List of top Questions asked in JEE Advanced- 2014

Let $E _{1}( r ), E _{2}( r )$ and $E _{3}( r )$ be the respective electric fields at a distance $r$ from a point charge $Q , an$ infinitely long wire with constant linear charge density $\lambda$, and an infinite plane with uniform surface charge density $\sigma$. If $E_{1}\left(r_{0}\right)=E_{2}\left(r_{0}\right)=E_{3}\left(r_{0}\right)$ at a given distance $r_{0}$, then

Coefficient of $ x^{11}$ in the expansion of $(1 + x^2)^4 (1 + x^3)^7 (1 + x^4)^{12} $

Let $f:(0, \infty) \rightarrow R$ be given by $f(x)=\int\limits_{1 / x}^{x} e^{-\left(t+\frac{1}{t}\right)} \frac{d t}{t}$, then

Let $f : [0,2] \rightarrow R$ be a function which is continuous on $[0,2]$ and is differentiable on $(0,2)$ with $f(0) = 1$. Let $F(x)= \int\limits_0^{x^2} \, f(\sqrt t)dt, \,$ for $\, x \in \, [0,2], if F'(x) \, = f'(x) , \forall $ $x \in \, (0,2) ,\,$ then $\, F(2)$ equals

Hydrogen peroxide in its reaction with $ KIO_4 $ and $ NH_2OH $ respectively, is acting as a

Heater of an electric kettle is made of a wire of length $L$ and diameter d. It takes $4$ minutes to raise the temperature of $0.5\, kg$ water by $40\, K$. This heater is replaced by a new heater having two wires of the same material, each of length $L$ and diameter $2 \,d$. The way these wires are connected is given in the options. How much time in minutes will it take to raise the temperature of the same amount of water by $40\, K$ ?

During an experiment with a meter bridge, the galvanometer shows a null point when the jockey is pressed at $40.0\, cm$ using a standard resistance of $90 \Omega$, as show in the scale used in the meter bridge is $1\, mm$. The unknown resistance is

For the elementary reaction, $M\rightarrow N$, the rate of disappearance of $M$ increases by a factor of $8$ upon doubling the concentration of $M$. The order of the reaction with respect to $M$ is

Charges Q, $2 Q$ and $4 Q$ are uniformly distributed in three dielectric solid spheres 1,2 and 3 of radii $R / 2, R$ and $2 R$ respectively, as shown in figure. If magnitudes of the electric fields at point $P$ at a distance $R$ from the centre of spheres 1,2 and 3 are $E_{1}, E_{2}$ and $E_{3}$ respectively, then

In a galvanic cell, the salt bridge

At time $t=0$, terminal $A$ in the circuit shown in the figure is connected to $B$ by a key and an alternating current $I ( t )= I _{0} \cos (\omega t)$, with $I _{0}=1 A$ and $\omega=500\, rad / s$ starts flowing in it with the initial direction shown in the figure. At $t=\frac{7 \pi}{6 \omega}$, the key is switched from $B$ to $D$. Now onwards only $A$ and $D$ are connected. $A$ total charge $Q$ flows from the battery to charge the capacitor fully. If $C =20 \,\mu F , R =10 \,\Omega$ and the battery is ideal with emf of $50\, V$, identify the correct statement $( s )$.

The radiation corresponding to $3\rightarrow2$ transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field of $3\times10^{-4}$T. If the radius of the largest circular path followed by these electrons is 10.0 mm, the work function of the metal is close to

In the reaction shown below, the major product(s) formed is/are

Two ideal batteries of $emf V _{1}$ and $V _{2}$ and three resistances $R _{1}, R _{2}$ and $R _{3}$ are connected as shown in the figure. The current in resistance $R _{2}$ would be zero if

The product formed in the reaction of $SOCl_2$ with white phosphorus is

The correct combination of names for isomeric alcohols with molecular formula $C_4H_{10}O $ is/are

The area enclosed by the curves $y = sin\, x + cos \,x$ and $y\, =\, | cos\, x - sin\, x |$ over the interval $ \Bigg [0 , \frac{\pi}{2} \Bigg] $ is

The acidic hydrolysis of ether $(X)$ shown below is fastest when

In the figure, a ladder of mass $m$ is shown leaning against a wall. It is in static equilibrium making an angle $\theta$ with the horizontal floor. The coefficient of friction between the wall and the ladder is $\mu_{1}$ and that between the floor and the ladder is $\mu_{2}$. The normal reaction of the wall on the ladder is $N _{1}$ and that of the floor is $N _{2}$. If the ladder is about to slip, then

For $x \in(0, \pi)$, the equation $\sin x+2 \sin 2 x-\sin 3 x=3$ has

Assuming $2s-2p$ mixing is not operative, the paramagnetic species among the following is

Isomers of hexane, based on their branching, can be divided into three distinct classes as shown in the figure. The correct order of their boiling point is

For the reaction: $I ^{-}+ ClO _{3}^{-}+ H _{2} SO _{4} \longrightarrow Cl ^{-}+ HSO _{4}^{-}+ I _{2}$ The correct statement(s) in the balanced equation is/are:

Upon heating with $Cu_2S.$ the reagent(s) that give copper metal is/are

A wire, which passes through the hole in a small bead, is bent in the form of quarter of a circle. The wire is fixed vertically on ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from $A$ to $B$, the force it applies on the wire is