrightarrow{c}$ is equal to :

asked Dec 11, 2018 by pady_1

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