Aspire's Library

A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations
  • JEE MAIN
    Previous Year Questions

JEE MAIN Previous Year Questions (PYQs)

JEE MAIN 2016 PYQ

JEE MAIN PYQ 2016
For $x \in \mathbb{R}$, $f(x) = |\log 2 - \sin x|$ and $g(x) = f(f(x))$, then:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

JEE MAIN PYQ 2016
Let $ p = \displaystyle \lim_{x \to 0^{+}} \left(1 + \tan^{2}\sqrt{x}\right)^{\tfrac{1}{x}} $ then $\log p$ is equal to:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

JEE MAIN PYQ 2016
A value of $\theta$ for which $ \displaystyle \frac{2 + 3i \sin \theta}{1 - 2i,} \cdot \frac{1}{\sin \theta} $ is purely imaginary, is:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

JEE MAIN PYQ 2016
If the standard deviation of the numbers $2, 3, a,$ and $11$ is $3.5$, then which of the following is true?





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

JEE MAIN PYQ 2016
Let two fair six-faced dice $A$ and $B$ be thrown simultaneously. If $E_{1}$ is the event that die $A$ shows up four, $E_{2}$ is the event that die $B$ shows up two, and $E_{3}$ is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

JEE MAIN PYQ 2016
If a curve $y = f(x)$ passes through the point $(1,-1)$ and satisfies the differential equation $ y(1+xy),dx = x,dy $, then $ f\left(-\dfrac{1}{2}\right) $ is equal to:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

JEE MAIN PYQ 2016
The area (in sq. units) of the region $ {(x,y) : y^{2} \ge 2x \ \text{and} \ x^{2} + y^{2} \le 4x,\ x \ge 0,\ y \ge 0} $ is:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

JEE MAIN PYQ 2016
The integral $ \displaystyle \int \frac{2x^{12} + 5x^{9}}{(x^{5} + x^{2} + 1)^{3}}, dx $ is equal to:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

JEE MAIN PYQ 2016
The system of linear equations
$ x + \lambda y - z = 0 $
$ \lambda x - y - z = 0 $
$ x + y - \lambda z = 0 $
has a non-trivial solution for:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

JEE MAIN PYQ 2016
A wire of length $2$ units is cut into two parts which are bent respectively to form a square of side $= x$ units and a circle of radius $= r$ units. If the sum of the areas of the square and the circle so formed is minimum, then:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

JEE MAIN PYQ 2016
The eccentricity of the hyperbola whose length of the latus rectum is equal to $8$ and the length of its conjugate axis is equal to half of the distance between its foci, is:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

JEE MAIN PYQ 2016
$A = \begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix}$ and $A \,\text{adj}\, A = A\,A^{T}$, then $5a + b$ is equal to:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

JEE MAIN PYQ 2016
If one of the diameters of the circle, given by the equation, $ x^{2} + y^{2} - 4x + 6y - 12 = 0 $, is a chord of a circle $S$, whose centre is at $(-3, 2)$, then the radius of $S$ is :





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

JEE MAIN PYQ 2016
Two sides of a rhombus are along the lines, $x - y + 1 = 0$ and $7x - y - 5 = 0$. If its diagonals intersect at $(-1, -2)$, then which one of the following is a vertex of this rhombus?





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

JEE MAIN PYQ 2016
If the $2^{\text{nd}}, 5^{\text{th}}$ and $9^{\text{th}}$ terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is :





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

JEE MAIN PYQ 2016
If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary, then the position of the word SMALL is :





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

JEE MAIN PYQ 2016
The sum of all real values of $x$ satisfying the equation $(x^{2} - 5x + 5)^{x^{2} + 4x - 60} = 1$ is :





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

JEE MAIN PYQ 2016
If $f(x) + 2f\left(\dfrac{1}{x}\right) = 3x,; x \ne 0,$ and $S = {x \in \mathbb{R} : f(x) = f(-x)}$, then $S$ :





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (Offline) PYQ

Solution

JEE MAIN PYQ 2016
Let $x, y, z$ be positive real numbers such that $x + y + z = 12$ and $x^{3} y^{4} z^{5} = (0.1)(600)^{3}$. Then $x^{3} + y^{3} + z^{3}$ is equal to:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
If the four-letter words (need not be meaningful) are to be formed using the letters from the word “MEDITERRANEAN” such that the first letter is $R$ and the fourth letter is $E$, then the total number of all such words is:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
The number of distinct real roots of the equation $ \begin{vmatrix} \cos x & \sin x & \sin x \\ \sin x & \cos x & \sin x \\ \sin x & \sin x & \cos x \end{vmatrix} = 0 $ in the interval $ \left[ -\frac{\pi}{4}, \frac{\pi}{4} \right] $ is:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
If the equations $x^{2} + bx - 1 = 0$ and $x^{2} + x + b = 0$ have a common root different from $-1$, then $|b|$ is equal to:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
The point represented by $2 + i$ in the Argand plane moves $1$ unit eastwards, then $2$ units northwards and finally from there $2\sqrt{2}$ units in the south-westwards direction. Then its new position in the Argand plane is at the point represented by:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
If $P = \begin{bmatrix} \dfrac{\sqrt{3}}{2} & \dfrac{1}{2} \\ -\dfrac{1}{2} & \dfrac{\sqrt{3}}{2} \end{bmatrix}$ and $A = \begin{bmatrix} 1 & 1 \\ 0 & 1 \end{bmatrix}$, $Q = P A P^{T}$, then $P^{T} Q^{2015} P$ is:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
For $x \in \mathbb{R}, x \ne 0$, let $f_{0}(x) = \dfrac{1}{1 - x}$ and $f_{n+1}(x) = f_{0}(f_{n}(x)),; n = 0,1,2,\ldots$ Then the value of $f_{100}(3) + f_{1}\left(\dfrac{2}{3}\right) + f_{2}\left(\dfrac{3}{2}\right)$ is equal to:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
The value of $\displaystyle \sum_{r=1}^{15} r^{2} \left( \dfrac{{}^{15}C_{r}}{{}^{15}C_{r-1}} \right)$ is equal to:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
A circle passes through $(-2,4)$ and touches the $y$-axis at $(0,2)$. Which one of the following equations can represent a diameter of this circle?





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
If $m$ and $M$ are the minimum and the maximum values of $4 + \dfrac{1}{2}\sin^{2} 2x - 2\cos^{4} x,; x \in \mathbb{R}$, then $M - m$ is equal to :





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
Let $a$ and $b$ respectively be the semitransverse and semi-conjugate axes of a hyperbola whose eccentricity satisfies the equation $9e^{2} - 18e + 5 = 0$. If $S(5,0)$ is a focus and $5x = 9$ is the corresponding directrix of this hyperbola, then $a^{2} - b^{2}$ is equal to :





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
In a triangle $ABC$, right angled at the vertex $A$, if the position vectors of $A,B$ and $C$ are respectively $3\hat{i} + \hat{j} - \hat{k}$, $-\hat{i} + 3\hat{j} + p\hat{k}$ and $5\hat{i} + q\hat{j} - 4\hat{k}$, then the point $(p,q)$ lies on a line:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
If $A$ and $B$ are any two events such that $P(A) = \dfrac{2}{5}$ and $P(A \cap B) = \dfrac{3}{20}$, then the conditional probability $P\big(A \mid (A' \cup B')\big)$, where $A'$ denotes the complement of $A$, is equal to:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
If the mean deviation of the numbers $1,, 1 + d,, \ldots,, 1 + 100d$ from their mean is $255$, then a value of $d$ is:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
The shortest distance between the lines $\dfrac{x}{2} = \dfrac{y}{2} = \dfrac{z}{1}$ and $\dfrac{x + 2}{-1} = \dfrac{y - 4}{8} = \dfrac{z - 5}{4}$ lies in the interval:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
The point $(2,1)$ is translated parallel to the line $L : x - y = 4$ by $2\sqrt{3}$ units. If the new point $Q$ lies in the third quadrant, then the equation of the line passing through $Q$ and perpendicular to $L$ is:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
The area (in sq. units) of the region described by $A = {(x,y)\mid y \ge x^{2} - 5x + 4,\ x + y \ge 1,\ y \le 0}$ is:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
If a variable line drawn through the intersection of the lines $\dfrac{x}{3} + \dfrac{y}{4} = 1$ and $\dfrac{x}{4} + \dfrac{y}{3} = 1$ meets the coordinate axes at $A$ and $B$ $(A \ne B)$, then the locus of the midpoint of $AB$ is:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
If $f(x)$ is a differentiable function in the interval $(0,\infty)$ such that $f(1) = 1$ and $\displaystyle \lim_{t \to x} \frac{t^{2}f(x) - x^{2}f(t)}{t - x} = 1$, for each $x > 0$, then $f\left(\dfrac{3}{2}\right)$ is equal to:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
If $2\displaystyle\int_{0}^{1} \tan^{-1} x , dx = \displaystyle\int_{0}^{1} \cot^{-1} (1 - x + x^{2}) , dx,$ then $\displaystyle\int_{0}^{1} \tan^{-1} (1 - x + x^{2}) , dx$ is equal to :





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
The minimum distance of a point on the curve $y = x^{2} - 4$ from the origin is :





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
If $\displaystyle \int \frac{dx}{\cos^{3}x\sqrt{2\sin 2x}} = (\tan x)^{A} + C(\tan x)^{B} + k,$ where $k$ is a constant of integration, then $A + B + C$ equals :





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
If the function

f(x) = $\left\{ {\matrix{ { - x} & {x < 1} \cr {a + {{\cos }^{ - 1}}\left( {x + b} \right),} & {1 \le x \le 2} \cr } } \right.$

is differentiable at x = 1, then ${a \over b}$ is equal to :





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
If $\displaystyle \lim_{x \to \infty} \left(1 + \frac{a}{x} - \frac{4}{x^{2}}\right)^{2x} = e^{3}$, then $a$ is equal to:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (9 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
Let $a_{1}, a_{2}, a_{3}, \ldots, a_{n}, \ldots$ be in A.P. If $a_{3} + a_{7} + a_{11} + a_{15} = 72$, then the sum of its first $17$ terms is equal to:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
If $\dfrac{{}^{n+2}C_{6}}{{}^{n-2}P_{2}} = 11$, then $n$ satisfies the equation:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
If the coefficients of $x^{-2}$ and $x^{-4}$ in the expansion of $\left(x^{\tfrac13} + \dfrac{1}{2x^{\tfrac13}}\right)^{18},\ (x>0)$ are $m$ and $n$ respectively, then $\dfrac{m}{n}$ is equal to:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
If $A = \begin{bmatrix} -4 & -1 \\ 3 & 1 \end{bmatrix}$, then the determinant of the matrix $(A^{2016} - 2A^{2015} - A^{2014})$ is:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
Let $A$ be a $3 \times 3$ matrix such that $A^{2} - 5A + 7I = 0$. \textbf{Statement I:} $A^{-1} = \dfrac{1}{7}(5I - A)$. \textbf{Statement II:} The polynomial $A^{3} - 2A^{2} - 3A + I$ can be reduced to $5(A - 4I)$. Then:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
If $x$ is a solution of the equation $\sqrt{2x+1} - \sqrt{2x-1} = 1,\ (x \ge \tfrac12)$, then $\sqrt{4x^{2}-1}$ is equal to:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
Let $P = \{\theta : \sin\theta - \cos\theta = \sqrt{2}\cos\theta\}$ and $Q = \{\theta : \sin\theta + \cos\theta = \sqrt{2}\sin\theta\}$ be two sets. Then





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
The sum $\displaystyle \sum_{r=1}^{10} (r^2 + 1)\,(r!)$ is equal to :





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
For $x \in \mathbb{R},\ x \ne 0$, if $y(x)$ is a differentiable function such that $x \int_{1}^{x} y(t)\,dt = (x+1) \int_{1}^{x} t\,y(t)\,dt,$ then $y(x)$ equals: (where $C$ is a constant.)





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
If $A>0,\ B>0$ and $A+B=\dfrac{\pi}{6}$, then the minimum value of $\tan A+\tan B$ is:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
The mean of $5$ observations is $5$ and their variance is $124$. If three of the observations are $1, 2$ and $6$, then the mean deviation from the mean of the data is:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
Let $\triangle ABC$ be a triangle whose circumcentre is at $P$. If the position vectors of $A, B, C$ and $P$ are $\vec a, \vec b, \vec c$ and $\dfrac{\vec a + \vec b + \vec c}{4}$ respectively, then the position vector of the orthocentre of this triangle is:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
ABC is a triangle in a plane with vertices $A(2,3,5)$, $B(-1,3,2)$ and $C(\lambda,5,\mu)$. If the median through $A$ is equally inclined to the coordinate axes, then the value of $(\lambda^3 + \mu^3 + 5)$ is:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
A hyperbola whose transverse axis is along the major axis of the conic $\dfrac{x^2}{3} + \dfrac{y^2}{4} = 4$ and has vertices at the foci of this conic. If the eccentricity of the hyperbola is $\dfrac{3}{2}$, then which of the following points does NOT lie on it?





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
A straight line through origin $O$ meets the lines $3y = 10 - 4x$ and $8x + 6y + 5 = 0$ at points $A$ and $B$ respectively. Then $O$ divides the segment $AB$ in the ratio :





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
A ray of light is incident along a line which meets another line $7x - y + 1 = 0$ at the point $(0,1)$. The ray is then reflected from this point along the line $y + 2x = 1$. Then the equation of the line of incidence of the ray of light is:





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
The value of the integral

$\int\limits_4^{10} {{{\left[ {{x^2}} \right]dx} \over {\left[ {{x^2} - 28x + 196} \right] + \left[ {{x^2}} \right]}}} ,$

where [x] denotes the greatest integer less than or equal to x, is :





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
The integral $\displaystyle \int \frac{dx}{(1+\sqrt{x})\sqrt{x - x^{2}}}$ is equal to :





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
Let $f(x)=\sin^{4}x+\cos^{4}x$. Then $f$ is an increasing function in the interval :





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
Let $a,b\in\mathbb{R}$, $(a\neq 0)$. If the function $f$ defined as $f(x)= \begin{cases} \dfrac{2x^{2}}{a}, & 0\le x<1 \\ a, & 1\le x<\sqrt{2} \\ \dfrac{2b^{2}-4b}{x^{3}}, & \sqrt{2}\le x<\infty \end{cases}$ is continuous in the interval $[0,\infty)$, then an ordered pair $(a,b)$ is :





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution

JEE MAIN PYQ 2016
$\displaystyle \lim_{x\to 0} \frac{(1-\cos 2x)^{2}}{2x\tan x - x\tan 2x}$ is :





Go to Discussion
JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2016 (10 April Morning Shift) PYQ

Solution


JEE MAIN

Online Test Series,
Information About Examination,
Syllabus, Notification
and More.

Click Here to
View More

JEE MAIN

Online Test Series,
Information About Examination,
Syllabus, Notification
and More.

Click Here to
View More
Ask Your Question or Put Your Review.

loading...