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Recent questions and answers in 1999
Questions
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JEEMAIN and NEET
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JEEMAIN PAST PAPERS
>>
1999
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 :
jeemain
math
past papers
1999
109
answered
18 hours
ago
by
nanigadumvnp
2
answers
The general solution of $\tan^2 \theta = 3$ is :
jeemain
math
past papers
1999
107
answered
Mar 29
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 :
jeemain
physics
past papers
1999
35
answered
Mar 1
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 :
jeemain
physics
past papers
1999
17
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 :
jeemain
physics
past papers
1999
20
answered
Aug 30, 2019
by
chandrasekharmoyila1993
1
answer
The focus of parabola $y^2-4y -8x-4=0$ is :
jeemain
math
past papers
1999
133
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 :
jeemain
physics
past papers
1999
22
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 :
jeemain
physics
past papers
1999
23
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?
jeemain
chemistry
past papers
1999
87
answered
Dec 30, 2018
by
fahadbuledi103
1
answer
The solution of $2xy \frac{dy}{dx} = 1 + y^2$, is :
jeemain
math
past papers
1999
200
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 :
jeemain
math
past papers
1999
199
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 :
jeemain
math
past papers
1999
198
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 :
jeemain
math
past papers
1999
197
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:
jeemain
math
past papers
1999
196
asked
Dec 19, 2018
by
pady_1
0
answers
$\begin{align*} \int_0^{\pi} \cos^3x \;dx \end{align*}$ is equal to :
jeemain
math
past papers
1999
195
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 :
jeemain
math
past papers
1999
194
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 :
jeemain
math
past papers
1999
193
asked
Dec 19, 2018
by
pady_1
0
answers
$\begin{align*} \int \frac{3dx}{2x^2 - x -1} \end{align*}$ is equal to
jeemain
math
past papers
1999
192
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 :
jeemain
math
past papers
1999
191
asked
Dec 19, 2018
by
pady_1
0
answers
$\begin{align*} \int \frac{dx}{x(1+\log x)^3} \end{align*}$ is equal to :
jeemain
math
past papers
1999
190
asked
Dec 19, 2018
by
pady_1
0
answers
The minimum distance from the point $(4, 2)$ to the parabola $y^2 = 8x$ is :
jeemain
math
past papers
1999
189
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 :
jeemain
math
past papers
1999
188
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 :
jeemain
math
past papers
1999
187
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 :
jeemain
math
past papers
1999
186
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 :
jeemain
math
past papers
1999
185
asked
Dec 19, 2018
by
pady_1
0
answers
If $x+y=12$, then the minimum value of $x^2+y^2$ is:
jeemain
math
past papers
1999
184
asked
Dec 19, 2018
by
pady_1
0
answers
If the acute angle between the curves $xy=2$ and $y^2 = 4x$ is $\theta$, then $\tan \theta$ is equal to :
jeemain
math
past papers
1999
183
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 :
jeemain
math
past papers
1999
182
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 :
jeemain
math
past papers
1999
181
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 :
jeemain
math
past papers
1999
180
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 :
jeemain
math
past papers
1999
179
asked
Dec 19, 2018
by
pady_1
0
answers
If $y=x^x$, then $\frac{dy}{dx}$ is equal to :
jeemain
math
past papers
1999
178
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 :
jeemain
math
past papers
1999
177
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 :
jeemain
math
past papers
1999
176
asked
Dec 19, 2018
by
pady_1
0
answers
$\frac{d}{dx} \{ \cos^{-1} x + \sin^{-1} \sqrt{1-x^2} \}$ is equal to :
jeemain
math
past papers
1999
175
asked
Dec 19, 2018
by
pady_1
0
answers
If $y = f(x) = \frac{2x-1}{x-2}$, then $f(y)$ is equal to :
jeemain
math
past papers
1999
174
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 :
jeemain
math
past papers
1999
173
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 :
jeemain
math
past papers
1999
172
asked
Dec 19, 2018
by
pady_1
0
answers
For the set $G = \{ -1, 1\}$ be a group the binary operation is equal to :
jeemain
math
past papers
1999
171
asked
Dec 19, 2018
by
pady_1
0
answers
If $a, \; b$ are elements of group, then $(aob)^{-1}$ is equal to :
jeemain
math
past papers
1999
170
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 :
jeemain
math
past papers
1999
169
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 :
jeemain
math
past papers
1999
168
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 :
jeemain
math
past papers
1999
167
asked
Dec 19, 2018
by
pady_1
0
answers
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 :
jeemain
math
past papers
1999
166
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 :
jeemain
math
past papers
1999
165
asked
Dec 19, 2018
by
pady_1
0
answers
The maximum value of $c + 2bx - x^2$ is equal to :
jeemain
math
past papers
1999
164
asked
Dec 19, 2018
by
pady_1
0
answers
If $2x - 7 - 5x^2$ has maximum value at $x=a$, then $a$ is equal to :
jeemain
math
past papers
1999
163
asked
Dec 19, 2018
by
pady_1
0
answers
The coefficient of the middle term in the expansion of $(1+x)^{40}$ is equal to :
jeemain
math
past papers
1999
162
asked
Dec 19, 2018
by
pady_1
0
answers
The coefficient of the $8^{th}$ term in expansion of $(1+x)^{10}$ is equal to :
jeemain
math
past papers
1999
161
asked
Dec 19, 2018
by
pady_1
0
answers
The term independent of $x$ in expansion of $\begin{pmatrix} x^2 - \frac{1}{x} \end{pmatrix}^6$ is equal to :
jeemain
math
past papers
1999
160
asked
Dec 19, 2018
by
pady_1
0
answers
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