JEE Main 2024 (Online) 5th April Evening Shift

60 words can be made using all the letters of the word \(\mathrm{BHBJO}\), with or without meaning. If these words are written as in a dictionary, then the \(50^{\text {th }}\) word is:

The coefficients \(\mathrm{a}, \mathrm{b}, \mathrm{c}\) in the quadratic equation \(\mathrm{a} x^2+\mathrm{bx}+\mathrm{c}=0\) are from the set \(\{1,2,3,4,5,6\}\). If the probability of this equation having one real root bigger than the oth...

The number of real solutions of the equation \(x|x+5|+2|x+7|-2=0\) is __________.

For \(x \geqslant 0\), the least value of \(\mathrm{K}\), for which \(4^{1+x}+4^{1-x}, \frac{\mathrm{K}}{2}, 16^x+16^{-x}\) are three consecutive terms of an A.P., is equal to :

If \(1+\frac{\sqrt{3}-\sqrt{2}}{2 \sqrt{3}}+\frac{5-2 \sqrt{6}}{18}+\frac{9 \sqrt{3}-11 \sqrt{2}}{36 \sqrt{3}}+\frac{49-20 \sqrt{6}}{180}+\ldots\) upto \(\infty=2+\left(\sqrt{\frac{b}{a}}+1\right) \log _e\left(\frac{a}{b}\right)\), where a ...

Let the mean and the standard deviation of the probability distribution

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Let \(\mathrm{A}(-1,1)\) and \(\mathrm{B}(2,3)\) be two points and \(\mathrm{P}\) be a variable point above the line \(\mathrm{AB}\) such that the area of \(\triangle \mathrm{PAB}\) is 10. If the locus of \(\mathrm{P}\) is $$\mathrm{a} x+\m...

The number of solutions of \(\sin ^2 x+\left(2+2 x-x^2\right) \sin x-3(x-1)^2=0\), where \(-\pi \leq x \leq \pi\), is ________.

Let \(\vec{a}=2 \hat{i}+5 \hat{j}-\hat{k}, \vec{b}=2 \hat{i}-2 \hat{j}+2 \hat{k}\) and \(\vec{c}\) be three vectors such that \((\vec{c}+\hat{i}) \times(\vec{a}+\vec{b}+\hat{i})=\vec{a} \times(\vec{c}+\hat{i})\). If $$\vec{a} \cdot \vec{c}=...

Consider three vectors \(\vec{a}, \vec{b}, \vec{c}\). Let \(|\vec{a}|=2,|\vec{b}|=3\) and \(\vec{a}=\vec{b} \times \vec{c}\). If \(\alpha \in\left[0, \frac{\pi}{3}\right]\) is the angle between the vectors \(\vec{b}\) and \(\vec{c}\), then ...

A series LCR circuit is subjected to an ac signal of \(200 \mathrm{~V}, 50 \mathrm{~Hz}\). If the voltage across the inductor \((\mathrm{L}=10 \mathrm{~mH})\) is \(31.4 \mathrm{~V}\), then the current in this circuit is _______.

The angular momentum of an electron in a hydrogen atom is proportional to : (Where \(\mathrm{r}\) is the radius of orbit of electron)

The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is \(915\mathop A\limits^o\). The longest wavelength of spectral lines in the Balmer series will be _______ \(\mathop A\limits^o\).

A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius \(9 \mathrm{~m}\) and completes 120 resolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is (in $$\mathrm{m} / \mathrm{s}^2...

A galvanometer of resistance \(100 \Omega\) when connected in series with \(400 \Omega\) measures a voltage of upto \(10 \mathrm{~V}\). The value of resistance required to convert the galvanometer into ammeter to read upto $$10 \mathrm{~A}$...

A wire of resistance \(20 \Omega\) is divided into 10 equal parts, resulting pairs. A combination of two parts are connected in parallel and so on. Now resulting pairs of parallel combination are connected in series. The equivalent resistan...

The ratio of heat dissipated per second through the resistance \(5 \Omega\) and \(10 \Omega\) in the circuit given below is:

Which of the following statement is not true about stopping potential \((\mathrm{V}_0)\) ?

The current in an inductor is given by \(\mathrm{I}=(3 \mathrm{t}+8)\) where \(\mathrm{t}\) is in second. The magnitude of induced emf produced in the inductor is \(12 \mathrm{~mV}\). The self-inductance of the inductor _________ $$\mathrm{...

Match List I with List II :

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The output (Y) of logic circuit given below is 0 only when :

The vehicles carrying inflammable fluids usually have metallic chains touching the ground:

The electric field at point \(\mathrm{p}\) due to an electric dipole is \(\mathrm{E}\). The electric field at point \(\mathrm{R}\) on equitorial line will be \(\frac{\mathrm{E}}{x}\). The value of \(x\) :

A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is :
(Given \(=\) Radius of geo-stationary orbit for earth is $$4.2 \times 10^...

During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of \(\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}\) for the gas is :

If \(\mathrm{n}\) is the number density and \(\mathrm{d}\) is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :

A particle moves in \(x\)-\(y\) plane under the influence of a force \(\vec{F}\) such that its linear momentum is \(\overrightarrow{\mathrm{p}}(\mathrm{t})=\hat{i} \cos (\mathrm{kt})-\hat{j} \sin (\mathrm{kt})\). If \(\mathrm{k}\) is consta...

A heavy box of mass \(50 \mathrm{~kg}\) is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is :

The electrostatic force \(\left(\vec{F_1}\right)\) and magnetic force \(\left(\vec{F}_2\right)\) acting on a charge \(q\) moving with velocity \(v\) can be written :

A solenoid of length \(0.5 \mathrm{~m}\) has a radius of \(1 \mathrm{~cm}\) and is made up of '\(\mathrm{m}\)' number of turns. It carries a current of \(5 \mathrm{~A}\). If the magnitude of the magnetic field inside the solenoid is $$6.28 ...

The maximum height reached by a projectile is \(64 \mathrm{~m}\). If the initial velocity is halved, the new maximum height of the projectile is ______ \(\mathrm{m}\).

Match List I with List II :

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A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of \(10 \mathrm{~N}\) is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the...

A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is \(\frac{x}{5}\). The value of \(x\) is _________.

What is the dimensional formula of \(a b^{-1}\) in the equation \(\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}\), where letters have their usual meaning.

A vernier callipers has 20 divisions on the vernier scale, which coincides with \(19^{\text {th }}\) division on the main scale. The least count of the instrument is \(0.1 \mathrm{~mm}\). One main scale division is equal to ________ mm.

Given below are two statements :
Statement I : When the white light passed through a prism, the red light bends lesser than yellow and violet.
Statement II : The refractive indices are different for different wavelengths in dispersive mediu...

In a single slit experiment, a parallel beam of green light of wavelength \(550 \mathrm{~nm}\) passes through a slit of width \(0.20 \mathrm{~mm}\). The transmitted light is collected on a screen \(100 \mathrm{~cm}\) away. The distance of f...

A sonometer wire of resonating length \(90 \mathrm{~cm}\) has a fundamental frequency of \(400 \mathrm{~Hz}\) when kept under some tension. The resonating length of the wire with fundamental frequency of \(600 \mathrm{~Hz}\) under same tens...

A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to :