List of top Questions asked in JEE Main- 2014

The radiation corresponding to \(3\to2\) transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of \(3\times10^{-4}\ \mathrm{T}\). If the radius of the largest circular path followed by these electrons is \(10.0\ \mathrm{mm}\), the work function of the metal is close to :

The coercivity of a small magnet where the ferromagnet gets demagnetized is \(3\times10^{3}\ \mathrm{A\,m^{-1}}\). The current required to be passed in a solenoid of length \(10\ \mathrm{cm}\) and number of turns \(100\), so that the magnet gets demagnetized when inside the solenoid, is :

In the circuit shown here, the point 'C' is kept connected to point 'A' till the current flowing through the circuit becomes constant. Afterward, suddenly, point 'C' is disconnected from point 'A' and connected to point 'B' at time \(t=0\). Ratio of the voltage across resistance and the inductor at \(t=L/R\) will be equal to :

A pipe of length \(85\ \mathrm{cm}\) is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below \(1250\ \mathrm{Hz}\). The velocity of sound in air is \(340\ \mathrm{m/s}\).

A green light is incident from the water to the air - water interface at the critical angle(\(\theta\)). Select the correct statement.

The pressure that has to be applied to the ends of a steel wire of length 10 cm to keep its length constant when its temperature is raised by \(100^\circ\mathrm{C}\) is :
(For steel Young's modulus is \(2\times10^{11}\ \mathrm{N\,m^{-2}}\) and coefficient of thermal expansion is \(1.1\times10^{-5}\ \mathrm{K^{-1}}\))

The current voltage relation of diode is given by \(I=\left(e^{1000V/T}-1\right)\) mA, where the applied voltage V is in volts and the temperature T is in degree Kelvin. If a student makes an error measuring \(\pm0.01\) V while measuring the current of 5 mA at 300 K, what will be the error in the value of current in mA ?

One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct statement :

A mass 'm' is supported by a massless string wound around a uniform hollow cylinder of mass m and radius R. If the string does not slip on the cylinder, with what acceleration will the mass fall on release ?

Let \(f_k(x)=\frac{1}{k}\left(\sin^k x+\cos^k x\right)\) where \(x\in\mathbf{R}\) and \(k\ge1\). Then \(f_4(x)-f_6(x)\) equals :

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 :

A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is \(45^\circ\). It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to \(30^\circ\). Then the speed (in m/s) of the bird is :

The statement \(\sim(p\leftrightarrow\sim q)\) is :

If \(\left[\vec{a}\times\vec{b}\ \ \vec{b}\times\vec{c}\ \ \vec{c}\times\vec{a}\right]=\lambda\left[\vec{a}\ \ \vec{b}\ \ \vec{c}\right]^2\) then \(\lambda\) is equal to :

The integral \(\displaystyle\int_0^{\pi}\sqrt{1+4\sin^2\frac x2-4\sin\frac x2}\,dx\) equals :

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 :

The integral \(\displaystyle\int\left(1+x-\frac1x\right)e^{x+\frac1x}\,dx\) is equal to :

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

\(\displaystyle\lim_{x\to0}\frac{\sin(\pi\cos^2x)}{x^2}\) is equal to :

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

If \(A\) is a \(3\times3\) non-singular matrix such that \(AA'=A'A\) and \(B=A^{-1}A'\), then \(BB'\) equals :

If the coefficients of \(x^3\) and \(x^4\) in the expansion of \((1+ax+bx^2)(1-2x)^{18}\) in powers of \(x\) are both zero, then \((a,b)\) is equal to :

If \(\alpha,\beta\neq0\), \(f(n)=\alpha^n+\beta^n\) 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 :

Let \(\alpha\) and \(\beta\) be the roots of the equation \(px^2+qx+r=0\), \(p\neq0\). If \(p, q, r\) are in A.P. and \(\frac{1}{\alpha}+\frac{1}{\beta}=4\), then the value of \(|\alpha-\beta|\) is :

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