List of top Questions asked in JEE Main- 2013

Air of density $1.2\, kg\, m^{-3}$ is blowing across the horizontal wings of an aeroplane in such a way that its speeds above and below the wings are $150\, ms^{-1}$ and $100\, ms^{-1}$, respectively. The pressure difference between the upper and lower sides of the wings, is :

In an experiment, a small steel ball falls through a liquid at a constant speed of $10\, cm/s$. If the steel ball is pulled upward with a force equal to twice its effective weight, how fast will it move upward ?

Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is $T$, density of liquid is $\rho$ and $L$ is its latent heat of vaporization.

Which one of the following is the wrong assumption of kinetic theory of gases?

For gaseous state, if most probable speed is denoted by $c *$, average speed by $\overline{C}$ and root square speed by $c$, then for a large number of molecules, the ratios of these speeds are

Select the correct statement from the following

An engine approaches a hill with a constant speed. When it is at a distance of $0.9\, km$, it blows a whistle whose echo is heard by the driver after $5$ seconds. If the speed of sound in air is $330\, m/s$, then the speed of the engine is :

A sonometer wire of length $114\, cm$ is fixed at both the ends. Where should the two bridges be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio $1 : 3 : 4$ ?

A uniform sphere of weight $W$ and radius $5\, cm$ is being held by a string as shown in the figure. The tension in the string will be :

Two blocks of mass $M_1 = 20\, kg$ and $M_2 = 12\, kg$ are connected by a metal rod of mass $8\, kg$. The system is pulled vertically up by applying a force of $480\, N$ as shown. The tension at the mid-point of the rod is :

A metallic rod of length $l$ is tied to a string of length $2l$ and made to rotate with angular speed ($\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field $B$ in the region, the emf induced across the ends of the rod is

Two short bar magnets of length $1\, cm$ each have magnetic moments $1.20 \,Am^2 $ and $1.00 \,Am^2 $ respectively. They are placed on a horizontal table parallel to each other with their $N$ poles pointing towards the south. They have a common magnetic equator and are separated by a distance of $20.0\, cm$. The value of the resultant horizontal magnetic induction at the mid-point $O$ of the line joining their centres is close to (Horizontal component of the earth's magnetic induction is $ 3.6 \times {10}^{-5} W b/m^2$

A uniform electric field $\overrightarrow{E}$ exists between the plates of a charged condenser. A charged particle enters the space between the plates and perpendicular to $\overrightarrow{E}$. The path of the particle between the plates is a :

In a metre bridge experiment null point is obtained at $40\, cm$ from one end of the wire when resistance $X$ is balanced against another resistance $Y$. If $X < Y$, then the new position of the null point from the same end, if one decides to balance a resistance of $3X$ against $Y$, will be close to:

Correct set up to verify Ohm?s law is :

The standard enthalpies of formation of $CO_2(g), H_2O(l)$ and glucose(.v) at 25$^{\circ}$C- are 400 kJ/ mol. -300 kJ/mol and - 1300 kJ/mol, respectively. The standard enthalpy of combustion per gram of glucose at 25$^{\circ}$C is

Let $A (-3,2)$ and $B (-2,1)$ be the vertices of a triangle $ABC$. If the centroid of this triangle lies on the line $3x + 4y+2 = 0$, then the vertex $C$ lies on the line :

\({(1) \,N_2(g) +3H_2(g)<=> 2NH_3(g), K_1}\)
\({(2) \,N_2(g) +O_2(g)<=> 2NHO(g), K_2}\) 
\({(3) \,H_2(g) +\frac{1}{2}O_2(g)<=> H_2O(g), K_3}\) 
The equation for the equilibrium constant of the reaction 
\({2NH_3(g) +\frac{5}{2}O_2(g)<=> 2NO(g), 3H_2O(g)}\), \((K_4)\) in terms of \(K_1\) and \(K_3\) is:

A tangent to the hyperbola $\frac{x^{4}}{4}-\frac{y^{2}}{2}=1$ meets x-axis at $P$ and y-axis at $Q$. Lines $PR$ and $QR$ are drawn such that $OPRQ$ is a rectangle (where $O$ is the origin). Then $R$ lies on :

Figure shows a circuit in which three identical diodes are used. Each diode has forward resistance of $20 \,\Omega$ and infinite backward resistance. Resistors $R_{1}=R_{2}=R_{3}=50\,\Omega$. Battery voltage is $6\, V$. The current through $R_3$ is:

If $f(x) = sin\, (sin\, x)$ and $f'' (x) + tan \,x\,f'(x)+ g(x) = 0,$ then $g(x) $ is :

Calcination is the process in which:

Let $R=\left\{ \left(3,3\right) \left(5,5\right), \left(9,9\right), \left(12,12\right), \left(5,12\right), \left(3,9\right), \left(3,12\right), \left(3,5\right)\right\}$ be a relation on the set $A=\left\{3,5,9,12\right\}$. Then, $R$ is:

Statement 1 : The only circle having radius $\sqrt{10}$ and a diameter along line $2 x+y=5 \, is\, x^{2}+y^{2}-6x+2y=0.$ Statement 2 : $2x + y = 5$ is a normal to the circle $x^{2}+y^{2}-6x+2y=0.$