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JEE MAIN Previous Year Questions (PYQs)

JEE MAIN 2018 PYQ

JEE MAIN PYQ 2018
A value of $\theta \in \left( {0,{\pi \over 3}} \right)$, for which
$\left| {\matrix{ {1 + {{\cos }^2}\theta } & {{{\sin }^2}\theta } & {4\cos 6\theta } \cr {{{\cos }^2}\theta } & {1 + {{\sin }^2}\theta } & {4\cos 6\theta } \cr {{{\cos }^2}\theta } & {{{\sin }^2}\theta } & {1 + 4\cos 6\theta } \cr } } \right| = 0$, is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 April Evening Shift) PYQ

Solution

JEE MAIN PYQ 2018
n–digit numbers are formed using only three digits 2,5,7. The smallest value of n for which 900 such distinct numbers can be formed is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
If $x_1, x_2,\ldots , x_n$ and $\frac{1}{h_1}, \frac{1}{h_2},\ldots , \frac{1}{h_n}$ are two A.P.s such that $x_3 = h_2 = 8$ and $x_8 = h_7 = 20$, then $x_5 \cdot h_{10}$ equals :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
Let $S$ be the set of all real values of $k$ for which the system of linear equations
$x + y + z = 2$
$2x + y - z = 3$
$3x + 2y + kz = 4$
has a unique solution. Then $S$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
Let $A$ be a matrix such that $A \begin{bmatrix} 1 & 2 \\ 0 & 3 \end{bmatrix}$ is a scalar matrix and $|3A| = 108$. Then $A^2$ equals :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
If $\lambda \in \mathbb{R}$ is such that the sum of the cubes of the roots of the equation $x^{2} + (2-\lambda)x + (10-\lambda)=0$ is minimum, then the magnitude of the difference of the roots of this equation is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
Consider the following two binary relations on the set $A = {a, b, c}$ : $R_1 = {(c, a), (b, b), (a, c), (c, c), (b, c), (a, a)}$ and $R_2 = {(a, b), (b, a), (c, c), (c, a), (a, a), (b, b), (a, c)}$. Then :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
The set of all $\alpha \in \mathbb{R}$ for which $w = \dfrac{1 + (1-8\alpha)z}{1-z}$ is purely imaginary number, for all $z \in \mathbb{C}$ satisfying $|z| = 1$ and $\operatorname{Re} z \ne 1$, is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
If the tangents drawn to the hyperbola $4y^{2}=x^{2}+1$ intersect the co-ordinate axes at the distinct points $A$ and $B$ then the locus of the mid point of $AB$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
If $\tan A$ and $\tan B$ are the roots of the quadratic equation $3x^{2}-10x-25=0$, then the value of $3\sin^{2}(A+B)-10\sin(A+B)\cos(A+B)-25\cos^{2}(A+B)$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
A box $A$ contains $2$ white, $3$ red and $2$ black balls. Another box $B$ contains $4$ white, $2$ red and $3$ black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box $B$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
The mean of set of $30$ observations is $75$. If each observation is multiplied by a non-zero number $\lambda$ and then each of them is decreased by $25$, their mean remains the same. Then $\lambda$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
If $\overrightarrow a ,\,\,\overrightarrow b ,$ and $\overrightarrow C $ are unit vectors such that $\overrightarrow a + 2\overrightarrow b + 2\overrightarrow c = \overrightarrow 0 ,$ then $\left| {\overrightarrow a \times \overrightarrow c } \right|$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
Let y = y(x) be the solution of the differential equation ${{dy} \over {dx}} + 2y = f\left( x \right),$

where $f\left( x \right) = \left\{ {\matrix{ {1,} & {x \in \left[ {0,1} \right]} \cr {0,} & {otherwise} \cr } } \right.$

If y(0) = 0, then $y\left( {{3 \over 2}} \right)$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
The value of the integral $\displaystyle \int_{-\pi/4}^{\pi/4} \sin^{4}x \left(1 + \log\left(\dfrac{2 + \sin 2x}{2 - \sin 2x}\right)\right),dx$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
The area (in sq. units) of the region ${(x,y)\in \mathbb{R}^{2} : x \ge 0,\ y \ge 0,\ y \ge x-2 \text{ and } y \le \sqrt{x}}$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
If a right circular cone, having maximum volume, is inscribed in a sphere of radius $3\ \text{cm}$, then the curved surface area (in $\text{cm}^{2}$) of this cone is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
If $f\left( {{{x - 4} \over {x + 2}}} \right) = 2x + 1,$ (x $ \in $ R $-${1, $-$ 2}), then $\int f \left( x \right)dx$ is equal to :
(where C is a constant of integration)





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
Let $S={(\lambda,\mu)\in\mathbb{R}\times\mathbb{R}: f(t)=(\lvert\lambda\rvert e^{\lvert t\rvert}-\mu)\cdot\sin(2\lvert t\rvert),\ t\in\mathbb{R},\text{ is a differentiable function}}$. Then $S$ is a subset of :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
If $x^{2} + y^{2} + \sin y = 4$, then the value of $\dfrac{d^{2}y}{dx^{2}}$ at the point $(-2,0)$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
If $f(x) = \begin{vmatrix} \cos x & x & 1 \\ 2\sin x & x^{2} & 2x \\ \tan x & x & 1 \end{vmatrix}$, then $\lim_{x \to 0} \dfrac{f'(x)}{x}$





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
If $a$, $b$, $c$ are in A.P. and $a^{2}$, $b^{2}$, $c^{2}$ are in G.P. such that $a < b < c$ and $a + b + c = \dfrac{3}{4}$, then the value of $a$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

JEE MAIN PYQ 2018
If the system of linear equations
$x + ay + z = 3$
$x + 2y + 2z = 6$
$x + 5y + 3z = b$
has no solution, then :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

JEE MAIN PYQ 2018
If $|z - 3 + 2i| \le 4$ then the difference between the greatest value and the least value of $|z|$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

JEE MAIN PYQ 2018
The number of four letter words that can be formed using the letters of the word $\text{BARRACK}$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

JEE MAIN PYQ 2018
Suppose $A$ is any $3\times 3$ non-singular matrix and $(A-3I)(A-5I)=0$ where $I=I_{3}$ and $O=O_{3}$. If $\alpha A+\beta A^{-1}=4I$, then $\alpha+\beta$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

JEE MAIN PYQ 2018
Let $f\colon A\to B$ be a function defined as $f(x)=\dfrac{x-1}{x-2}$, where $A=\mathbb{R}-{2}$ and $B=\mathbb{R}-{1}$. Then $f$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

JEE MAIN PYQ 2018
If $f(x)$ is a quadratic expression such that $f(1)+f(2)=0$, and $-1$ is a root of $f(x)=0$, then the other root of $f(x)=0$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

JEE MAIN PYQ 2018
If the position vectors of the vertices $A$, $B$ and $C$ of a $\triangle ABC$ are respectively $4\hat{i}+7\hat{j}+8\hat{k}$, $2\hat{i}+3\hat{j}+4\hat{k}$ and $2\hat{i}+5\hat{j}+7\hat{k}$, then the position vector of the point where the bisector of $\angle A$ meets $BC$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

JEE MAIN PYQ 2018
If the mean of the data $7, 8, 9, 7, 8, 7, \lambda, 8$ is $8$, then the variance of this data is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

JEE MAIN PYQ 2018
A player $X$ has a biased coin whose probability of showing heads is $p$ and a player $Y$ has a fair coin. They start playing a game with their own coins and play alternately. The player who throws a head first is a winner. If $X$ starts the game, and the probability of winning the game by both the players is equal, then the value of $p$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

JEE MAIN PYQ 2018
Tangents drawn from the point $(-8,0)$ to the parabola $y^{2} = 8x$ touch the parabola at $P$ and $Q$. If $F$ is the focus of the parabola, then the area of the triangle $PFQ$ (in sq. units) is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

JEE MAIN PYQ 2018
The foot of the perpendicular drawn from the origin, on the line, $3x + y = \lambda\ (\lambda \ne 0)$ is $P$. If the line meets $x$-axis at $A$ and $y$-axis at $B$, then the ratio $BP : PA$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

JEE MAIN PYQ 2018
The sides of a rhombus $ABCD$ are parallel to the lines, $x - y + 2 = 0$ and $7x - y + 3 = 0$. If the diagonals of the rhombus intersect $P(1,2)$ and the vertex $A$ (different from the origin) is on the $y$-axis, then the coordinate of $A$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

JEE MAIN PYQ 2018
The curve satisfying the differential equation $(x^{2}-y^{2}),dx + 2xy,dy = 0$ and passing through the point $(1,1)$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

JEE MAIN PYQ 2018
If $\displaystyle \int \frac{2x+5}{\sqrt{7-6x-x^{2}}},dx = A\sqrt{7-6x-x^{2}} + B\sin^{-1}!\left(\frac{x+3}{4}\right) + C$ (where $C$ is a constant of integration), then the ordered pair $(A,B)$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

JEE MAIN PYQ 2018
If $I_1=\displaystyle\int_{0}^{1} e^{-x}\cos^{2}x,dx$; $I_2=\displaystyle\int_{0}^{1} e^{-x^{2}}\cos^{2}x,dx$ and $I_3=\displaystyle\int_{0}^{1} e^{-x^{3}},dx$; then





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

JEE MAIN PYQ 2018
The value of the integral $\displaystyle\int_{\pi/4}^{3\pi/4}\frac{x}{1+\sin x},dx$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

JEE MAIN PYQ 2018
Let $f(x)$ be a polynomial of degree $4$ having extreme values at $x=1$ and $x=2$. If $\lim_{x\to 0}\left(\dfrac{f(x)}{x^{2}}+1\right)=3$ then $f(-1)$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

JEE MAIN PYQ 2018
If $f(x)=\sin^{-1}\left(\dfrac{2x^{3}}{1+9x^{2}}\right)$, then $f'!\left(-\dfrac{1}{2}\right)$ equals





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

JEE MAIN PYQ 2018
Let f(x) = $\left\{ {\matrix{ {{{\left( {x - 1} \right)}^{{1 \over {2 - x}}}},} & {x > 1,x \ne 2} \cr {k\,\,\,\,\,\,\,\,\,\,\,\,\,\,} & {,x = 2} \cr } } \right.$

Thevaue of k for which f s continuous at x = 2 is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

JEE MAIN PYQ 2018
$\displaystyle \lim_{x\to 0} \frac{x\tan 2x - 2x\tan x}{(1-\cos 2x)^{2}}$ equals :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (15 April Evening Shift) PYQ

Solution

JEE MAIN PYQ 2018
From $6$ different novels and $3$ different dictionaries, $4$ novels and $1$ dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (Offline) PYQ

Solution

JEE MAIN PYQ 2018
Let $S = {x \in \mathbb{R} : x \ge 0 \text{ and } 2\lvert\sqrt{x}-3\rvert + \sqrt{x}(\sqrt{x}-6)+6=0}$. Then $S$ :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (Offline) PYQ

Solution

JEE MAIN PYQ 2018
If $\alpha, \beta \in \mathbb{C}$ are the distinct roots of the equation $x^{2} - x + 1 = 0$, then $\alpha^{101} + \beta^{107}$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (Offline) PYQ

Solution

JEE MAIN PYQ 2018
If the system of linear equations
$x + ky + 3z = 0$
$3x + ky - 2z = 0$
$2x + 4y - 3z = 0$
has a non-zero solution $(x, y, z)$, then $\dfrac{xz}{y^{2}}$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (Offline) PYQ

Solution

JEE MAIN PYQ 2018
Two sets $A$ and $B$ are as under : $A = {(a,b) \in \mathbb{R} \times \mathbb{R} : |a-5| < 1 \text{ and } |b-5| < 1}$ $B = {(a,b) \in \mathbb{R} \times \mathbb{R} : 4(a-6)^{2} + 9(b-5)^{2} \le 36}$ Then





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (Offline) PYQ

Solution

JEE MAIN PYQ 2018
If $\left|\begin{bmatrix} x-4 & 2x & 2x \\ 2x & x-4 & 2x \\ 2x & 2x & x-4 \end{bmatrix}\right| = (A+Bx)(x-A)^{2}$ then the ordered pair $(A,B)$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (Offline) PYQ

Solution

JEE MAIN PYQ 2018
Let $a_1, a_2, a_3, \ldots, a_{49}$ be in A.P. such that $\displaystyle \sum_{k=0}^{12} a_{4k+1} = 416$ and $a_9 + a_{43} = 66$. If $a_1^{2} + a_2^{2} + \cdots + a_{17}^{2} = 140m$, then $m$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (Offline) PYQ

Solution

JEE MAIN PYQ 2018
A bag contains $4$ red and $6$ black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (Offline) PYQ

Solution

JEE MAIN PYQ 2018
If $\displaystyle \sum_{i=1}^{9}(x_i-5)=9$ and $\displaystyle \sum_{i=1}^{9}(x_i-5)^{2}=45$, then the standard deviation of the $9$ items $x_1,x_2,\ldots,x_9$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (Offline) PYQ

Solution

JEE MAIN PYQ 2018
Let $\vec{u}$ be a vector coplanar with the vectors $\vec{a}=2\hat{i}+3\hat{j}-\hat{k}$ and $\vec{b}=\hat{j}+\hat{k}$. If $\vec{u}$ is perpendicular to $\vec{a}$ and $\vec{u}\cdot\vec{b}=24$, then $\lvert\vec{u}\rvert^{2}$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (Offline) PYQ

Solution

JEE MAIN PYQ 2018
A straight line through a fixed point $(2,3)$ intersects the coordinate axes at distinct points $P$ and $Q$. If $O$ is the origin and the rectangle $OPRQ$ is completed, then the locus of $R$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (Offline) PYQ

Solution

JEE MAIN PYQ 2018
Let $y = y(x)$ be the solution of the differential equation $\sin x \dfrac{dy}{dx} + y \cos x = 4x,\ x \in (0,\pi).$ If $y\left(\dfrac{\pi}{2}\right) = 0$, then $y\left(\dfrac{\pi}{6}\right)$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (Offline) PYQ

Solution

JEE MAIN PYQ 2018
The integral $\displaystyle \int \frac{\sin^{2}x \cos^{2}x}{\left(\sin^{5}x + \cos^{3}x \sin^{2}x + \sin^{3}x \cos^{2}x + \cos^{5}x\right)^{2}},dx$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (Offline) PYQ

Solution

JEE MAIN PYQ 2018
The value of $\displaystyle \int_{-\pi/2}^{\pi/2} \frac{\sin^{2}x}{1+2^{x}},dx$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (Offline) PYQ

Solution

JEE MAIN PYQ 2018
Let $g(x)=\cos x^{2}$, $f(x)=\sqrt{x}$ and $\alpha,\beta\ (\alpha<\beta)$ be the roots of the quadratic equation $18x^{2}-9\pi x+\pi^{2}=0$. Then the area (in sq. units) bounded by the curve $y=(g\circ f)(x)$ and the lines $x=\alpha$, $x=\beta$ and $y=0$ is :





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Solution

JEE MAIN PYQ 2018
Let $S={t\in\mathbb{R}: f(x)=|x-\pi|,(e^{|x|}-1)\sin|x|\ \text{is not differentiable at }t}$. Then the set $S$ is equal to





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (Offline) PYQ

Solution

JEE MAIN PYQ 2018
Let $f(x) = x^{2} + \dfrac{1}{x^{2}}$ and $g(x) = x - \dfrac{1}{x}$, $x \in \mathbb{R} - {-1,0,1}$. If $h(x) = \dfrac{f(x)}{g(x)}$, then the local minimum value of $h(x)$ is





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Solution

JEE MAIN PYQ 2018
For each $t \in \mathbb{R}$, let $[t]$ be the greatest integer less than or equal to $t$. Then $\displaystyle \lim_{x \to 0^{+}} x\left(\left[\frac{1}{x}\right] + \left[\frac{2}{x}\right] + \cdots + \left[\frac{15}{x}\right]\right)$





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Solution

JEE MAIN PYQ 2018
If $f(x) = \displaystyle\int_{0}^{x} t(\sin x - \sin t),dt$ then :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
If $\displaystyle \int \frac{\tan x}{1+\tan x+\tan^{2}x},dx = x - \frac{K}{\sqrt{A}}\tan^{-1}\left(\frac{K\tan x + 1}{\sqrt{A}}\right) + C,\ (C\ \text{is a constant of integration})$ then the ordered pair $(K,A)$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
If $x = \sqrt{2^{\csc^{-1} t}}$ and $y = \sqrt{2^{\sec^{-1} t}}$ $(\lvert t \rvert \ge 1)$, then $\dfrac{dy}{dx}$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
Let A = $\left[ {\matrix{ 1 & 0 & 0 \cr 1 & 1 & 0 \cr 1 & 1 & 1 \cr } } \right]$ and B = A20. Then the sum of the elements of the first column of B is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
If the function $f$ defined as $f(x) = \dfrac{1}{x} - \dfrac{kx - 1}{e^{2x} - 1}, ; x \ne 0$, is continuous at $x = 0$, then the ordered pair $(k, f(0))$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
Let $M$ and $m$ be respectively the absolute maximum and the absolute minimum values of the function $f(x) = 2x^{3} - 9x^{2} + 12x + 5$ in the interval $[0, 3]$. Then $M - m$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
Let $\dfrac{1}{x_1},\dfrac{1}{x_2},\ldots,\dfrac{1}{x_n}$ $(x_i\ne0\text{ for }i=1,2,\ldots,n)$ be in A.P. such that $x_1=4$ and $x_{21}=20$. If $n$ is the least positive integer for which $x_n>50$, then $\displaystyle\sum_{i=1}^n \left(\dfrac{1}{x_i}\right)$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
$\displaystyle\lim_{x\to0} \dfrac{(27+x)^{1/3}-3}{9-(27+x)^{2/3}}$ equals :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
The number of numbers between $2000$ and $5000$ that can be formed with the digits $0,1,2,3,4$ (repetition of digits is not allowed) and are multiples of $3$ is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
If $\displaystyle \int \frac{\tan x}{1+\tan x+\tan^2 x},dx = x - \frac{K}{\sqrt{A}}\tan^{-1}!\left(\frac{K\tan x + 1}{\sqrt{A}}\right) + C,\ (C\text{ is a constant of integration})$ then the ordered pair $(K,A)$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

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JEE MAIN PYQ 2018
Let $M$ and $m$ be respectively the absolute maximum and the absolute minimum values of the function $f(x)=2x^{3}-9x^{2}+12x+5$ in the interval $[0,3]$. Then $M-m$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

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JEE MAIN PYQ 2018
If the function $f$ defined as $f(x)=\dfrac{1}{x}-\dfrac{kx-1}{e^{2x}-1},\ x\ne0$, is continuous at $x=0$, then the ordered pair $(k,f(0))$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

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JEE MAIN PYQ 2018
Let $p, q$ and $r$ be real numbers $(p \ne q,, r \ne 0)$, such that the roots of the equation $\dfrac{1}{x+p} + \dfrac{1}{x+q} = \dfrac{1}{r}$ are equal in magnitude but opposite in sign, then the sum of squares of these roots is equal to:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

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JEE MAIN PYQ 2018
The least positive integer $n$ for which $\left(\dfrac{1 + i\sqrt{3}}{1 - i\sqrt{3}}\right)^{n} = 1$ is:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

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JEE MAIN PYQ 2018
Let $\mathbb{N}$ denote the set of all natural numbers. Define two binary relations on $\mathbb{N}$ as $R_1 = {(x,y) \in \mathbb{N} \times \mathbb{N} : 2x + y = 10}$ and $R_2 = {(x,y) \in \mathbb{N} \times \mathbb{N} : x + 2y = 10}$. Then:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

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JEE MAIN PYQ 2018
Two different families $A$ and $B$ are blessed with equal number of children. There are $3$ tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family $B$ is $\dfrac{1}{12}$, then the number of children in each family is:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

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JEE MAIN PYQ 2018
If an angle $A$ of $\triangle ABC$ satisfies $5\cos A + 3 = 0$, then the roots of the quadratic equation $9x^{2} + 27x + 20 = 0$ are :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

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JEE MAIN PYQ 2018
The mean and the standard deviation (s.d.) of five observations are $9$ and $0$, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes $10$, then their s.d. is:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

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JEE MAIN PYQ 2018
Let A, B and C be three events, which are pair-wise independent and $\overrightarrow E $ denotes the completement of an event E. If $P\left( {A \cap B \cap C} \right) = 0$ and $P\left( C \right) > 0,$ then $P\left[ {\left( {\overline A \cap \overline B } \right)\left| C \right.} \right]$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
Let $\vec{a} = \hat{i} + \hat{j} + \hat{k}$, $\vec{c} = \hat{j} - \hat{k}$, and a vector $\vec{b}$ be such that $\vec{a} \times \vec{b} = \vec{c}$ and $\vec{a} \cdot \vec{b} = 3$. Then $|\vec{b}|$ equals:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2018
If the angle between the lines $\dfrac{x}{2}=\dfrac{y}{2}=\dfrac{z}{1}$ and $\dfrac{5-x}{-2}=\dfrac{7y-14}{p}=\dfrac{z-3}{4}$ is $\cos^{-1}\left(\dfrac{2}{3}\right)$, then $p$ is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

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JEE MAIN PYQ 2018
If the length of the latus rectum of an ellipse is $4$ units and the distance between a focus an its nearest vertex on the major axis is $\dfrac{3}{2}$ units, then its eccentricity is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

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JEE MAIN PYQ 2018
The locus of the point of intersection of the lines $ \sqrt{2}x - y + 4\sqrt{2}k = 0$ and $\sqrt{2}kx + ky - 4\sqrt{2} = 0$ $(k$ is any non-zero real parameter$)$, is :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

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JEE MAIN PYQ 2018
If a circle $C$, whose radius is $3$, touches externally the circle $x^{2}+y^{2}+2x-4y-4=0$ at the point $(2,2)$, then the length of the intercept cut by this circle $C$ on the $x$-axis is equal to :





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2018 (16 April Morning Shift) PYQ

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JEE MAIN PYQ 2018
A $2,\text{m}$ ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate of $25,\text{cm/sec}$, then the rate (in $\text{cm/sec}$) at which the bottom of the ladder slides away from the wall on the horizontal ground when the top of the ladder is $1,\text{m}$ above the ground is:





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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2019 (12 April Morning Shift) PYQ

Solution


JEE MAIN

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