Recent questions tagged 1999

The solution of $2xy \frac{dy}{dx} = 1 + y^2$, is :

asked Dec 19, 2018 by pady_1

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The order of the differential equation $(\frac{dy}{dx})^{^3} + (\frac{dy}{dx})^{^2} + y^4 = 0$ is :

asked Dec 19, 2018 by pady_1

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$\displaystyle \lim_{n \to \infty} \displaystyle\sum_{r=1}^{n} (\frac{1}{n}) \frac{\sqrt{n+r}}{n-r} $ is equal to :

asked Dec 19, 2018 by pady_1

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The approximate value of $\begin{align} \int_{-3}^3 x^4 \;dx \end{align}$, using trapezoidal rule and taking six equal intervals, is :

asked Dec 19, 2018 by pady_1

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The area bounded by the parabola $x = 4 - y^2$ and the $y$-axis (in sq unit) is:

asked Dec 19, 2018 by pady_1

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$\begin{align} \int_0^{\pi} \cos^3x \;dx \end{align}$ is equal to :

asked Dec 19, 2018 by pady_1

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$\begin{align} \int_0^{\pi/4} (\tan^4 x + \tan^2 x) dx \end{align}$ is equal to :

asked Dec 19, 2018 by pady_1

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$\begin{align} \frac{\sin^3 x + \cos^3 x}{\sin^2x \cos^2 x } dx \end{align}$ is equal to :

asked Dec 19, 2018 by pady_1

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$\begin{align} \int \frac{3dx}{2x^2 - x -1} \end{align}$ is equal to

asked Dec 19, 2018 by pady_1

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$\begin{align} \int \frac{1}{x} \frac{\sqrt{x-1}}{x+1}dx \end{align}$ is equal to :

asked Dec 19, 2018 by pady_1

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$\begin{align} \int \frac{dx}{x(1+\log x)^3} \end{align}$ is equal to :

asked Dec 19, 2018 by pady_1

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The minimum distance from the point $(4, 2)$ to the parabola $y^2 = 8x$ is :

asked Dec 19, 2018 by pady_1

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$\displaystyle\lim_{n \to \infty} \begin{bmatrix}\frac{1}{n+1} + \frac{1}{n+2} + ... +\frac{1}{2n} \end{bmatrix} $ is equal to :

asked Dec 19, 2018 by pady_1

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If $u =x + y$ and $v = x^2 - y^2$, then $\begin {vmatrix} \frac{ \partial u}{ \partial x} & \frac{ \partial u}{ \partial y} \\ \frac{ \partial v}{ \partial x} & \frac{ \partial v}{ \partial y} \end{vmatrix}$ is equal to :

asked Dec 19, 2018 by pady_1

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If $z^2 = \frac{x^{1/2} + y^{1/2}}{x^{1/3} + y^{1/3}}$ then $x \frac{ \partial z}{\partial x} + y \frac{ \partial z}{ \partial y}$ is :

asked Dec 19, 2018 by pady_1

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If $y = sin (7 \sin^{-1} x)$, then $(1-x^2) y_2 - xy_1$ is equal to :

asked Dec 19, 2018 by pady_1

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If $x+y=12$, then the minimum value of $x^2+y^2$ is:

asked Dec 19, 2018 by pady_1

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If the acute angle between the curves $xy=2$ and $y^2 = 4x$ is $\theta$, then $\tan \theta$ is equal to :

asked Dec 19, 2018 by pady_1

1 answer

The equation of the tangent to the curve $y = x^3-2x+7$ at the point $(1,6)$, is :

asked Dec 19, 2018 by pady_1

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A cylindrical vessel of radius $0.5\; m$ is filled with oil at the rate of $0.25\; \pi m^3/min$. The rate, at which the level of oil is increasing, is :

asked Dec 19, 2018 by pady_1

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In a cube the percentage increase in side is 1. The percentage increase in the volume of the cube is :

asked Dec 19, 2018 by pady_1

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If $y = \cot^{-1} \begin{bmatrix} \tan ( \frac{\pi}{2} - x ) \end{bmatrix}$, then $\frac{dy}{dx}$ is equal to :

asked Dec 19, 2018 by pady_1

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If $y=x^x$, then $\frac{dy}{dx}$ is equal to :

asked Dec 19, 2018 by pady_1

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If $x = \theta - \frac{1}{\theta}$ and $y = \theta + \frac{1}{\theta}$, then $\frac{dy}{dx}$ is equal to :

asked Dec 19, 2018 by pady_1

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The derivative of $\sin^{-1}x$ w.r. to $\cos^{-1} \sqrt{1-x^2}$ is :

asked Dec 19, 2018 by pady_1

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$\frac{d}{dx} \{ \cos^{-1} x + \sin^{-1} \sqrt{1-x^2} \}$ is equal to :

asked Dec 19, 2018 by pady_1

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If $y = f(x) = \frac{2x-1}{x-2}$, then $f(y)$ is equal to :

asked Dec 19, 2018 by pady_1

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$\displaystyle\lim_{x \to \infty} \frac{2x + 7 \sin x } {4x + 3 \cos x} $ is equal to :

asked Dec 19, 2018 by pady_1

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In a group $(G,o)$ the elements $a$ and $b$ are such that $a^3 = e = b^3$ when $e$ is the identity element, then $a^7 ob^{-4}$ is equal to :

asked Dec 19, 2018 by pady_1

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For the set $G = \{ -1, 1\}$ be a group the binary operation is equal to :

asked Dec 19, 2018 by pady_1

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If $a, \; b$ are elements of group, then $(aob)^{-1}$ is equal to :

asked Dec 19, 2018 by pady_1

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If $\begin{bmatrix} x & y^3 \\ 2 & 0 \end{bmatrix} = \begin{bmatrix} 1 & 8 \\ 2 & 0 \end{bmatrix}$, then $\begin{bmatrix} x&y\\ 2 & 0 \end{bmatrix}^{-1}$ is equal to :

asked Dec 19, 2018 by pady_1

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If $x \neq 0$ and $\begin{vmatrix}1 & x & 2x \\ 1 & 3x & 5x \\ 1 & 3 & 4 \end{vmatrix}=0$, then $x$ is equal to :

asked Dec 19, 2018 by pady_1

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If the matrix $\begin{bmatrix} \cos \theta & \sin \theta & 0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix}$ is singular, then $\theta$ is equal to :

asked Dec 19, 2018 by pady_1

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The real part of $\begin{vmatrix} \cos \alpha + i \sin \alpha & \cos \beta + i \sin \beta \\ \sin \beta + i \cos \beta & \sin \alpha + i \cos \alpha \end{vmatrix}$ is equal to :

asked Dec 19, 2018 by pady_1

0 answers

If $A(\alpha) = \begin{bmatrix} \cos \alpha & \sin \alpha \\ -\sin \alpha & \cos \alpha \end{bmatrix}$, then $A(\alpha), \; A(\beta)$ is equal to :

asked Dec 19, 2018 by pady_1

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The maximum value of $c + 2bx - x^2$ is equal to :

asked Dec 19, 2018 by pady_1

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If $2x - 7 - 5x^2$ has maximum value at $x=a$, then $a$ is equal to :

asked Dec 19, 2018 by pady_1

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The coefficient of the middle term in the expansion of $(1+x)^{40}$ is equal to :

asked Dec 19, 2018 by pady_1

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The coefficient of the $8^{th}$ term in expansion of $(1+x)^{10}$ is equal to :

asked Dec 19, 2018 by pady_1

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The term independent of $x$ in expansion of $\begin{pmatrix} x^2 - \frac{1}{x} \end{pmatrix}^6$ is equal to :

asked Dec 19, 2018 by pady_1

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If $\frac{1}{(1-2x)(1+3x)} = \frac{A}{1-2x} + \frac{B}{1+3x}$, then $2B$ is equal to :

asked Dec 19, 2018 by pady_1

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$f : R \to R$, defined by $f(x)=\sin x$ and $g : R \to R$, defined by $g(x) = x^2, \; (fog) (x)$ is equal to :

asked Dec 19, 2018 by pady_1

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$\log_8 128$ is equal to :

asked Dec 19, 2018 by pady_1

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If $x=27$ and $y=\log_3 4$, then $x^y$ is equal to :

asked Dec 19, 2018 by pady_1

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If $x=7 + 4\sqrt{3}$ and $xy=1$, then $\frac{1}{x^2} + \frac{1}{y^2}$ is equal to :

asked Dec 19, 2018 by pady_1

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The least value of $n$ that satisfies $^{n-1}C_3 + ^{n-1}C_4 >^nC_3$ is :

asked Dec 19, 2018 by pady_1

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If $^nP_7 = 42 \;^nP_5$, then $n$ is equal to :

asked Dec 19, 2018 by pady_1

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If $f : R \to R$ is defined by $f(x) = 3x-2$, then $fof(x) +2$ is equal to :

asked Dec 19, 2018 by pady_1

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If the mean of 9 binomial distribution is 6, then its variance is :

asked Dec 19, 2018 by pady_1

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