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Recent questions in 1998
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JEEMAIN and NEET
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JEEMAIN PAST PAPERS
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1998
10.6 g of a substance of molecular weight 106 was dissolved in 100 mL. 10 mL of this solution was pipetted out into a 1000 mL flask and made up to the mark with distilled water. The molarity of the resulting solution is :
jeemain
chemistry
past papers
1998
53
asked
Dec 20, 2018
by
pady_1
0
answers
If the vectors $\overrightarrow{a} = ( 1, x, -2)$ and $\overrightarrow{b} = (x, 3, -4)$ are mutually perpendicular, then is :
jeemain
math
past papers
1998
200
asked
Dec 19, 2018
by
pady_1
1
answer
If $|\overrightarrow{a}| = 5, |\overrightarrow{b} |= 6, |\overrightarrow{a}. \overrightarrow{b} | = 24$ then $|\overrightarrow{a} \times \overrightarrow{b} |$ is equal to :
jeemain
math
past papers
1998
199
asked
Dec 19, 2018
by
pady_1
1
answer
If $\overrightarrow{\alpha}$ and $\overrightarrow{\beta}$ are non zero and different vector such that $|\overrightarrow{\alpha} + \overrightarrow{\beta}| = |\overrightarrow{\beta} - \overrightarrow{\alpha}|$, then the angle between $\overrightarrow{\alpha} $ and $\overrightarrow{\beta}$ is :
jeemain
math
past papers
1998
198
asked
Dec 19, 2018
by
pady_1
1
answer
If $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ are unit vectors such that $\overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} = 0$. Then $\overrightarrow{a}. \overrightarrow{b} + \overrightarrow{b}. \overrightarrow{c} + \overrightarrow{c} . \overrightarrow{a}$ is equal to :
jeemain
math
past papers
1998
197
asked
Dec 19, 2018
by
pady_1
1
answer
The angle between the planes <br> $\overrightarrow{r} ( 2 \hat{i} - \hat{j} + 2 \hat{k}) = 3$ and <br> $\overrightarrow{r}(3 \hat{i} - 6 \hat{j} + 2 \hat{k} )= 4$ is :
jeemain
math
past papers
1998
196
asked
Dec 19, 2018
by
pady_1
0
answers
If $\overrightarrow{A}, \overrightarrow{B}, \overrightarrow{C}$ are three vectors such that $|\overrightarrow{A} | = 4, \; |\overrightarrow{B}| = 5,\; |\overrightarrow{C}|=6$, then $[\overrightarrow{A} - \overrightarrow{B} \; \; \overrightarrow{B} - \overrightarrow{C} \; \; \overrightarrow{C} - \overrightarrow{A} ] $ is equal to :
jeemain
math
past papers
1998
195
asked
Dec 19, 2018
by
pady_1
1
answer
If $\overrightarrow{A} = \hat{i} + \lambda \hat{j} + \hat{k}, \; \overrightarrow{B} = \hat{i} + \hat{j} + \hat{k}$, then for $|\overrightarrow{A} + \overrightarrow{B}| = |\overrightarrow{A} | + |\overrightarrow{B}|$ to be true, the value of $\lambda$ is equal to :
jeemain
math
past papers
1998
194
asked
Dec 19, 2018
by
pady_1
0
answers
If $2\hat{i} + 3 \hat{j} - 6\hat{k}, \; 6\hat{i} - 2\hat{j} + 3 \hat{k}, \; 3 \hat{i} - 6 \hat{j} - 2 \hat{k}$ represent the sides of a triangle, then the perimeter of the triangle is:
jeemain
math
past papers
1998
193
asked
Dec 19, 2018
by
pady_1
0
answers
The three points whose position vectors are $\hat{i} +2 \hat{j} +3\hat{k}, \; 3 \hat{i} + 4 \hat{j} +7 \hat{k}$ and $- 3 \hat{i} - 2 \hat{j} - 5 \hat{k}$ :
jeemain
math
past papers
1998
192
asked
Dec 19, 2018
by
pady_1
0
answers
The probability of a man hitting a target is $\frac{1}{4}$. If he fires 7 times, the probability of hitting the target at least twice is :
jeemain
math
past papers
1998
191
asked
Dec 19, 2018
by
pady_1
0
answers
A random variable $X$ has the following distribution <br> <br> the mean and the variance are :
jeemain
math
past papers
1998
190
asked
Dec 19, 2018
by
pady_1
0
answers
A coin tossed 3 times. The probability of getting head once and tails two times, is :
jeemain
math
past papers
1998
189
asked
Dec 19, 2018
by
pady_1
1
answer
A random variable $X$ has the following distribution <br> <br> the values of $k$ and $P(X < 3)$ are equal to :
jeemain
math
past papers
1998
188
asked
Dec 19, 2018
by
pady_1
0
answers
Two dice are thrown at a time and the sum of the numbers on them is 6. The probability of getting the number 4 on any of the dice, is :
jeemain
math
past papers
1998
187
asked
Dec 19, 2018
by
pady_1
1
answer
A problem in EAMCET examination is given to 3 students A, B and C whose chance of solving it are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively, the probability that the problem is solved, is :
jeemain
math
past papers
1998
186
asked
Dec 19, 2018
by
pady_1
0
answers
A and B are mutually exclusive events with $P(A) = \frac{1}{2} P(B)$ and $A \cup B = S$ the sample space, then $P(A)$ is equal to :
jeemain
math
past papers
1998
185
asked
Dec 19, 2018
by
pady_1
0
answers
The equation $r = 5 \cos \theta + 12 \sin \theta$ represents :
jeemain
math
past papers
1998
184
asked
Dec 19, 2018
by
pady_1
0
answers
$\begin{align*} \int_0^a \sqrt{a^2 - x^2} dx \end{align*}$ is equal to :
jeemain
math
past papers
1998
183
asked
Dec 19, 2018
by
pady_1
1
answer
The area bounded by $y = 3x$ and $y =x^2$ is (in sq unit) :
jeemain
math
past papers
1998
182
asked
Dec 19, 2018
by
pady_1
1
answer
$\begin{align*} \int_0^{\pi/2} \sin^6 x \cos^5 x \; dx \end{align*}$ is equal to :
jeemain
math
past papers
1998
181
asked
Dec 19, 2018
by
pady_1
1
answer
$\begin{align*} \int \frac{e^x (1+x \log x)}{x}\;dx \end{align*}$ is equal to :
jeemain
math
past papers
1998
180
asked
Dec 19, 2018
by
pady_1
0
answers
$\begin{align*} \int \frac{x^5}{x^2 + 1} \;dx \end{align*}$ is equal to :
jeemain
math
past papers
1998
179
asked
Dec 19, 2018
by
pady_1
0
answers
The value of $(127)^{1/3}$ upto 4 decimal places, is :
jeemain
math
past papers
1998
178
asked
Dec 19, 2018
by
pady_1
0
answers
The point on the curve $y^2 = 4x$ which is the nearest to the point $(2, 1)$ is :
jeemain
math
past papers
1998
177
asked
Dec 19, 2018
by
pady_1
0
answers
The maximum value of $fx) = 2x^3 - 21x^2 + 36 x + 20$, in the interval $0 \leq x \leq 2$, is
jeemain
math
past papers
1998
176
asked
Dec 19, 2018
by
pady_1
0
answers
The solution of the differential equation $\frac{dy}{dx} - \frac{2xy}{1+x^2}=0$ is :
jeemain
math
past papers
1998
175
asked
Dec 19, 2018
by
pady_1
0
answers
$y = x^2 \sin 2x$, then $n^{th}$ derivative of $y ( n = 4m)$ is :
jeemain
math
past papers
1998
174
asked
Dec 19, 2018
by
pady_1
0
answers
$\frac{d}{dx} (x^x)$ is equal to :
jeemain
math
past papers
1998
173
asked
Dec 19, 2018
by
pady_1
1
answer
Derivative of $\sin^2x$ with respect to $(\log x)^2$ is:
jeemain
math
past papers
1998
172
asked
Dec 19, 2018
by
pady_1
0
answers
$\frac{d}{dx} (\cos x*)$ is equal to :
jeemain
math
past papers
1998
171
asked
Dec 19, 2018
by
pady_1
0
answers
If $f(x) = \frac{\sin x }{x}, \; x \neq 0$, if $f(x)$ is to be continuous at $x=0$, then $f(0)$ is equal to :
jeemain
math
past papers
1998
170
asked
Dec 19, 2018
by
pady_1
0
answers
One of the focii of hyperbola is origin and the corresponding directrix is $3x + 4y + 1=0$. The eccentricity of the hyperbola is $\sqrt{5}$. The equation to the hyperbola is :
jeemain
math
past papers
1998
169
asked
Dec 19, 2018
by
pady_1
0
answers
The eccentricity of ellipse $9x^2 + 4y^2 = 36$ is :
jeemain
math
past papers
1998
168
asked
Dec 19, 2018
by
pady_1
0
answers
The pole of the line $2x + 3y- 4=0$ with respect to the parabola $y^2 = 4x$ is :
jeemain
math
past papers
1998
167
asked
Dec 19, 2018
by
pady_1
0
answers
The equation of the directrix to the parabola $y^2 -2x - 6y -5 = 0$ is
jeemain
math
past papers
1998
166
asked
Dec 19, 2018
by
pady_1
1
answer
The equation of the normal to the circle $x^2 + y^2 - 2x - 2y - 2 = 0$ at the point $(3,1)$ on it is :
jeemain
math
past papers
1998
165
asked
Dec 19, 2018
by
pady_1
0
answers
The length of the tangent from (6, 8) to the circle $x^2 + y^2 = 4$ is :
jeemain
math
past papers
1998
164
asked
Dec 19, 2018
by
pady_1
0
answers
If $(1,2), \; (4, 3)$ are the limiting points of a system of coaxial circles, then the radical axis of the system is :
jeemain
math
past papers
1998
163
asked
Dec 19, 2018
by
pady_1
0
answers
The radical axis of cirlces $x^2 + y^2 - 6x -4y - 44=0$ and $x^2 +y^2- 14 x - 5y-24=0$ is :
jeemain
math
past papers
1998
162
asked
Dec 19, 2018
by
pady_1
0
answers
The pole of line $8x-2y=11$ with respect to the circle $2x^2 + 2y^2 = 11$ is :
jeemain
math
past papers
1998
161
asked
Dec 19, 2018
by
pady_1
0
answers
The locus of point of intersection of perpendicular tangents to the circle $x^2+y^2=a^2$ is:
jeemain
math
past papers
1998
160
asked
Dec 19, 2018
by
pady_1
0
answers
The equation of a circle with centre $(4, 1)$ and having $3x + 4y - 1 =0$ as tangent is
jeemain
math
past papers
1998
159
asked
Dec 19, 2018
by
pady_1
0
answers
If $z = \sin^{-1} \{ \frac{x+y}{\sqrt{x} + \sqrt{y} } \}$, then $x \frac{\partial z}{\partial x} + y \frac{\partial z}{\partial y}$ is equal to :
jeemain
math
past papers
1998
158
asked
Dec 19, 2018
by
pady_1
0
answers
If $x^xy^yz^z$ = constant, then $\frac{dz}{dx}$ is equal to :
jeemain
math
past papers
1998
157
asked
Dec 19, 2018
by
pady_1
0
answers
If the operation $*$ is defined on $R$, the set of all real numbers, as $a*b = ab +1 \; \forall\; a, b \in R$ then $a * (b *c) $ is equal to :
jeemain
math
past papers
1998
156
asked
Dec 19, 2018
by
pady_1
0
answers
Let $Q_1 = Q - \{1 \}$ the set of all rationals except 1, $*$ is the operation defined on $Q_1$, as $a * b = a + b - ab \; \forall a, b \in Q_1$. The inverse of 2 is :
jeemain
math
past papers
1998
155
asked
Dec 19, 2018
by
pady_1
0
answers
The inverse of the matrix $\begin{bmatrix} 2 & 1 \\ 1 & 3 \end{bmatrix}$ is :
jeemain
math
past papers
1998
154
asked
Dec 19, 2018
by
pady_1
0
answers
If $a+b+c=0$, then one root of $\begin{vmatrix} a-x & c & b \\ c & b-x& a \\ b & a & c-x \end{vmatrix}=0$ is :
jeemain
math
past papers
1998
153
asked
Dec 19, 2018
by
pady_1
0
answers
If the system of equations <br> $3x-2y+z=0 $ <br> $\lambda x - 14 y +15z =0$ <br> $x+2y-3z=0$ <br> have non-zero solution, then $\lambda$ is equal to
jeemain
math
past papers
1998
152
asked
Dec 19, 2018
by
pady_1
0
answers
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