Recent questions in JEEMAIN and NEET

A fair die is tossed eight times. The probability that a third six is observed on the eight throw, is :

asked Dec 11, 2018 by pady_1

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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 :

asked Dec 11, 2018 by pady_1

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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 :

asked Dec 11, 2018 by pady_1

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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 :

asked Dec 11, 2018 by pady_1

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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 :

asked Dec 11, 2018 by pady_1

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$\sin^2 \theta = \frac{4xy}{(x+y)^2}$ is true if and only is :

asked Dec 11, 2018 by pady_1

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If $\begin{vmatrix} 6 {i} & - 3 {i} & 1 \\ 4 & 3 {i} & -1 \\ 20 &3 & i \end{vmatrix} = x + i y$, then :

asked Dec 11, 2018 by pady_1

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If $\omega$ is an imaginary cube root of unity, then $(1 + \omega - \omega^2 )^7 $ equals :

asked Dec 11, 2018 by pady_1

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If the vectors $\overrightarrow{a}, \overrightarrow{b}$ and $\overrightarrow{c}$ from the sides $BC, CA$ and $AB$ respectively of a triangle $ABC$, then :

asked Dec 11, 2018 by pady_1

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The incentre of the triangle with vertices $(1, \sqrt{3}), \; (0,0)$ and $(2, 0)$ is :

asked Dec 11, 2018 by pady_1

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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 :

asked Dec 11, 2018 by pady_1

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In a triangle ABC, $2ca \sin \frac{A - B + C}{2}$ is equal to :

asked Dec 11, 2018 by pady_1

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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 :

asked Dec 11, 2018 by pady_1

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The equation of the directrix of the parabola $y^2 + 4y + 4x + 2 =0$ is :

asked Dec 11, 2018 by pady_1

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If A and B are two mutually exclusive events, then :

asked Dec 11, 2018 by pady_1

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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 :

asked Dec 11, 2018 by pady_1

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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 :

asked Dec 11, 2018 by pady_1

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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 :

asked Dec 11, 2018 by pady_1

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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 :

asked Dec 11, 2018 by pady_1

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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 :

asked Dec 11, 2018 by pady_1

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The differential equation of all non-vertical lines in a plane is :

asked Dec 11, 2018 by pady_1

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The area bounded by the curve $y = 2x - x^2$ and the straight line $y = -x$ is given by :

asked Dec 11, 2018 by pady_1

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

asked Dec 11, 2018 by pady_1

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Evaluate $\begin{align} \int_0^{\pi/2} \frac{\sqrt{\sin x}}{\sqrt{\sin x} + \sqrt{\cos x} } dx \end{align}$

asked Dec 11, 2018 by pady_1

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The greatest value of $f(x) = (x+1)^{1/3} -(x-1)^{1/3}$ on $[0,1]$ is :

asked Dec 11, 2018 by pady_1

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The function $f(x) = \cot^{-1} x + x$ increases in the interval :

asked Dec 11, 2018 by pady_1

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The two curves $x^3 - 3xy^2 + 2 = 0$ and $3x^2y - y^3 - 2 =0$ :

asked Dec 11, 2018 by pady_1

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

asked Dec 11, 2018 by pady_1

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If $\sin y = x \sin (a + y) $, then $\frac{dy}{dx}$ is :

asked Dec 11, 2018 by pady_1

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The domain of definition of the function $f(x) = \sqrt{log_{10} (\frac{5x-x^2}{4})}$ is :

asked Dec 11, 2018 by pady_1

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The period of the function $f(x) = \sin^4 x + \cos^4 x$ is :

asked Dec 11, 2018 by pady_1

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$\begin{align} \int_{-\pi}^{\pi} \frac{2x ( 1+\sin x)} {1 + \cos^2 x} dx \end{align}$ is :

asked Dec 11, 2018 by pady_1

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$\begin{align}\int_0^2 [x^2] dx \end{align}$ is :

asked Dec 11, 2018 by pady_1

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$I_n = \begin{align} \int_0^{\pi/4} \tan^n x \; dx \end{align}$ then $\displaystyle\lim_{n \to \infty} n [I_n + I_{n+2} ]$ equals :

asked Dec 11, 2018 by pady_1

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$\begin{align} \int_0^{10 \pi} | \sin x |\; dx \end{align}$ is

asked Dec 11, 2018 by pady_1

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Fifth term of a GP is 2, then the product of its 9 terms is :

asked Dec 11, 2018 by pady_1

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The value of $2^{1/4}. 4^{1/8}. 8^{1/16}.....\infty$ is :

asked Dec 11, 2018 by pady_1

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The domain the $\sin^{-1} [\log_3 ( x/3)]$ is:

asked Dec 11, 2018 by pady_1

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$\displaystyle\lim_{x \to \infty}$ $\begin{pmatrix} \frac{x^2 + 5x + 3}{x^2 + x + 2} \end{pmatrix}^x$ is :

asked Dec 11, 2018 by pady_1

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The solution of the equation $\frac{d^2y}{dx^2} = e^{-2x}$ is

asked Dec 11, 2018 by pady_1

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A plane which passes through the point (3, 2, 0) and the line $\frac{x-4}{1} = \frac{y-7}{5} = \frac{z-4}{4} $ is :

asked Dec 11, 2018 by pady_1

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The order and degree of the differential equation $(1 + 3 \frac{dy}{dx})^{2/3} = 4 \frac{d^3y}{dx^3}$ are :

asked Dec 11, 2018 by pady_1

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$\cot^{-1} ( \cos \alpha ) - \tan^{-1} (\sqrt{\cos \alpha}) = x$ then $\sin x$ is equal to :

asked Dec 11, 2018 by pady_1

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In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls ?

asked Dec 11, 2018 by pady_1

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A triangle with vertices (4, 0), (-1, -1), (3, 5) is :

asked Dec 11, 2018 by pady_1

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$\displaystyle\lim_{x \to 0} \frac{\sqrt{1-\cos 2x}}{\sqrt{2}x}$ is :

asked Dec 11, 2018 by pady_1

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$l, \; m, n$ are the $p^{th}, q^{th}$ and $r^{th}$ term of an GP and all positive, then $\begin{vmatrix} \log l & p & 1 \\ \log m & q&1 \\ \log n & r & 1 \end{vmatrix}$ equals :

asked Dec 11, 2018 by pady_1

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The period of $\sin^2 \theta$ is:

asked Dec 11, 2018 by pady_1

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A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$. Probability that the problem is solved, is :

asked Dec 11, 2018 by pady_1

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If 1, $\log_3 \sqrt{(3^{1-x} +2)}, \; \log_3 (4.3^x -1)$ are in AP, then $x$ equals :

asked Dec 11, 2018 by pady_1

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