JEE Main 2014 Question Paper with Solutions

On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of radius R and making a circular contact of radius r with the bottom R and making a circular contact of radius r with the bottom of the vessel. If r << R and the surface tension of water is T , value of r just before bubbles detach is: (density of water is ρ w )

A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?

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

A block of mass m is placed on a surface with a vertical cross section given by y = x 3 6 . If the coefficient of friction is 0.5 , the maximum height above the ground at which the block can be placed without slipping is:

A pipe of length 85 c m is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below 1250 H z . The velocity of sound in air is 340 m / s .

If Z is a compressibility factor, van der Waals equation at low pressure can be written as:

For the estimation of nitrogen, 1.4 g of organic compound was digested by Kjeldahl method and the evolved ammonia was absorbed in 60 mL of M/10 sulphuric acid. The unreacted acid required 20 ml of M/10 sodium hydroxide for complete neutralization. The percentage of nitrogen in the compound is:

The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is 1 : 4. The ratio of number of their molecule is:

For the reaction SO 2 (g) + 1 2 O 2 ( g ) ⇋ SO 3 (g). if K P = K C (RT) x where the symbols have usual meaning then the value of x is: (assuming ideality)

For complete combustion of ethanol, C 2 H 5 OH(l) + 3O 2 (g) → 2CO 2 (g) + 3H 2 O(l) the amount of heat produced as measured in bomb calorimeter, is 1364.47 kJ mol –1 at 25 o C. Assuming ideality the Enthalpy of combustion, Δ C H , for the reaction will be : (R = 8.314 kJ mol –1 )

The statement ∼ ( p ↔∼ q ) is :

The variance of first 50 even natural numbers is

Let a , b , c and d be non-zero numbers. If the point of intersection of the lines 4 a x + 2 a y + c = 0 and 5 b x + 2 b y + d = 0 lies in the fourth quadrant and is equidistant from the two axes then :

Let f k ( x ) = 1 k ( sin k x + cos k x ) where x ∈ R and k ≥ 1. Then f 4 ( x ) − f 6 ( x ) equals :

The locus of the foot of perpendicular drawn from the centre of the ellipse ${x^2} + 3{y^2} = 6$ on any tangent to it is :

The coercivity of a small magnet where the ferromagnet gets demagnetized is 3 × 10 3 A m − 1 . The current required to be passed in a solenoid of length 10 c m and number of turns 100 , so that the magnet gets demagnetized when inside the solenoid, is :

The radiation corresponding to $3 \to 2$ transition of hydrogen atom falls on a metal surface to produce photoelectrons. These electrons are made to enter a magnetic field $3 \times {10^{ - 4}}\,T.$ If the radius of the larger circular path followed by these electrons is $10.0$ $mm$ , the work function of the metal is close to:

A conductor lies along the $z$ -axis at $- 1.5 \le z < 1.5\,m$ and carries a fixed current of $10.0$ $A$ in $- {\widehat a_z}$ direction (see figure). For a field $\overrightarrow B = 3.0 \times {10^{ - 4}}\,{e^{ - 0.2x}}\,\,{\widehat a_y}\,\,T,$ find the power required to move the conductor at constant speed to $x=2.0$ $m$ , $y=0$ $m$ in $5 \times {10^{ - 3}}s.$ Assume parallel motion along the $x$ -axis.

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 :

Two beams, $A$ and $B$ , of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam $A$ has maximum intensity (and beam $B$ has zero intensity), a rotation of polaroid through ${30^ \circ }$ makes the two beams appear equally bright. If the initial intensities of the two beams are ${{\rm I}_A}$ and ${{\rm I}_B}$ respectively, then ${{{{\rm I}_A}} \over {{{\rm I}_B}}}$ equals:

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

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

The integral $\int\limits_0^\pi {\sqrt {1 + 4{{\sin }^2}{x \over 2} - 4\sin {x \over 2}{\mkern 1mu} } } dx$ equals:

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

The area of the region described by $A = \left\{ {\left( {x,y} \right):{x^2} + {y^2} \le 1} \right.$ and $\left. {{y^2} \le 1 - x} \right\}$ is :

Which one of the following properties is not shown by NO?

Consider separate solutions of 0.500 M C 2 H 5 OH(aq), 0.100 M Mg 3 (PO 4 ) 2 (aq), 0.250 M KBr(aq) and 0.125 M Na 3 PO 4 (aq) at 25 o C. Which statement is true about these solutions, assuming all salts to be strong electrolytes?

The major organic compound formed by the reaction of 1, 1, 1– trichloroethane with silver powder is:

Which one of the following bases is not present in DNA?

Which one is classified as a condensation polymer?