JEE Main 2018 Question Paper with Solutions

Two masses m 1 = 5 kg and m 2 = 10 kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight m that should be put on top of m 2 to stop the motion is :

All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.

A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is 2.7 × 10 3 kg/m 3 and its Young’s modulus is 9.27 × 10 10 Pa. What will be the fundamental frequency of the longitudinal vibrations ?

In a collinear collision, a particle with an initial speed v 0 strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnitude of the relative velocity between the two particles, after collision, is :

Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is :

Which of the following are Lewis acids?

Total number of lone pair of electrons in I 3 − ion is

The trans-alkenes are formed by the reduction of alkynes with

The ratio of mass percent of C and H of an organic compound (C X H Y O Z ) is 6 : 1. If one molecule of the above compound (C X H Y O Z ) contains half as much oxygen as required to burn one molecule of compound C X H Y completely to CO 2 and H 2 O. The empirical formula of compound C X H Y O Z is

An aqueous solution contains an unknown concentration of Ba 2+ . When 50 mL of a 1 M solution of Na 2 SO 4 is added, BaSO 4 just begins to precipitate. The final volume is 500 mL. The solubility product of BaSO 4 is 1 × 10 –10 . What is the original concentration of Ba 2+ ?

Let the orthocentre and centroid of a triangle be A(-3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter, is :

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :

The Boolean expression ∼ ( p ∨ q ) ∨ ( ∼ p ∧ q ) is equvalent to :

If $\sum\limits_{i = 1}^9 {\left( {{x_i} - 5} \right)} = 9$ and $\sum\limits_{i = 1}^9 {{{\left( {{x_i} - 5} \right)}^2}} = 45$ , then the standard deviation of the 9 items ${x_1},{x_2},.......,{x_9}$ is

The number of solutions of sin3x = cos 2x, in the interval ( π 2 , π ) is :

The reading of the ammeter for a silicon diode in the given circuit is :

On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm. The resistance of their series combination is 1 k $\Omega$ . How much was the resistance on the left slot before interchanging the resistances?

It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is p d ; while for its similar collision with carbon nucleus at rest, fractional loss of energy is p c . The values of p d and p c are respectively :

Two batteries with e.m.f 12 V and 13 V are connected in parallel across a load resistor of 10 Ω . The internal resistances of the two batteries are 1 Ω and 2 Ω respectively. The voltage across the load lies between :

Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be I/2. Now another identical polarizer C is placed between A and B. The intensity beyond B is now found to be I/8. The angle between polarizer A and C is :

Let y = y(x) be the solution of the differential equation $\sin x{{dy} \over {dx}} + y\cos x = 4x$ , $x \in \left( {0,\pi } \right)$ . If $y\left( {{\pi \over 2}} \right) = 0$ , then $y\left( {{\pi \over 6}} \right)$ is equal to :

A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is :

If the system of linear equations x + ay + z = 3 x + 2y + 2z = 6 x + 5y + 3z = b has no solution, then :

Suppose A is any 3 × 3 non-singular matrix and ( A − 3I) (A − 5I) = O where I = I 3 and O = O 3 . If α A + β A -1 = 4I, then α + β is equal to :

An aeroplane flying at a constant speed, parallel to the horizontal ground, 3 kmabove it, is obsered at an elevation of 60 o from a point on the ground. If, after five seconds, its elevation from the same point, is 30 o , then the speed (in km / hr) of the aeroplane, is :

Phenol on treatment with CO 2 in the presence of NaOH followed by acidification produces compound X as the major product. X on treatment with (CH 3 CO) 2 O in the presence of catalytic amount of H 2 SO 4 produces:

Phenol reacts with methyl chloroformate in the presence of NaOH to form product A. A reacts with Br 2 to form product B. A and B are respectively :

The oxidation states of Cr in [Cr(H 2 O) 6 ]Cl 3 , [Cr(C 6 H 6 ) 2 ] and K 2 [Cr(CN) 2 (O) 2 (O 2 )(NH 3 )] respectively are :

The compound that does not produce nitrogen gas by the thermal decomposition is :

The increasing order of basicity of the following compounds is :