JEE Main 2015 Question Paper with Solutions

A pendulum made of a uniform wire of cross sectional area $A$ has time period $T.$ When an additional mass $M$ is added to its bob, the time period changes to ${T_{M.}}$ If the Young's modulus of the material of the wire is $Y$ then ${1 \over Y}$ is equal to : ( $g=$ $gravitational$ $acceleration$ )

Distance of the center of mass of a solid uniform cone from its vertex is $z{}_0$ . If the radius of its base is $R$ and its height is $h$ then $z{}_0$ is equal to :

A solid body of constant heat capacity 1 J / ∘ C is being heated by keeping it in contact with reservoirs in two ways: ( i ) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies same amount of heat. ( i i ) Sequentially keeping in contact with 8 reservoirs such that each reservoir supplies same amount of heat. In both the cases body is brought from initial temperature 100 ∘ C to final temperature 200 ∘ C . Entropy change of the body in the two cases respectively is :

A particle of mass $m$ moving in the $x$ direction with speed $2v$ is hit by another particle of mass $2m$ moving in the $y$ direction with speed $v.$ If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to:

Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as V q , where V is the volume of the gas. The value of q is: ( γ = C p C v )

Which of the following compounds will exhibit geometrical isomerism?

Which of the following is the energy of a possible excited state of hydrogen?

The following reaction is performed at 298 K 2NO(g) + O 2 (g) $\leftrightharpoons$ 2NO 2 (g) The standard free energy of formation of NO(g) is 86.6 kJ/mol at 298 K. What is the standard free energy of formation of NO 2 (g) at 298 K? (KP = 1.6 × 10 12 )

The molecular formula of a commercial resin used for exchanging ions in water softening is C 8 H 7 SO 3 Na (Mol. Wt. 206). What would be the maximum uptake of Ca 2+ ions by the resin when expressed in mole per gram resin?

The intermolecular interaction that is dependent on the inverse cube of distance between the molecule is:

Let A and B be two sets containing four and two elements respectively. Then, the number of subsets of the set A $\times$ B , each having atleast three elements are

Let $O$ be the vertex and $Q$ be any point on the parabola, ${{x^2} = 8y}$ . If the point $P$ divides the line segment $OQ$ internally in the ratio $1:3$ , then locus of $P$ is :

A complex number z is said to be unimodular if $\,\left| z \right| = 1$ . Suppose ${z_1}$ and ${z_2}$ are complex numbers such that ${{{z_1} - 2{z_2}} \over {2 - {z_1}\overline {{z_2}} }}$ is unimodular and ${z_2}$ is not unimodular. Then the point ${z_1}$ lies on a :

The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices ( 0 , 0 ) ( 0 , 41 ) and ( 41 , 0 ) is :

The number of integers greater than 6,000 that can be formed, using the digits 3, 5, 6, 7 and 8, without repetition, is:

When $5V$ potential difference is applied across a wire of length $0.1$ $m,$ the drift speed of electrons is $2.5 \times {10^{ - 4}}\,\,m{s^{ - 1}}.$ If the electron density in the wire is $8 \times {10^{28}}\,\,{m^{ - 3}},$ the resistivity of the material is close to :

A uniformly charged solid sphere of radius $R$ has potential ${V_0}$ (measured with respect to $\infty$ ) on its surface. For this sphere the equipotential surfaces with potentials ${{3{V_0}} \over 2},\,{{5{V_0}} \over 4},\,{{3{V_0}} \over 4}$ and ${{{V_0}} \over 4}$ have radius ${R_1},\,\,{R_2},\,\,{R_3}$ and ${R_4}$ respectively. Then

Two coaxial solenoids of different radius carry current I in the same direction. F 1 → be the magnetic force on the inner solenoid due to the outer one and F 2 → be the magnetic force on the outer solenoid due to the inner one. Then :

A rectangular loop of sides 10 c m and 5 c m carrying a current 1 of 12 A is placed in different orientations as shown in the figures below : If there is a uniform magnetic field of 0.3 T in the positive z direction, in which orientations the loop would be in ( i ) stable equilibrium and ( i i ) unstable equilibrium ?

A signal of $5$ $kHz$ frequency is amplitude modulated on a carrier wave of frequency $2$ $MHz.$ The frequencies of the resultant signal is/are :

If 12 different balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is :

The integral $\int {{{dx} \over {{x^2}{{\left( {{x^4} + 1} \right)}^{3/4}}}}}$ equals :

Let ${\tan ^{ - 1}}y = {\tan ^{ - 1}}x + {\tan ^{ - 1}}\left( {{{2x} \over {1 - {x^2}}}} \right),$ where $\left| x \right| < {1 \over {\sqrt 3 }}.$ Then a value of $y$ is :

If the function. g ( x ) = { k x + 1 , 0 ≤ x ≤ 3 m x + 2 , 3 < x ≤ 5 is differentiable, then the value of $k+m$ is :

Let y ( x ) be the solution of the differential equation ( x log ⁡ x ) d y d x + y = 2 x log ⁡ x , ( x ≥ 1 ) . Then y ( e ) is equal to :

The number of geometric isomers that can exist for square planar [Pt (Cl) (py) (NH 3 ) (NH 2 OH)]+ is (py = pyridine) :

The colour of KMnO 4 is due to :

Which polymer is used in the manufacture of paints and lacquers?

In the context of the Hall-Heroult process for the extraction of Al, which of the following statements is false ?

The synthesis of alkyl fluorides is best accomplished by: