JEE MAIN 2014 Previous Year Question Paper and Solution with PDF

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Previous Year Questions

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Previous Year Questions
JEE MAIN

JEE MAIN Previous Year Questions (PYQs)

JEE MAIN 2014 PYQ

Qus : 1 JEE MAIN PYQ 2014

$\displaystyle \lim_{x\to 0}\frac{\sin(\pi \cos^{2}x)}{x^{2}}$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2014 (Offline) PYQ

Solution

Qus : 2 JEE MAIN PYQ 2014

Let the population of rabbits surviving at time $t$ be governed by the differential equation $\dfrac{dp(t)}{dt}=\dfrac{1}{2}p(t)-200$. If $p(0)=100$, then $p(t)$ equals:

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Solution

Qus : 3 JEE MAIN PYQ 2014

The integral $\displaystyle \int_{0}^{\pi}\sqrt{1+4\sin^{2}\frac{x}{2}-4\sin\frac{x}{2}}\,dx$ equals:

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2014 (Offline) PYQ

Solution

Qus : 4 JEE MAIN PYQ 2014

The area of the region described by $A=\{(x,y):x^{2}+y^{2}\le 1 \text{ and } y^{2}\le 1-x\}$ is :

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Solution

Qus : 5 JEE MAIN PYQ 2014

The integral $\displaystyle \int (1+x-\frac{1}{x})e^{x+\frac{1}{x}}\,dx$ is equal to

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2014 (Offline) PYQ

Solution

Qus : 6 JEE MAIN PYQ 2014

If $A$ is a $3\times 3$ non-singular matrix such that $AA' = A'A$ and $B = A^{-1}A'$, then $BB'$ equals :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2014 (Offline) PYQ

Solution

Qus : 7 JEE MAIN PYQ 2014

If $\alpha,\beta \ne 0$, and $f(n) = \alpha^{n} + \beta^{n}$ and $\begin{vmatrix} 3 & 1 + f(1) & 1 + f(2) \\ 1+f(1) & 1 + f(2) & 1 + f(3) \\ 1+f(2) & 1 + f(3) & 1 + f(4) \end{vmatrix} = K(1-\alpha)^{2}(1-\beta)^{2}(\alpha-\beta)^{2}$, then $K$ is equal to :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2014 (Offline) PYQ

Solution

Qus : 8 JEE MAIN PYQ 2014

If $g$ is the inverse of a function $f$ and $f'(x)=\dfrac{1}{1+x^{5}}$, then $g'(x)$ is equal to:

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Solution

Qus : 9 JEE MAIN PYQ 2014

If $x=-1$ and $x=2$ are extreme points of $f(x)=\alpha\log|x|+\beta x^{2}+x$ then

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Solution

Qus : 10 JEE MAIN PYQ 2014

Let $A$ and $B$ be two events such that $P(\overline{A\cup B})=\dfrac{1}{6}$, $P(A\cap B)=\dfrac{1}{4}$ and $P(\overline{A})=\dfrac{1}{4}$, where $\overline{A}$ stands for the complement of the event $A$. Then the events $A$ and $B$ are :

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Solution

Qus : 11 JEE MAIN PYQ 2014

The locus of the foot of perpendicular drawn from the centre of the ellipse $x^{2}+3y^{2}=6$ on any tangent to it is :

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Solution

Qus : 12 JEE MAIN PYQ 2014

Let $a,b,c$ and $d$ be non-zero numbers. If the point of intersection of the lines $4ax+2ay+c=0$ and $5bx+2by+d=0$ lies in the fourth quadrant and is equidistant from the two axes then :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2014 (Offline) PYQ

Solution

Qus : 13 JEE MAIN PYQ 2014

Let $PS$ be the median of the triangle with vertices $P(2,2)$, $Q(6,-1)$ and $R(7,3)$. The equation of the line passing through $(1,-1)$ and parallel to $PS$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2014 (Offline) PYQ

Solution

Qus : 14 JEE MAIN PYQ 2014

Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. then the common ratio of the G.P. is :

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Solution

Qus : 15 JEE MAIN PYQ 2014

Let $\alpha$ and $\beta$ be the roots of equation $px^{2}+qx+r=0$, $p\ne 0$. If $p,q,r$ are in A.P. and $\dfrac{1}{\alpha}+\dfrac{1}{\beta}=4$, then the value of $|\alpha-\beta|$ is :

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JEE MAIN JEE Mains PYQ JEE MAIN JEE Main 2014 (Offline) PYQ

Solution

Qus : 16 JEE MAIN PYQ 2014

If $a\in\mathbb{R}$ and the equation $-3(x-[x])^{2}+2(x-[x])+a^{2}=0$ (where $[x]$ denotes the greatest integer $\le x$) has no integral solution, then all possible values of $a$ lie in the interval :

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Solution

Qus : 17 JEE MAIN PYQ 2014

If $z$ is a complex number such that $|z|\ge 2$, then the minimum value of $\left|z+\dfrac{1}{2}\right|$ :

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Solution

Qus : 18 JEE MAIN PYQ 2014

Let $f_{k}(x)=\dfrac{1}{k}(\sin^{k}x+\cos^{k}x)$ where $x\in\mathbb{R}$ and $k\ge 1$. Then $f_{4}(x)-f_{6}(x)$ equals :

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Solution

Qus : 19 JEE MAIN PYQ 2014

The angle between the lines whose direction cosines satisfy the equations $l+m+n=0$ and $l^{2}=m^{2}+n^{2}$ is :

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Solution

Qus : 20 JEE MAIN PYQ 2014

The variance of first $50$ even natural numbers is :

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Solution

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