JEE Main 2017 Question Paper with Solutions

A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75 o C. T is given by: (Given : room temperature = 30 o C, specific heat of copper = 0.1 cal/gm o C)

A time dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the force during the first 1 sec. will be:

The variation of acceleration due to gravity g with distance d from centre of the earth is best represented by (R = Earth’s radius):

The temperature of an open room of volume 30 m 3 increases from 17 o C to 27 o C due to the sunshine. The atmospheric pressure in the room remains 1 $\times$ 10 5 Pa. If N i and N f are the number of molecules in the room before and after heating, then N f – N i will be :

An external pressure P is applied on a cube at 0 o C so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and α is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by:

$\Delta$ U is equal to :

Sodium salt of an organic acid ‘X’ produces effervescence with conc. H 2 SO 4 . ‘X’ reacts with the acidified aqueous CaCl 2 solution to give a white precipitate which decolourises acidic solution of KMnO 4 . ‘X’ is :

Which of the following molecules is least resonance stabilized?

The group having isoelectronic species is:

Which of the following species is not paramagnetic?

Let a , b, c ∈ R . If f (x) = ax 2 + bx + c is such that a + b + c = 3 and f (x + y) = f (x) + f (y) + xy, ∀ x , y ∈ R , then ∑ n = 1 10 f ( n ) is equal to

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is:

If $5\left( {{{\tan }^2}x - {{\cos }^2}x} \right) = 2\cos 2x + 9$ , then the value of $\cos 4x$ is :

Let k be an integer such that the triangle with vertices (k, – 3k), (5, k) and (–k, 2) has area 28 sq. units. Then the orthocentre of this triangle is at the point :

The following statement ( p → q ) → [ ( ∼ p → q ) → q ] is :

When a current of 5 mA is passed through a galvanometer having a coil of resistance 15 Ω , it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range 0 – 10V is:

A magnetic needle of magnetic moment 6.7 × 10 -2 A m 2 and moment of inertia 7.5 × 10 -6 kg m 2 is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillations is:

A capacitance of 2 $\mu$ F is required in an electrical circuit across a potential difference of 1.0 kV. A large number of 1 $\mu$ F capacitors are available which can withstand a potential difference of not more than 300 V. The minimum number of capacitors required to achieve this is:

In the given circuit, the current in each resistance is:

In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be:

The integral $\int\limits_{{\pi \over 4}}^{{{3\pi } \over 4}} {{{dx} \over {1 + \cos x}}}$ is equal to

If ( 2 + sin ⁡ x ) d y d x + ( y + 1 ) cos ⁡ x = 0 and y(0) = 1, then y ( π 2 ) is equal to :

The area (in sq. units) of the region $\left\{ {\left( {x,y} \right):x \ge 0,x + y \le 3,{x^2} \le 4y\,and\,y \le 1 + \sqrt x } \right\}$ is

If S is the set of distinct values of 'b' for which the following system of linear equations x + y + z = 1 x + ay + z = 1 ax + by + z = 0 has no solution, then S is :

If for $x \in \left( {0,{1 \over 4}} \right)$ , the derivatives of ${\tan ^{ - 1}}\left( {{{6x\sqrt x } \over {1 - 9{x^3}}}} \right)$ is $\sqrt x .g\left( x \right)$ , then $g\left( x \right)$ equals

The formation of which of the following polymers involves hydrolysis reaction?

3-Methyl-pent-2-ene on reaction with HBr in presence of peroxide forms an addition product. The number of possible stereoisomers for the product is :

Which of the following compounds will behave as a reducing sugar in an aqueous KOH solution?

Which of the following, upon treatment with tert -BuONa followed by addition of bromine water, fails to decolorize the colour of bromine?

The increasing order of the reactivity of the following halides for the S N 1 reaction is :