Recent questions and answers in 1999

If $\lambda x^2 + 6xy + 9y^2 +4x + 12y+3=0$ represents a pair of straight lines, then $\lambda$ is equal to :

answered Aug 14, 2020 by shadowdragon123345

1 answer

The solvent used in the preparation of Grignard reagent is :

answered Jul 20, 2020 by kphasnashirin

1 answer

A solid organic compound $X$ on heating is directly converted into the vapour phase which on cooling solidifies. The best method for purifying $X$ is :

answered Jul 20, 2020 by yathapusaikumarreddy2003

1 answer

Tinstone is contaminated with Wolframite. Which one of the following methods can be employed to dress the tinstone ore ?

answered Jun 20, 2020 by nalamasuabhinay

1 answer

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

answered Jun 6, 2020 by bmreddy497

1 answer

A ball A moving with a speed of $99\;ms^{-1}$ collides directly with another identical ball B moving with a speed $v$ in the opposite direction, A comes to rest after the collision. If the coefficients of restitution is 0.8, the speed of B before collision, is :

answered Jun 2, 2020 by bheemsenkulkarni181

1 answer

If the circle $x^2 +y^2 +2x -2y+4=0$ cuts the circle $x^2 +y^2 + 4x + 2fy+2=0$ orthogonally, then $f$ is equal to :

answered May 3, 2020 by rongalisanthi3

1 answer

A magnetic needle is placed with its north pole facing north in north south direction. In its map of magnetic field the null point will be :

answered Apr 19, 2020 by adeuttamrao

1 answer

In a triangle $ABC, \; r_1 \cot \frac{A}{2} + r_2 \cot \frac{B}{2} + r_3 \cot \frac{C}{2}$ is equal to :

answered Apr 2, 2020 by nanigadumvnp

2 answers

The general solution of $\tan^2 \theta = 3$ is :

answered Mar 29, 2020 by vinnu636

1 answer

In a spectrometer experiment three prisms $A,\;B$ and $C$ with same angle of prism but of different materials of refractive indices $\mu_A = 1.33, \; \mu_B = 1.55, \; \mu_C = 1.44$ are used. The corresponding angles of minimum deviation $D_A,\;D_B,\;D_C$ measured will be such that :

answered Mar 1, 2020 by kishore.mulpuri

1 answer

Taking that earth revolves round the sun in a circular orbit of radius $15 \times 10^{10}m$, with a time period of 1 year the time taken by another planet, which is at a distance of $540 \times 10^{10}m$, to revolve round the sun in circular orbit once, will be :

answered Oct 14, 2019 by pskswamy1973

1 answer

Two simple pendulums of lengths $16 l$ and $l$ are in phase at the mean position at a certain time. If $T$ is the time period of shorter pendulum, the minimum time after which they will be again in phase :

answered Aug 30, 2019 by chandrasekharmoyila1993

1 answer

The focus of parabola $y^2-4y -8x-4=0$ is :

answered Jun 15, 2019 by junaidiqbal7051

1 answer

When a cylindrical tube is dipped vertically into a liquid then the angle of contact is $140^{\circ}$, if the tube is dipped, with an inclination of $40^{\circ}$ then angle of contact is :

answered Apr 3, 2019 by nsravni180

1 answer

In a compensated pendulum two rods of different metals are used with their lengths in ratio of $2:3$. The coefficients of linear expansions for metals in the ratio is :

answered Jan 10, 2019 by sangeetadhadiya

1 answer

Among the first lines of Lyman, Balmer, Paschen and Brackett series in hydrogen atomic spectra, which has the highest energy?

answered Dec 30, 2018 by fahadbuledi103

1 answer

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

asked Dec 19, 2018 by pady_1

0 answers

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

0 answers

$\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

0 answers

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

0 answers

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

0 answers

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

asked Dec 19, 2018 by pady_1

0 answers

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

asked Dec 19, 2018 by pady_1

0 answers

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

asked Dec 19, 2018 by pady_1

0 answers

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

asked Dec 19, 2018 by pady_1

0 answers

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

asked Dec 19, 2018 by pady_1

0 answers

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

asked Dec 19, 2018 by pady_1

0 answers

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

asked Dec 19, 2018 by pady_1

0 answers

$\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

0 answers

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

0 answers

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

0 answers

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

0 answers

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

asked Dec 19, 2018 by pady_1

0 answers

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

0 answers

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

0 answers

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

0 answers

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

0 answers

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

asked Dec 19, 2018 by pady_1

0 answers

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

0 answers

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

asked Dec 19, 2018 by pady_1

0 answers

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

asked Dec 19, 2018 by pady_1

0 answers

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

asked Dec 19, 2018 by pady_1

0 answers

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

asked Dec 19, 2018 by pady_1

0 answers

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

0 answers

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

asked Dec 19, 2018 by pady_1

0 answers

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

asked Dec 19, 2018 by pady_1

0 answers

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

0 answers

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

0 answers

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

0 answers

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