JEE Main 2022 (Online) 25th July Morning Shift

The sum of diameters of the circles that touch (i) the parabola \(75 x^{2}=64(5 y-3)\) at the point \(\left(\frac{8}{5}, \frac{6}{5}\right)\) and (ii) the \(y\)-axis, is equal to ______________.

The letters of the word 'MANKIND' are written in all possible orders and arranged in serial order as in an English dictionary. Then the serial number of the word 'MANKIND' is _____________.

If the sum and the product of mean and variance of a binomial distribution are 24 and 128 respectively, then the probability of one or two successes is :

If the numbers appeared on the two throws of a fair six faced die are \(\alpha\) and \(\beta\), then the probability that \(x^{2}+\alpha x+\beta>0\), for all \(x \in \mathbf{R}\), is :

If \(\alpha, \beta, \gamma, \delta\) are the roots of the equation \(x^{4}+x^{3}+x^{2}+x+1=0\), then \(\alpha^{2021}+\beta^{2021}+\gamma^{2021}+\delta^{2021}\) is equal to :

Let \(a, b\) be two non-zero real numbers. If \(p\) and \(r\) are the roots of the equation \(x^{2}-8 \mathrm{a} x+2 \mathrm{a}=0\) and \(\mathrm{q}\) and s are the roots of the equation \(x^{2}+12 \mathrm{~b} x+6 \mathrm{~b}=0\), such that...

Let \(a_{1}=b_{1}=1, a_{n}=a_{n-1}+2\) and \(b_{n}=a_{n}+b_{n-1}\) for every natural number \(n \geqslant 2\). Then \(\sum\limits_{n = 1}^{15} {{a_n}.{b_n}}\) is equal to ___________.

A line, with the slope greater than one, passes through the point \(A(4,3)\) and intersects the line \(x-y-2=0\) at the point B. If the length of the line segment \(A B\) is \(\frac{\sqrt{29}}{3}\), then \(B\) also lies on the line :

The number of solutions of \(|\cos x|=\sin x\), such that \(-4 \pi \leq x \leq 4 \pi\) is :

Let \(\mathrm{ABC}\) be a triangle such that $$\overrightarrow{\mathrm{BC}}=\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{CA}}=\overrightarrow{\mathrm{b}}, \overrightarrow{\mathrm{AB}}=\overrightarrow{\mathrm{c}},|\overrightarrow{\ma...

To increase the resonant frequency in series LCR circuit,

The momentum of an electron revolving in \(\mathrm{n}^{\text {th }}\) orbit is given by :
(Symbols have their usual meanings)

The magnetic moment of an electron (e) revolving in an orbit around nucleus with an orbital angular momentum is given by :

A condenser of \(2 \,\mu \mathrm{F}\) capacitance is charged steadily from 0 to \(5 \,\mathrm{C}\). Which of the following graph represents correctly the variation of potential difference \((\mathrm{V})\) across it's plates with respect to ...

A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is \(60 \mathrm{~m}\), then the magnitude of displacement would be :
(Given \(\left.\cos 135^{\circ}=-0.7\right)\)

The required height of a TV tower which can cover the population of \(6.03\) lakh is \(h\). If the average population density is 100 per square \(\mathrm{km}\) and the radius of earth is \(6400 \mathrm{~km}\), then the value of \(h\) will b...

Which of the following physical quantities have the same dimensions?

In the given figure, the value of Vo will be _____________ V.

Eight copper wire of length \(l\) and diameter \(d\) are joined in parallel to form a single composite conductor of resistance \(R\). If a single copper wire of length \(2 l\) have the same resistance \((R)\) then its diameter will be _____...

A metal exposed to light of wavelength \(800 \mathrm{~nm}\) and and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of photo-electron doubles when light of wavelength \(500 \mathrm{~nm}\) is used. The workfunc...

A small square loop of wire of side \(l\) is placed inside a large square loop of wire \(\mathrm{L}(\mathrm{L}>>l)\). Both loops are coplanar and their centres coincide at point \(\mathrm{O}\) as shown in figure. The mutual inductance of th...

The rms value of conduction current in a parallel plate capacitor is \(6.9 \,\mu \mathrm{A}\). The capacity of this capacitor, if it is connected to \(230 \mathrm{~V}\) ac supply with an angular frequency of $$600 \,\mathrm{rad} / \mathrm{s...

In the circuit, the logical value of \(A=1\) or \(B=1\) when potential at \(A\) or \(B\) is \(5 \mathrm{~V}\) and the logical value of \(A=0\) or \(B=0\) when potential at \(A\) or \(B\) is \(0 \mathrm{~V}\).

The truth table of the given c...

The energy band gap of semiconducting material to produce violet (wavelength = 4000\(\mathop A\limits^o\) ) LED is ______________ \(\mathrm{eV}\). (Round off to the nearest integer).

The volume charge density of a sphere of radius \(6 \mathrm{~m}\) is \(2 \,\mu \mathrm{C} \,\mathrm{cm}^{-3}\). The number of lines of force per unit surface area coming out from the surface of the sphere is _______________ $$\times 10^{10}...

Which of the following statement is correct?

Time taken by light to travel in two different materials \(A\) and \(B\) of refractive indices \(\mu_{A}\) and \(\mu_{B}\) of same thickness is \(t_{1}\) and \(t_{2}\) respectively. If \(t_{2}-t_{1}=5 \times 10^{-10}\) s and the ratio of $$...

Three identical particles \(\mathrm{A}, \mathrm{B}\) and \(\mathrm{C}\) of mass \(100 \mathrm{~kg}\) each are placed in a straight line with \(\mathrm{AB}=\mathrm{BC}=13 \mathrm{~m}\). The gravitational force on a fourth particle $$\mathrm{...

A certain amount of gas of volume \(\mathrm{V}\) at \(27^{\circ} \mathrm{C}\) temperature and pressure \(2 \times 10^{7} \mathrm{Nm}^{-2}\) expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume ...

Following statements are given :
(A) The average kinetic energy of a gas molecule decreases when the temperature is reduced.
(B) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature.
(C) T...

A unit scale is to be prepared whose length does not change with temperature and remains \(20 \mathrm{~cm}\), using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way...

Four forces are acting at a point \(\mathrm{P}\) in equilibrium as shown in figure. The ratio of force \(\mathrm{F}_{1}\) to \(\mathrm{F}_{2}\) is \(1: x\) where \(x=\) _____________.

Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is \(6: 5\) and their respective masses ratio is...

A car is moving with speed of \(150 \mathrm{~km} / \mathrm{h}\) and after applying the break it will move \(27 \mathrm{~m}\) before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after tra...

A wire of length \(\mathrm{L}\) and radius \(\mathrm{r}\) is clamped rigidly at one end. When the other end of the wire is pulled by a force \(\mathrm{F}\), its length increases by \(5 \mathrm{~cm}\). Another wire of the same material of le...

A solid cylinder and a solid sphere, having same mass \(M\) and radius \(R\), roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with w...

In figure \((\mathrm{A})\), mass '\(2 \mathrm{~m}^{\text {' }}\) is fixed on mass '\(\mathrm{m}\) ' which is attached to two springs of spring constant \(\mathrm{k}\). In figure (B), mass '\(\mathrm{m}\)' is attached to two springs of spri...

If momentum [P], area \([\mathrm{A}]\) and time \([\mathrm{T}]\) are taken as fundamental quantities, then the dimensional formula for coefficient of viscosity is :

An observer is riding on a bicycle and moving towards a hill at \(18 \,\mathrm{kmh}^{-1}\). He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the ...

A body of mass \(0.5 \mathrm{~kg}\) travels on straight line path with velocity \(v=\left(3 x^{2}+4\right) \mathrm{m} / \mathrm{s}\). The net workdone by the force during its displacement from \(x=0\) to \(x=2 \mathrm{~m}\) is :