JEE Main 2016 Question Paper with Solutions

A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t is given by n 2 R t 2 where n is a constant. The power delivered to the particle by the force acting on it, is :

A particle of mass m is acted upon by a force F given by the empirical law F = ${R \over {{t^2}}}\,v\left( t \right).$ If this law is to be tested experimentally by observing the motion starting from rest, the best way is to plot :

A thin 1 m long rod has a radius of 5 mm. A force of 50 π kN is applied at one end to determine its Young’s modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is 0.01 mm, which of the following statements is false ?

Which of the following shows the correct relationship between the pressure ‘P’ and density ρ of an ideal gas at constant temperature ?

An astronaut of mass m is working on a satellite orbiting the earth at a distance h from the earth’s surface. The radius of the earth is R, while its mass is M. The gravitational pull F G on the astronaut is :

A stream of electrons from a heated filament was passed between two charged plates kept at a potential difference V esu. If e and m are charge and mass of an electron, respectively, then the value of h / $\lambda$ (where $\lambda$ is wavelength associated with electron wave) is given by :

Two closed bulbs of equal volume $(V)$ containing an ideal gas initially at pressure ${p_i}$ and temperature ${T_1}$ are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to ${T_2}.$ The final pressure ${p_f}$ is :

Which one of the following statements about water is FALSE?

Which of the following atoms has the highest first ionization energy?

The equilibrium constant at 298 K for a reaction A + B ⇋ C + D is 100. If the initial concentration of all the four species were 1M each, then equilibrium concentration of D (in mol L –1 ) will be:

If one of the diameters of the circle, given by the equation, ${x^2} + {y^2} - 4x + 6y - 12 = 0,$ is a chord of a circle $S$ , whose centre is at $(-3, 2)$ , then the radius of $S$ is :

If all the words (with or without meaning) having five letters,formed using the letters of the word SMALL and arranged as in a dictionary, then the position of the word SMALL is :

If the ${2^{nd}},{5^{th}}\,and\,{9^{th}}$ terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is :

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is :

The sum of all real values of x satisfying the equation ( x 2 − 5 x + 5 ) x 2 + 4 x − 60 = 1 is :

Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed ‘v’ in a uniform magnetic field B going into the plane of the paper (See figure). If charge densities $\sigma$ 1 and $\sigma$ 2 are induced on the left and right surfaces, respectively, of the sheet then (ignore fringe effects) :

Within a spherical charge distribution of charge density $\rho$ (r), N equipotential surfaces of potential V 0 , V 0 + $\Delta$ V, V 0 + 2 $\Delta$ V, .......... V 0 + N $\Delta$ V ( $\Delta$ V > 0), are drawn and have increasing radii r 0 , r 1 , r 2 ,..........r N , respectively. If the difference in the radii of the surfaces is constant for all values of V 0 and $\Delta$ V then :

Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30 cm. The wavelength of light is 600 nm. To see the stars just resolved by the telescope, the minimum distance between them should be (1 light year = 9.46 $\times$ 10 15 m) of the order of :

A hemispherical glass body of radius 10 cm and refractive index 1.5 is silvered on its curved surface. A small air bubble is 6 cm below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen :

Consider an electromagnetic wave propagating in vacuum. Choose the correct statement :

If A = [ 5 a − b 3 2 ] and $A$ adj $A=A$ ${A^T},$ then $5a+b$ is equal to :

If a curve y = f ( x ) passes through the point ( 1 , − 1 ) and satisfies the differential equation, y ( 1 + x y ) d x = x d y , then f ( − 1 2 ) is equal to :

Let $p = \mathop {\lim }\limits_{x \to {0^ + }} {\left( {1 + {{\tan }^2}\sqrt x } \right)^{{1 \over {2x}}}}$ then $log$ $p$ is equal to :

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30 o . After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60 o . Then the time taken (in minutes) by him, from B to reach the pillar, is :

The system of linear equations x + λ y − z = 0 λ x − y − z = 0 x + y − λ z = 0 has a non-trivial solution for :

The reaction of zinc with dilute and concentrated nitric acid, respectively, produces :

2 -chloro- 2 -methylpentane on reaction with sodium methoxide in methanol yields:

Which one of the following ores is best concentrated by froth floatation method?

Which of the following statements about low density polythene is FALSE ?

In the Hofmann bromamide degradation reaction, the number of moles of NaOH and Br 2 used per mole of amine produced are: