List of top Questions asked in JEE Main- 2014

Match List - I (Event) with List - II (Order of the time interval for happening of the event) and select the correct option from the options given below the lists.

List - I	List - II
(a) Rotation period of earth	(i) \(10^{5}\) s
(b) Revolution period of earth	(ii) \(10^{7}\) s
(c) Period of a light wave	(iii) \(10^{-15}\) s
(d) Period of a sound wave	(iv) \(10^{-3}\) s

If the angle between the line \(2(x+1)=y=z+4\) and the plane \(2x-y+\sqrt{\lambda}\,z+4=0\) is \(\frac{\pi}{6}\), then the value of \(\lambda\) is :

Let A and E be any two events with positive probabilities :
Statement - 1 : \(P(E/A)\ge P(A/E)P(E)\)
Statement - 2 : \(P(A/E)\ge P(A\cap E)\).

A chord is drawn through the focus of the parabola \(y^2=6x\) such that its distance from the vertex of this parabola is \(\frac{\sqrt5}{2}\), then its slope can be :

If \(\vec x=3\hat i-6\hat j-\hat k,\ \vec y=\hat i+4\hat j-3\hat k\) and \(\vec z=3\hat i-4\hat j-12\hat k\), then the magnitude of the projection of \(\vec x\times\vec y\) on \(\vec z\) is :

The tangent at an extremity (in the first quadrant) of latus rectum of the hyperbola \(\frac{x^2}{4}-\frac{y^2}{5}=1\), meets \(x\)-axis and \(y\)-axis at A and B respectively. Then \((OA)^2-(OB)^2\), where O is the origin, equals :

If a line L is perpendicular to the line \(5x-y=1\), and the area of the triangle formed by the line L and the coordinate axes is \(5\), then the distance of line L from the line \(x+5y=0\) is :

The circumcentre of a triangle lies at the origin and its centroid is the mid point of the line segment joining the points \((a^2+1,\ a^2+1)\) and \((2a,\ -2a),\ a\neq 0\). Then for any \(a\), the orthocentre of this triangle lies on the line :

If \(\frac{dy}{dx}+y\tan x=\sin 2x\) and \(y(0)=1\), then \(y(\pi)\) is equal to :

The equation of the circle described on the chord \(3x+y+5=0\) of the circle \(x^2+y^2=16\) as diameter is :

The area of the region above the \(x\)-axis bounded by the curve \(y=\tan x,\ 0\le x\le \frac{\pi}{2}\) and the tangent to the curve at \(x=\frac{\pi}{4}\) is :

If m is a non-zero number and \(\displaystyle\int\frac{x^{5m-1}+2x^{4m-1}}{\left(x^{2m}+x^m+1\right)^3}\,dx=f(x)+c\), then \(f(x)\) is :

If non-zero real numbers b and c are such that \(\min f(x)>\max g(x)\), where \(f(x)=x^2+2bx+2c^2\) and \(g(x)=-x^2-2cx+b^2\) \((x\in\mathbf{R})\); then \(\left|\frac cb\right|\) lies in the interval :

Let function F be defined as \(F(x)=\displaystyle\int_1^x\frac{e^t}{t}\,dt,\ x>0\), then the value of the integral \(\displaystyle\int_1^x\frac{e^t}{t+a}\,dt\), where \(a>0\), is :

If the volume of a spherical ball is increasing at the rate of \(4\pi\) cc/sec, then the rate of increase of its radius (in cm/sec), when the volume is \(288\pi\) cc, is :

If \(\Delta_r=\begin{vmatrix} r & 2r-1 & 3r-2\\ \frac{n}{2} & n-1 & a\\ \frac12 n(n-1) & (n-1)^2 & \frac12 (n-1)(3n+4)\end{vmatrix}\), then the value of \(\displaystyle\sum_{r=1}^{n-1}\Delta_r\) :

If the function \(f(x)=\begin{cases}\dfrac{\sqrt{2+\cos x}-1}{(\pi-x)^2}, & x\ne\pi\\ k, & x=\pi\end{cases}\) is continuous at \(x=\pi\), then k equals :

Let \(f:\mathbf{R}\to\mathbf{R}\) be a function such that \(|f(x)|\le x^2\), for all \(x\in\mathbf{R}\). Then, at \(x=0\), \(f\) is :

Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between themselves exceeds the number of games that the men played with the women by 66, then the number of men who participated in the tournament lies in the interval :

Let A and B be any two \(3\times 3\) matrices. If A is symmetric and B is skewsymmetric, then the matrix AB \(-\) BA is :

The equation \(\sqrt{3x^2+x+5}=x-3\), where \(x\) is real, has :

Let \(f : \mathbf{R}\to\mathbf{R}\) be defined by \(f(x)=\frac{|x|-1}{|x|+1}\), then \(f\) is :

Phthalic acid reacts with resorcinol in the presence of concentrated \(\mathrm{H_2SO_4}\) to give:

Which one of the following exhibits the large number of oxidation states?

Among the following species the one which causes the highest CFSE, \(\Delta_0\) as a ligand is: