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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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…

Topic: JEE Main 2014 (Offline)

2

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. …

Topic: JEE Main 2014 (Offline)

3

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…

Topic: JEE Main 2014 (Offline)

4

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…

Topic: JEE Main 2014 (Offline)

5

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 :

Topic: JEE Main 2014 (Offline)

6

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…

Topic: JEE Main 2014 (Offline)

7

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

Topic: JEE Main 2014 (Offline)

8

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

Topic: JEE Main 2014 (Offline)

9

If $\alpha,\beta \ne 0$, and $f(n) = \alpha^{n} + \beta^{n}$ and $\begin{vmatrix} 3 & 1 + f(1) & 1 + f(2) \\ 1+…

Topic: JEE Main 2014 (Offline)

10

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)

1

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)

2

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 :

Topic: JEE Main 2014 (Offline)

3

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

Topic: JEE Main 2014 (Offline)