JEE Main 2019 (Online) 10th January Evening Slot

If  \(\sum\limits_{r = 0}^{25} {\left\{ {{}^{50}{C_r}.{}^{50 - r}{C_{25 - r}}} \right\} = K\left( {^{50}{C_{25}}} \right)} ,\,\,\) then K is equal to :

If the probability of hitting a target by a shooter, in any shot, is \({1 \over 3}\), then the minimum number of independent
shots at the target required by him so that the probability of hitting the target atleast once is greater than $${5...

With the usual notation, in \(\Delta\)ABC, if \(\angle A + \angle B\) = 120o, a = \(\sqrt 3\) \(+\) 1, b = \(\sqrt 3\) \(-\) 1 then the ratio \(\angle A:\angle B,\) is :

The value of \(\lambda\) such that sum of the squares of the roots of the quadratic equation, x2 + (3 – \(\lambda\))x + 2 = \(\lambda\) has the least value is -

Let a1, a2, a3, ..... a10 be in G.P. with ai > 0 for i = 1, 2, ….., 10 and S be the set of pairs (r, k), r, k \(\in\) N (the set of natural numbers) for which
$$\left| {\matrix{
{{{\log }_e}\,{a_1}^r{a_2}^k} & {{{\log }_e}\,{a_2}^r{a_3...

If mean and standard deviation of 5 observations x1, x2, x3, x4, x5 are 10 and 3, respectively, then the variance of 6 observations x1, x2, ….., x5 and –50 is equal to

Two sides of a parallelogram are along the lines, x + y = 3 & x – y + 3 = 0. If its diagonals intersect at (2, 4), then one of its vertex is :

Two vertices of a triangle are (0, 2) and (4, 3). If its orthocenter is at the origin, then its third vertex lies in which quadrant :

The value of \(\cos {\pi \over {{2^2}}}.\cos {\pi \over {{2^3}}}\,.....\cos {\pi \over {{2^{10}}}}.\sin {\pi \over {{2^{10}}}}\) is -

If \(\overrightarrow \alpha\) = \(\left( {\lambda - 2} \right)\overrightarrow a + \overrightarrow b\)  and  \(\overrightarrow \beta = \left( {4\lambda - 2} \right)\overrightarrow a + 3\overrightarrow b\) be two given vectors $$\ov...

Consider the nuclear fission
Ne20 \(\to\) 2He4 + C12
Given that the binding energy/ nucleon of Ne20, He4 and C12 are, respectively, 8.03 MeV, 7.07 MeV and 7.86 MeV, identify the correct statement -

A parallel plate capacitor having capacitance 12 pF is charged by a battery to a potential difference of 10 V between its plates. The charging battery is now disconnected and a porcelain slab of dielectric constant 6.5 is slipped between th...

The modulation frequency of an AM radio station is 250 kHz, which is 10% of the carrier wave. If another AM station approaches you for license what broadcast frequency will you allot ?

The actual value of resistance R, shown in the figure is 30\(\Omega\). This is measuered in an experiment as shown
using the standard formula R = \({V \over {\rm I}}\), where V and I are the readings of the voltmeter and ammeter, respectiv...

A current of 2 mA was passed through an unknown resistor which dissipated a power of 4.4 W. Dissipated power when an ideal power supply of 11 V is connected across it is -

The Wheatstone bridge shown in figure, here, gets balanced when the carbon resistor used as R1 has the colour code (Orange, Red, Brown). The resistors R2 and R4 are 80\(\Omega\) and 40\(\Omega\), respectively. Assuming that the colour cod...

A metal plate of area 1 \(\times\) 10–4 m2 is illuminated by a radiation of intensity 16 mW/m2. The work function of the metal is 5 eV. The energy of the incident photons is 10 eV and only 10% of it produces photo electrons.
The number of...

The self induced emf of a coil is 25 volts. When the current in it is changed at uniform rate from 10 A to 25 A in 1s, the change in the energy of the inductance is -

The electric field of a plane polarized electromagnetic wave in free space at time t = 0 is given by an expression \(\overrightarrow E \left( {x,y} \right) = 10\widehat j\cos \left[ {\left( {6x + 8z} \right)} \right].\) The magnetic field $...

For the circuit shown below, the current through the Zener diode is -

Four equal point charges Q each are placed in the xy plane at (0, 2), (4, 2), (4, –2) and (0, –2). The work required to put a fifth charge Q at the origin of the coordinate system will be -

Charges –q and +q located at A and B, respectively, constitude an electric dipole. Distance AB = 2a, O is the mid point of the dipole and OP is perpendicular to AB. A charge Q is placed at P where OP = y and y >> 2a. The charge Q experience...

The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of cornea (7.8 mm). This surface separateds two media of refractive indices 1 and 1.34. Calculate the distance from the refract...

Two stars of masses 3 \(\times\) 1031 kg each, and at distance 2 \(\times\) 1011 m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star’s rotation plane. In order to escape...

Two kg of a monoatomic gas is at a pressure of 4 \(\times\) 104 N/m2. The density of the gas is 8 kg/m3. What is the order of energy of the gas due to its thermal motion ?

Half mole of an ideal monoatomic gas is heated at constant pressure of 1 atm from 20oC to 90oC. Work done
by gas is close to – (Gas constant R = 8.31 J/mol.K)

An unknown metal of mass 192 g heated to a temperature of 100oC was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of 8.4oC. Calculate the specific heat of the unknown metal if water temperature s...

Two forces P and Q, of magnitude 2F and 3F, respectively, are at an angle \(\theta\) with each other. If the force Q is doubled, then their resultant also gets doubled. Then, the angle \(\theta\) is -

At some location on earth, the horizontal component of earth’s magnetic field is 18 × 10–6 T. At this location, magnetic needle of length 0.12 m and pole strength 1.8 Am is suspended from its mid-point using a thread, it makes 45o angle wit...

A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their magnetic moment parallel to their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uni...

A particle starts from the origin at time t = 0 and moves along the positive x-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time t = 5s ?

Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and mass M (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is :

A rigid massless rod of length 3l has two masses attached at each end as shown in the figure. The rod is pivoted at point P on the horizontal axis (see figure). When released from initial horizontal position, its
instantaneous angular accel...

A particle executes simple harmonic motion with an amplitude of 5 cm. When the particle is at 4 cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds is...

A cylindrical plastic bottle of negligible mass is filled with 310 ml of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency $$\omeg...

A closed organ pipe has a fundamental frequency of 1.5 kHz. The number of overtones that can be distinctly heard by a person with this organ pipe will be (Assume that the highest frequency a person can hear is 20,000 Hz)

The diameter and height of a cylinder are measured by a meter scale to be 12.6 \(\pm\) 0.1 cm and 34.2 \(\pm\) 0.1 cm, respectively. What will be the value of its volume in appropriate significant figures ?

Two vectors \(\overrightarrow A\) and \(\overrightarrow B\) have equal magnitudes. The magnitude of \(\left( {\overrightarrow A + \overrightarrow B } \right)\) is 'n' times the magnitude of $$\left( {\overrightarrow A - \overrightarrow...

Consider a Young’s double slit experiment as shown in figure. What should be the slit separation d in terms of wavelength \(\lambda\) such that the first minima occurs directly in front of the slit (S1) ?

A particle which is experiencing a force, given by \(\overrightarrow F = 3\widehat i - 12\widehat j,\) undergoes a displacement of \(\overrightarrow d = 4\overrightarrow i\) particle had a kinetic energy of 3 J at the beginning of the di...