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Recent questions in 2002
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JEEMAIN and NEET
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JEEMAIN PAST PAPERS
>>
2002
For the following reaction in gaseous phase : <br> $CO + \frac{1}{2}O_2 \to CO_2 \; \; \; \; K_c/K_p$ is :
jeemain
chemistry
past papers
2002
123
asked
Dec 11, 2018
by
pady_1
0
answers
The number of real roots of $3^{2x^2 - 7x + 7} =9$ is :
jeemain
math
past papers
2002
225
asked
Dec 11, 2018
by
pady_1
0
answers
If $|x| < 1$, then the coefficient of $x^n$ in expansion of $(1 + x + x^2 + x^3 + ...)^2$ is :
jeemain
math
past papers
2002
224
asked
Dec 11, 2018
by
pady_1
0
answers
The coefficient of $x^5$ in $(1 + 2x + 3x^2 + ....)^{-3/2}$ is :
jeemain
math
past papers
2002
223
asked
Dec 11, 2018
by
pady_1
0
answers
$e^{(x-1) - \frac{1}{2} (x-1)^2 + \frac{(x-1)^3}{3} - \frac{(x-1)^4}{4} + . . . } $ equal to :
jeemain
math
past papers
2002
222
asked
Dec 11, 2018
by
pady_1
0
answers
$\displaystyle \lim_{n = 0}^{\infty} \frac{(\log_e x)^n}{n!}$ is equal to
jeemain
math
past papers
2002
221
asked
Dec 11, 2018
by
pady_1
0
answers
$\tan^{-1} (\frac{1}{4}) + \tan^{-1} (\frac{2}{9})$ is equal to :
jeemain
math
past papers
2002
220
asked
Dec 11, 2018
by
pady_1
0
answers
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 :
jeemain
math
past papers
2002
219
asked
Dec 11, 2018
by
pady_1
0
answers
The equation $a \sin x + b \cos x = c$ where $|c| > \sqrt{a^2 + b^2}$ has :
jeemain
math
past papers
2002
218
asked
Dec 11, 2018
by
pady_1
0
answers
In a $\Delta ABC$, $\tan \frac{A}{2} = \frac{5}{6}, \; \tan \frac{C}{2} = \frac{2}{5}$, then :
jeemain
math
past papers
2002
217
asked
Dec 11, 2018
by
pady_1
1
answer
In a triangle $ABC, \; a = 4, \; b = 3, \; \angle{A} = 60^{\circ}$, then $c$ is the root of the equation :
jeemain
math
past papers
2002
216
asked
Dec 11, 2018
by
pady_1
0
answers
If $y = \sin^2 \theta + \mathrm{cosec}^2 \theta, \; \theta \neq 0$, then :
jeemain
math
past papers
2002
215
asked
Dec 11, 2018
by
pady_1
0
answers
If $\sin (\alpha + \beta) = 1$, $\sin (\alpha- \beta) = \frac{1}{2}$, then $\tan (\alpha + 2\beta) \tan (2 \alpha +\beta)$ is equal to :
jeemain
math
past papers
2002
214
asked
Dec 11, 2018
by
pady_1
0
answers
If $\tan \theta = -\frac{4}{3} $, then $\sin \theta$ is :
jeemain
math
past papers
2002
213
asked
Dec 11, 2018
by
pady_1
0
answers
The value of $\frac{1 - \tan^2 15^{\circ}}{1+ \tan^2 15^{\circ}}$ is :
jeemain
math
past papers
2002
212
asked
Dec 11, 2018
by
pady_1
0
answers
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 :
jeemain
math
past papers
2002
211
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 :
jeemain
math
past papers
2002
210
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 :
jeemain
math
past papers
2002
209
asked
Dec 11, 2018
by
pady_1
0
answers
The equation of the ellipse whose foci are $(\pm 2, 0)$ and eccentricity is $1/2$ is :
jeemain
math
past papers
2002
208
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 :
jeemain
math
past papers
2002
207
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 :
jeemain
math
past papers
2002
206
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 :
jeemain
math
past papers
2002
205
asked
Dec 11, 2018
by
pady_1
0
answers
Three straight lines $2x+ 11y - 5 = 0, \; 24x + 7y - 20 = 0$ and $4x - 3y - 2 = 0$ :
jeemain
math
past papers
2002
204
asked
Dec 11, 2018
by
pady_1
0
answers
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 :
jeemain
math
past papers
2002
203
asked
Dec 11, 2018
by
pady_1
0
answers
A fair die is tossed eight times. The probability that a third six is observed on the eight throw, is :
jeemain
math
past papers
2002
202
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 :
jeemain
math
past papers
2002
201
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 :
jeemain
math
past papers
2002
200
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 :
jeemain
math
past papers
2002
199
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 :
jeemain
math
past papers
2002
198
asked
Dec 11, 2018
by
pady_1
0
answers
$\sin^2 \theta = \frac{4xy}{(x+y)^2}$ is true if and only is :
jeemain
math
past papers
2002
197
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 :
jeemain
math
past papers
2002
196
asked
Dec 11, 2018
by
pady_1
0
answers
If $\omega$ is an imaginary cube root of unity, then $(1 + \omega - \omega^2 )^7 $ equals :
jeemain
math
past papers
2002
195
asked
Dec 11, 2018
by
pady_1
0
answers
If the vectors $\overrightarrow{a}, \overrightarrow{b}$ and $\overrightarrow{c}$ from the sides $BC, CA$ and $AB$ respectively of a triangle $ABC$, then :
jeemain
math
past papers
2002
194
asked
Dec 11, 2018
by
pady_1
0
answers
The incentre of the triangle with vertices $(1, \sqrt{3}), \; (0,0)$ and $(2, 0)$ is :
jeemain
math
past papers
2002
193
asked
Dec 11, 2018
by
pady_1
0
answers
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 :
jeemain
math
past papers
2002
192
asked
Dec 11, 2018
by
pady_1
0
answers
In a triangle ABC, $2ca \sin \frac{A - B + C}{2}$ is equal to :
jeemain
math
past papers
2002
191
asked
Dec 11, 2018
by
pady_1
0
answers
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 :
jeemain
math
past papers
2002
190
asked
Dec 11, 2018
by
pady_1
0
answers
The equation of the directrix of the parabola $y^2 + 4y + 4x + 2 =0$ is :
jeemain
math
past papers
2002
189
asked
Dec 11, 2018
by
pady_1
0
answers
If A and B are two mutually exclusive events, then :
jeemain
math
past papers
2002
188
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 :
jeemain
math
past papers
2002
187
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 :
jeemain
math
past papers
2002
186
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 :
jeemain
math
past papers
2002
185
asked
Dec 11, 2018
by
pady_1
0
answers
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 :
jeemain
math
past papers
2002
184
asked
Dec 11, 2018
by
pady_1
0
answers
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 :
jeemain
math
past papers
2002
183
asked
Dec 11, 2018
by
pady_1
0
answers
The differential equation of all non-vertical lines in a plane is :
jeemain
math
past papers
2002
182
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 :
jeemain
math
past papers
2002
181
asked
Dec 11, 2018
by
pady_1
0
answers
$\begin{align*} \int \frac{dx}{x(x^n+1)} \end{align*}$ is equal to :
jeemain
math
past papers
2002
180
asked
Dec 11, 2018
by
pady_1
0
answers
Evaluate $\begin{align*} \int_0^{\pi/2} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x} } dx \end{align*}$
jeemain
math
past papers
2002
179
asked
Dec 11, 2018
by
pady_1
0
answers
The greatest value of $f(x) = (x+1)^{1/3} -(x-1)^{1/3}$ on $[0,1]$ is :
jeemain
math
past papers
2002
178
asked
Dec 11, 2018
by
pady_1
0
answers
The function $f(x) = \cot^{-1} x + x$ increases in the interval :
jeemain
math
past papers
2002
177
asked
Dec 11, 2018
by
pady_1
0
answers
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