JEE Main 2023 (Online) 25th January Evening Shift

\(\sum\limits_{k = 0}^6 {{}^{51 - k}{C_3}}\) is equal to :

A triangle is formed by X-axis, Y-axis and the line \(3x+4y=60\). Then the number of points P(a, b) which lie strictly inside the triangle, where a is an integer and b is a multiple of a, is ____________.

Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges. If in the selected 5 fruits, at least 2 oranges, at least one red apple and at least one white apple must be given, then...

Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that \(N-2,\sqrt{3N},N+2\) are in geometric progression be \(\frac{k}{48}\). Then the value of k is :

25% of the population are smokers. A smoker has 27 times more chances to develop lung cancer than a non smoker. A person is diagnosed with lung cancer and the probability that this person is a smoker is \(\frac{k}{10}%\). Then the value of ...

Let \(\alpha \in\mathbb{R}\) and let \(\alpha,\beta\) be the roots of the equation \({x^2} + {60^{{1 \over 4}}}x + a = 0\). If \({\alpha ^4} + {\beta ^4} = - 30\), then the product of all possible values of \(a\) is ____________.

For the two positive numbers \(a,b,\) if \(a,b\) and \(\frac{1}{18}\) are in a geometric progression, while \(\frac{1}{a},10\) and \(\frac{1}{b}\) are in an arithmetic progression, then \(16a+12b\) is equal to _________.

If m and n respectively are the numbers of positive and negative values of \(\theta\) in the interval \([-\pi,\pi]\) that satisfy the equation \(\cos 2\theta \cos {\theta \over 2} = \cos 3\theta \cos {{9\theta } \over 2}\), then mn is equa...

Let \(\overrightarrow a = - \widehat i - \widehat j + \widehat k,\overrightarrow a \,.\,\overrightarrow b = 1\) and \(\overrightarrow a \times \overrightarrow b = \widehat i - \widehat j\). Then $$\overrightarrow a - 6\overrightarrow ...

If the four points, whose position vectors are \(3\widehat i - 4\widehat j + 2\widehat k,\widehat i + 2\widehat j - \widehat k, - 2\widehat i - \widehat j + 3\widehat k\) and \(5\widehat i - 2\alpha \widehat j + 4\widehat k\) are coplanar, ...

A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance R = 80\(\Omega\), an inductor of inductive reactance \(\mathrm{X_L=70\Omega}\), and a capacitor of capacitive reactance $$\mathrm{X_C=130\O...

The energy levels of an atom is shown in figure.

Which one of these transitions will result in the emission of a photon of wavelength 124.1 nm?
Given (h = 6.62 \(\times\) 10\(^{-34}\) Js)

A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3 : 2. The ratio of their nuclear sizes will be \({\left( {{x \over 3}} \right)^{{1 \over 3}}}\). The value of '\(x\)' is :-

A capacitor has capacitance 5\(\mu\)F when it's parallel plates are separated by air medium of thickness d. A slab of material of dielectric constant 1.5 having area equal to that of plates but thickness \(\frac{d}{2}\) is inserted between ...

A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After collision, the smaller body reverses its direction of motion and moves with a speed of 2 m/s. The initial speed of the smaller body before collision...

Match List I with List II

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;word-break:normal;}
...

The resistance of a wire is 5 \(\Omega\). It's new resistance in ohm if stretched to 5 times of it's original length will be :

Two cells are connected between points A and B as shown. Cell 1 has emf of 12 V and internal resistance of 3\(\Omega\). Cell 2 has emf of 6V and internal resistance of 6\(\Omega\). An external resistor R of 4\(\Omega\) is connected across A...

Given below are two statements :
Statement I : Stopping potential in photoelectric effect does not depend on the power of the light source.
Statement II : For a given metal, the maximum kinetic energy of the photoelectron depends on the wav...

A wire of length 1m moving with velocity 8 m/s at right angles to a magnetic field of 2T. The magnitude of induced emf, between the ends of wire will be __________.

Match List I with List II

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;word-break:normal;}
...

Statement I : When a Si sample is doped with Boron, it becomes P type and when doped by Arsenic it becomes N-type semi conductor such that P-type has excess holes and N-type has excess electrons.
Statement II : When such P-type and N-type s...

A point charge of 10 \(\mu\)C is placed at the origin. At what location on the X-axis should a point charge of 40 \(\mu\)C be placed so that the net electric field is zero at \(x=2\)cm on the X-axis?

The light rays from an object have been reflected towards an observer from a standard flat mirror, the image observed by the observer are :-
A. Real
B. Erect
C. Smaller in size then object
D. Laterally inverted
Choose the most appropriate a...

An object is placed on the principal axis of convex lens of focal length 10cm as shown. A plane mirror is placed on the other side of lens at a distance of 20 cm. The image produced by the plane mirror is 5cm inside the mirror. The distance...

Every planet revolves around the sun in an elliptical orbit :-
A. The force acting on a planet is inversely proportional to square of distance from sun.
B. Force acting on planet is inversely proportional to product of the masses of the pla...

A body of mass is taken from earth surface to the height h equal to twice the radius of earth (R\(_e\)), the increase in potential energy will be :
(g = acceleration due to gravity on the surface of Earth)

Match List I with List II

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;word-break:normal;}
...

The graph between two temperature scales P and Q is shown in the figure. Between upper fixed point and lower fixed point there are 150 equal divisions of scale P and 100 divisions on scale Q. The relationship for conversion between the two ...

According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is :-

Consider a block kept on an inclined plane (incline at 45\(^\circ\)) as shown in the figure. If the force required to just push it up the incline is 2 times the force required to just prevent it from sliding down, the coefficient of frictio...

For a moving coil galvanometer, the deflection in the coil is 0.05 rad when a current of 10 mA is passes through it. If the torsional constant of suspension wire is \(4.0\times10^{-5}\mathrm{N~m~rad^{-1}}\), the magnetic field is 0.01T and ...

Two long parallel wires carrying currents 8A and 15A in opposite directions are placed at a distance of 7 cm from each other. A point P is at equidistant from both the wires such that the lines joining the point P to the wires are perpendic...

Two objects are projected with same velocity 'u' however at different angles \(\alpha\) and \(\beta\) with the horizontal. If \(\alpha+\beta=90^\circ\), the ratio of horizontal range of the first object to the 2nd object will be :

The distance travelled by a particle is related to time t as \(x=4\mathrm{t}^2\). The velocity of the particle at t=5s is :-

A spherical drop of liquid splits into 1000 identical spherical drops. If u\(_\mathrm{i}\) is the surface energy of the original drop and u\(_\mathrm{f}\) is the total surface energy of the resulting drops, the (ignoring evaporation), $${{{...

If a solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius. Then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be \(\frac{x}{7}\). The ...

A particle executes simple harmonic motion between \(x=-A\) and \(x=+A\). If time taken by particle to go from \(x=0\) to \(\frac{A}{2}\) is 2 s; then time taken by particle in going from \(x=\frac{A}{2}\) to A is

Match List I with List II

.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family:Arial, sans-serif;font-size:14px;
overflow:hidden;padding:10px 5px;word-break:normal;}
...

A train blowing a whistle of frequency 320 Hz approaches an observer standing on the platform at a speed of 66 m/s. The frequency observed by the observer will be (given speed of sound = 330 ms\(^{-1}\)) __________ Hz.