JEE Main 2019 (Online) 9th January Morning Slot

If \(\theta\) denotes the acute angle between the curves, y = 10 – x2 and y = 2 + x2 at a point of their intersection, the |tan \(\theta\)| is equal to :

Axis of a parabola lies along x-axis. If its vertex and focus are at distances 2 and 4 respectively from the
origin, on the positive x-axis then which of the following points does not lie on it?

Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can
be formed from this class, if there are two specific boys A and B, who refuse to be the members of the same
team, is :

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two drawn cards. Then P(X = 1) + P (X = 2) equals :

Let \({a_1},{a_2},.......,{a_{30}}\) be an A.P.,
\(S = \sum\limits_{i = 1}^{30} {{a_i}}\) and \(T = \sum\limits_{i = 1}^{15} {{a_{\left( {2i - 1} \right)}}}\).
If \(a_5\) = 27 and S - 2T = 75, then \(a_{10}\) is equal to :

If a, b, c be three distinct real numbers in G.P. and a + b + c = xb , then x cannot be

5 students of a class have an average height 150 cm and variance 18 cm2. A new student, whose height is 156 cm, joined them. The variance (in cm2) of the height of these six students is :

Consider the set of all lines px + qy + r = 0 such that 3p + 2q + 4r = 0. Which one of the following statements
is true?

For any \(\theta \in \left( {{\pi \over 4},{\pi \over 2}} \right)\), the expression
\(3{(\cos \theta - \sin \theta )^4}\)\(+ 6{(\sin \theta + \cos \theta )^2} + 4{\sin ^6}\theta\)
equals :

Let \(\overrightarrow a\) = \(\widehat i - \widehat j\), \(\overrightarrow b\) = \(\widehat i + \widehat j + \widehat k\) and \(\overrightarrow c\)
be a vector such that \(\overrightarrow a\) × \(\overrightarrow c\) + $$\overrightarro...

A sample of radioactive material A, that has an activity of 10 mCi(1 Ci = 3.7 \(\times\) 1010 decays/s), has twice the number of nuclei as another sample of a different radioactive materail B which has an activity of 20 mCi. The correct c...

A parallel plate capacitor is made of two square plates of side 'a', separated by a distance d (d < < a). The lower triangular portion is filled with a dielectric of dielectric constant K, as shown in the figure. Capacitance of this capacit...

Three blocks A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, m while C has mass M, Block A is given an initial speed \(\upsilon\) towards B due to which it collides with B perfectly i...

Two masses m and \({m \over 2}\) are connected at the two ends of a massless rigid rod of length l. The rod is suspended by a thin wire of torsional constant k, at the centre of mass of the rod-mass system(see figure). Because of torsional ...

Drift speed of electrons, when 1.5 A of current flows in a copper wire of cross section 5 mm2, is \(\upsilon\). If the electron density in copper is 9 \(\times\) 1028/m3 the value of \(\upsilon\). in mm/s is close to (Take charge of ele...

When the switch S, in the circuit shown, is closed, then the value of current i will be :

A resistance is shown in the figure. Its value and tolerance are given respectively by :

Surface of certain metal is first illuminated with light of wavelength \(\lambda\)1 = 350 nm and then, by light of wavelength \(\lambda\)2 = 540 nm. It is found that the maximum speed of the photo electrons in the two cases differ by a fa...

A conducting circular loop made of a thin wire, has area 3.5 \(\times\) 10\(-\)3 m2 and resistance 10 \(\Omega\). It is placed perpendicular to a time dependent magnetic field B(t) = (0.4T)sin(50\(\pi\)t). The field is uniform in space....

A plane electromagnetic wave of frequency 50 MHz travels in free space along the positive x-direction. At a particular point in space and time, \(\overrightarrow E = 6.3\widehat j\,V/m.\) The corresponding magnetic field $$\overrightarrow...

Mobility of electrons in a semiconductor is defined as the ratio of their drift velocity to the applied electric field. If, for an n-type semiconductor, the density of electrons is 1019 m\(-\)3 and their mobility is 1.6 m2/(V.s) then the re...

Three charges + Q, q, + Q are placed respectively, at distance, 0, d/2 and d from the origin, on the x-axis. If the net force experienced by + Q, placed at x = 0, is zero, then value of q is :

For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its center. Then value of h is :

A convex lens is put 10 cm from a light source and it makes a sharp image on a screen, kept 10 cm from the lens. Now a glass block (refractive index 1.5) of 1.5 cm thickness is placed in contact with the light source. To get the sharp imag...

A mixture of 2 moles of helium gas (atomic mass = 4 u), and 1 mole of argon gas (atomic mass = 40 u) is kept at 300 K in a container. The ratio of their rms speeds \(\left[ {{{{V_{rms}}\,(helium)} \over {{V_{rms}}\,(\arg on)}}} \right],\) i...

A rod, of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion \(\alpha\)/oC. It is observed that an external compressive force F, is applied on each of its ends, preve...

Temperature difference of 120oC is maintained between ends of a uniform rod AB of length 2L. Another bent rod PQ, of same cross-section as AB and length \({{3L} \over 2},\) is connected across AB (see figure). In steady state, temperature ...

A gas can be taken from A to B via two different processes ACB and ADB.

When path ACB is used 60 J of heat flows into the system and 30 J of work is done by the system. If path ADB is used work done by the system is 10 J. The heat Flow in...

A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, ...

A bar magnet is demagnetized by inserting it inside a solenoid of length 0.2 m, 100 turns, and carrying a current of 5.2 A. The corecivity of the bar magnet is :

A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of 10 A. The magnetic field at point O will be close to :

An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. The radius of the loop is a and distance of its centre from the wire is d (d > > a). If the loop a applies a force F on the...

A particle is moving with a velocity
\(\overrightarrow v \, = K(y\widehat i + x\widehat j),\) where K is a constant.
The general equation for its path is :

If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the center of the Sun, its areal velocity is :

An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB = BC, and the angle made by AB with downward vertical is \(\theta\), thrown :

A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume remains unchanged is :

Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio :

Consider a tank made of glass(refractive index 1.5) with a thick bottom. It is filled with a liquid of refractive index \(\mu\). A student finds that, irrespective of what the incident angle i (see figure) is for a beam of light entering t...

A heavy ball of mass M is suspendeed from the ceiling of a car by a light string of mass m (m < < M). When the car is at rest, the speed of transverse waves in the string is 60 ms\(-\)1. When the car has acceleration a, the wave-speed incre...

A block of mass m, lying on a smooth horizontal surface, is attached to a sring (of negligible mass) of spring constant k. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its equilibrium posit...