JEE Main 2019 (Online) 9th January Evening Slot

The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7, 9 (repitition of digits allowed) is equal to :

An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not r...

If both the roots of the quadratic equation x2 \(-\) mx + 4 = 0 are real and distinct and they lie in the interval [1, 5], then m lies in the interval :

The number of all possible positive integral values of \(\alpha\)  for which the roots of the quadratic equation, 6x2 \(-\) 11x + \(\alpha\) = 0 are rational numbers is :

Let a, b and c be the 7th, 11th and 13th terms respectively of a non-constant A.P. If these are also three consecutive terms of a G.P., then \({a \over c}\) equal to :

The sum of the following series
\(1 + 6 + {{9\left( {{1^2} + {2^2} + {3^2}} \right)} \over 7} + {{12\left( {{1^2} + {2^2} + {3^2} + {4^2}} \right)} \over 9}\)
       $$ + {{15\left( {{1^2} + {2^2} + ... + {5^2}} \right)} \over {11}} + ........

A data consists of n observations : x1, x2, . . . . . . ., xn.    
If     \(\sum\limits_{i = 1}^n {{{\left( {{x_i} + 1} \right)}^2}} = 9n\)    and
\(\sum\limits_{i = 1}^n {{{\left( {{x_i} - 1} \right)}^2}} = 5n,\)
then the standard devi...

Let the equations of two sides of a triangle be 3x \(-\) 2y + 6 = 0 and 4x + 5y \(-\) 20 = 0. If the orthocentre of this triangle is at (1, 1), then the equation of its third side is :

If  0 \(\le\) x < \({\pi \over 2}\),  then the number of values of x for which sin x \(-\) sin 2x + sin 3x = 0, is :

Let  \(\overrightarrow a = \widehat i + \widehat j + \sqrt 2 \widehat k,\)   \(\overrightarrow b = {b_1}\widehat i + {b_2}\widehat j + \sqrt 2 \widehat k\),    \(\overrightarrow c = 5\widehat i + \widehat j + \sqrt 2 \widehat k\)   be th...

A series AC circuit containing an inductor (20 mH), a capacitor (120 \(\mu\)F) and a resistor (60 \(\Omega\)) is driven by an AC source of 24V/50 Hz. The energy dissipated in the circuit in 60 s is :

A power transmission line feeds input power at 2300 V to a srep down transformer with its primary windings having 4000 turns. The output power is delivered at 230 V by the transformer. If the current in the primary of the transformer is 5A ...

At a given instant, say t = 0, two radioactive substance A and B have equal activities. the ratio \({{{R_B}} \over {{R_A}}}\) of their activities after time t itself decays with time t as e\(-\)3t. If the half-life of A is ln2, the half-li...

A parallel plate capacitor with square plates is filled with four dielecytrics of dielectrics constants K1, K2, K3, K4 arranged as shown in the figure. The effective dielectric constant K will be :

In a communication system operating at wavelength 800 nm, only one percent of source frequency is available as signal bandwith. The number of channels accomodated for transmitting TV signals of band width 6 MHz are (Take velocity of light c...

A carbon resistance has a following colour code. What is the value of the resistance ?

In the given circuit the the internal resistance of the 18 V cell is negligible. If R1 = 400 \(\Omega\), R3 = 100 \(\Omega\) and R4 = 500 \(\Omega\) and the reading of an ideal voltmeter across R4 is 5V, then the value of R2 will be :

The magnetic field associated with a light wave is given, at the origin, by B = B0 [sin(3.14 \(\times\) 107)ct + sin(6.28 \(\times\) 107)ct]. If this light falls on a silver plate having a work function of 4.7 eV, what will be the maxim...

The energy associated with electric field is (UE) and with magnetic field is (UB) for an electromagnetic wave in free space. Then :

Ge and Si diodes start conducting at 0.3 V and 0.7 V respectively. In the following figure if Ge diode connection are reversed, the value of V0 changes by : (assume that the Ge diode has large breakdown voltage)

Charge is distributed within a sphere of radius R with a volume charge density \(\rho \left( r \right) = {A \over {{r^2}}}{e^{ - {{2r} \over s}}},\) where A and a are constants. If Q is the total charge of this charge distribution, the radi...

Two point charges q1\(\left( {\sqrt {10} \mu C} \right)\) and q2(\(-\) 25 \(\mu\)C) are placed on the x-axis at x = 1 m and x = 4 m respectively. The electric field (in V/m) at a point y = 3 m on y-axis is,
[take $${1 \over {4\pi { \in _0...

Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror (M1) and parallel to the second mirror (M2) is finally reflected from the second mirror (M2) parallel to the first mirror (M1). The angle bet...

The energy required to take a satellite to a height 'h' above Earth surface (radius of Earth = 6.4 \(\times\) 103 km) is E1 and kinetic energy required for the satellite to be in a circular orbit at this height is E2. The value of h for w...

Two Carnot engines A and B are operated in series. The first one, A, receives heat at T1 (= 600 K) and rejects to a reservoir at temperature T2. The second engine B receives heat rejected by the first engine and, in tum, rejects to a heat r...

A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature 27oC. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about : [Take R = 8.3 J/K mole]

A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point. the rope deviated at an angle of 45o at the roof point. If the suspended mass is at equilibrium, the magnitude of...

A particle having the same charge as of electron moves in a ciurcular path of radius 0.5 cm under the influence of a magnetic field 0f 0.5 T. If an electric field of 100 V/m makes it to move in a straight path, then the mass of the particle...

One of the two identical conducting wires of length L is bent in the form of a circular loop and the other one into a circular coil of N identical turns. If the same current is passed in both, the radio of the magnetic field at the central ...

The position co-ordinates of a particle moving in a 3-D coordinate system is given by
x = a cos\(\omega\)t
y = a sin\(\omega\)t and
z = a\(\omega\)t
The speed of the particle is :

In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed '\(\upsilon\)' more than that of car B. Both the cars start from rest and travel with constant acceleration a1 and a...

The top of a water tank is open to air and its water level is mainted. It is giving out 0.74 m3 water per minute through a circular opening of 2 cm radius in its wall. The depth of the center of the opening from the level of water in the ta...

A rod of length 50 cm is pivoted at one end. It is raised such that if makes an angle of 30o from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in rad s\(-\)1) will be (g = 10 ms$$...

A rod of mass 'M' and length '2L' is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of 'm' are attached at distance 'L/2' from its centre on both sides, it reduces the oscillation frequency by 20%....

A particle is executing simple harmonic motion (SHM) of amplitude A, along the x-axis, about x = 0. When its potential Energy (PE) equals kinetic energy (KE), the position of the particle will be :

The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies 3 divisions below the me...

Expression for time in terms of G(universal gravitional constant), h (Planck constant) and c (speed of light) is proportional to :

In a Young's double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength \(\lambda\) = 500 nm is incident on the slits. The total number of bright fringes that are observed in the angular range \(-\) 30o\(\le\)$$\the...

A musician using an open flute of length 50 cm producess second harmonic sound waves. A person runs towards the musician from another end of hall at a speed of 10 km/h. If the wave speed is 330 m/s, the frequency heard by the running perso...

A force acts on a 2 kg object so that its position is given as a function of time as x = 3t2 + 5. What is the work done by this force in first 5 seconds ?