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 :

1

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

Topic: JEE Main 2014 (Offline)

2

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

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3

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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4

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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5

Let the population of rabbits surviving at time $t$ be governed by the differential equation $\dfrac{dp(t)}{dt}=\dfrac{…

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6

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

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7

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

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1

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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2

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

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3

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(\overlin…

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4

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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5

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…

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6

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…

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7

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. …

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8

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}{\alp…

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9

If $a\in\mathbb{R}$ and the equation $-3(x-[x])^{2}+2(x-[x])+a^{2}=0$ (where $[x]$ denotes the greatest integer $\le x$…

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10

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

Topic: JEE Main 2014 (Offline)