JEE Main 2019 (Online) 12th January Morning Slot

Consider three boxes, each containing, 10 balls labelled 1, 2, … , 10. Suppose one ball is randomly drawn from each of the boxes. Denote by ni, the label of the ball drawn from the ith box, (i = 1, 2, 3). Then, the number of ways in which t...

In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to :

If \(\lambda\) be the ratio of the roots of the quadratic equation in x, 3m2x2 + m(m – 4)x + 2 = 0, then the least value of m for which \(\lambda + {1 \over \lambda } = 1,\) is

The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an A.P. Then the sum of the original three terms of the given G.P. is :

Let  Sk = \({{1 + 2 + 3 + .... + k} \over k}.\) If   \(S_1^2 + S_2^2 + .....\, + S_{10}^2 = {5 \over {12}}\)A,  then A is equal to :

Let S = {1, 2, 3, … , 100}. The number of non-empty subsets A of S such that the product of elements in A is even is :

If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is :

If the straight line, 2x – 3y + 17 = 0 is perpendicular to the line passing through the points (7, 17) and (15, \(\beta\)), then \(\beta\) equals :

The maximum value of 3cos\(\theta\) + 5sin \(\left( {\theta - {\pi \over 6}} \right)\) for any real value of \(\theta\) is :

The sum of the distinct real values of \(\mu\), for which the vectors, \(\mu \widehat i + \widehat j + \widehat k,\)   \(\widehat i + \mu \widehat j + \widehat k,\)   \(\widehat i + \widehat j + \mu \widehat k\)  are co-planar, is :

In the figure shown, a circuit contains two identical resistors with resistance R = 5\(\Omega\) and an inductance with L = 2mH. An ideal battery of 15 V is connected in the circuit. What will be the current through the battery long after t...

A particle of mass m moves in a circular orbit in a central potential field U(r) = \({1 \over 2}\) kr2. If Bohr 's
quantization conditions are applied, radii of possible orbitls and energy levels vary with quantum number n as :

In the figure shown, after the switch 'S' is turned from position 'A' to position 'B', the energy dissipated in the circuit in terms of capacitance 'C' and total charge 'Q' is :

The position vector of the centre of mass \(\overrightarrow r {\,_{cm}}\,\) of an asymmetric uniform bar of negligible area of crosssection as shown in figure is :

A simple pendulum, made of a string of length \(\ell\) and a bob of mass m, is released from a small angle \({{\theta _0}}\). It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, elastically. It
b...

A 100 V carrier wave is made to vary between 160 V and 40 V by a modulating signal. What is the modulation index ?

In a meter bridge, the wire of length 1 m has a non-uniform cross-section such that, the variation \({{dR} \over {d\ell }}\) of its resistance R with length \(\ell\) is \({{dR} \over {d\ell }}\) \(\propto\) \({1 \over {\sqrt \ell }}\)....

Two electric bulbs, rated at (25 W, 220 V) and (100 W, 220 V), are connected in series across a 220 V voltage source. If the 25 W and 100 W bulbs draw powers P1 and P2 respectively, then :

The galvanometer deflection, when key K1 is closed but K2 is open, equals \(\theta\)0 (see figure). On closing K2 also and adjusting R2 to 5\(\Omega\), the deflection in galvanometer becomes \({{{\theta _0}} \over 5}.\) . The resistance o...

An ideal battery of 4 V and resistance R are connected in series in the primary circuit of a potentiometer of length 1 m and esistance 5 \(\Omega\). The value of R, to give a potential difference of 5 mV across 10 cm of potentiometer wire...

A particle A of mass 'm' and charge 'q' is accelerated by a potential difference of 50 V. Another particle B of mass ' 4 m' and charge 'q' is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths $${{{\lambda ...

A light wave is incident normally on a glass slab of refractive index 1.5. If 4 % of light gets reflected and the amplitude of the electric field of the incident light is 30 V/m, then the amplitude of the electric field for the wave propaga...

The output of the given logic circuit is :

Determine the electric dipole moment of the system of the three charges, placed on the vertices of an equilateral triangle, as shown in the figure :

There is a uniform spherically symmetric surface charge density at a distance R0 from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V (R(...

A point source of light, S is placed at distance L in front of the centre of plane mirror of width d which is hanging vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror, at a distance 2L as shown be...

What is the position and nature of image formed by lens combination shown in figure ? (f1, f2 are focal lengths)

A straight rod of length L extends from x = a to x = L + a. The gravitational force it exerts on a point mass 'm' at x = 0, if the mass per unit length of the rod is A + Bx2 , is given by :

A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastically. The speeds of the satellite and the meteo...

For the given cyclic process CAB as shown for a gas, the work done is :

A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is K1 and the of the outer cylinder is K2. Assuming no loss of heat, the effec...

An ideal gas occupies a volume of 2m3 at a pressure of 3 \(\times\) 106 Pa. The energy of the gas is :

As shown in the figure, two infinitely long, identical wires are bent by 90o and placed in such a way that the segments LP and QM are along the x-axis, while segments PS and QN are parallel to the y-axis. If OP = OQ = 4cm, and the magnitude...

A proton and an \(\alpha\)-particle (with their masses in the ratio of 1 : 4 and charges in the ratio of 1 : 2) are accelerated from rest through a potential difference V. If a uniform magnetic field (B) is set up perpendicular to their ve...

A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60o with ground level. But he finds the aeroplane right vertically above his position. If v is the speed of sound, speed of the plane is :...

A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr. The ratio of times taken by the passenger train to completely cross the freight train when : (i) they are...

Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm), about its axis be I. The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also I, is :

Two light identical springs of spring constant k are attached horizontally at the two ends of a uniform horizontal rod AB of length \(\ell\) and mass m. The rod is pivoted at its centre 'O' and can rotate freely in horizontal plane. The ot...

The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5 \(\mu\)m diameter of a wire is :

A travelling harmonic wave is represented by the equation y(x,t) = 10–3sin (50t + 2x), where, x and y are in mater and t is in seconds. Which of the following is a correct statement about the wave ?