JEE Main 2024 (Online) 29th January Morning Shift

All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word "GTWENTY" is _________.

A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, is

Let \(\left(5, \frac{a}{4}\right)\) be the circumcenter of a triangle with vertices \(\mathrm{A}(a,-2), \mathrm{B}(a, 6)\) and \(C\left(\frac{a}{4},-2\right)\). Let \(\alpha\) denote the circumradius, \(\beta\) denote the area and $$\gamma$...

If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio of the G.P. is equal to

In an A.P., the sixth term \(a_6=2\). If the product \(a_1 a_4 a_5\) is the greatest, then the common difference of the A.P. is equal to

Let \(R\) be a relation on \(Z \times Z\) defined by \((a, b) R(c, d)\) if and only if \(a d-b c\) is divisible by 5. Then \(R\) is

If the mean and variance of the data \(65,68,58,44,48,45,60, \alpha, \beta, 60\) where \(\alpha> \beta\), are 56 and 66.2 respectively, then \(\alpha^2+\beta^2\) is equal to _________.

In a \(\triangle A B C\), suppose \(y=x\) is the equation of the bisector of the angle \(B\) and the equation of the side \(A C\) is \(2 x-y=2\). If \(2 A B=B C\) and the points \(A\) and \(B\) are respectively \((4,6)\) and $$(\alpha, \bet...

If \(\alpha,-\frac{\pi}{2}<\alpha<\frac{\pi}{2}\) is the solution of \(4 \cos \theta+5 \sin \theta=1\), then the value of \(\tan \alpha\) is

Let \(\vec{a}, \vec{b}\) and \(\vec{c}\) be three non-zero vectors such that \(\vec{b}\) and \(\vec{c}\) are non-collinear. If \(\vec{a}+5 \vec{b}\) is collinear with \(\vec{c}, \vec{b}+6 \vec{c}\) is collinear with \(\vec{a}\) and $$\vec{a...

A capacitor of capacitance \(100 \mu \mathrm{F}\) is charged to a potential of \(12 \mathrm{~V}\) and connected to a \(6.4 \mathrm{~mH}\) inductor to produce oscillations. The maximum current in the circuit would be :

The explosive in a Hydrogen bomb is a mixture of \({ }_1 \mathrm{H}^2,{ }_1 \mathrm{H}^3\) and \({ }_3 \mathrm{Li}^6\) in some condensed form. The chain reaction is given by
$$\begin{aligned}
& { }_3 \mathrm{Li}^6+{ }_0 \mathrm{n}^1 \righta...

When a hydrogen atom going from \(n=2\) to \(n=1\) emits a photon, its recoil speed is \(\frac{x}{5} \mathrm{~m} / \mathrm{s}\). Where \(x=\) ________. (Use, mass of hydrogen atom \(=1.6 \times 10^{-27} \mathrm{~kg}\))

A \(16 \Omega\) wire is bend to form a square loop. A \(9 \mathrm{~V}\) battery with internal resistance \(1 \Omega\) is connected across one of its sides. If a \(4 \mu F\) capacitor is connected across one of its diagonals, the energy stor...

If the radius of curvature of the path of two particles of same mass are in the ratio \(3: 4\), then in order to have constant centripetal force, their velocities will be in the ratio of :

The deflection in moving coil galvanometer falls from 25 divisions to 5 division when a shunt of \(24 \Omega\) is applied. The resistance of galvanometer coil will be :

A galvanometer having coil resistance \(10 \Omega\) shows a full scale deflection for a current of \(3 \mathrm{~mA}\). For it to measure a current of \(8 \mathrm{~A}\), the value of the shunt should be:

The electric current through a wire varies with time as \(I=I_0+\beta t\), where \(I_0=20 \mathrm{~A}\) and \(\beta=3 \mathrm{~A} / \mathrm{s}\). The amount of electric charge crossed through a section of the wire in \(20 \mathrm{~s}\) is :

The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is \(25 \%\) of the velocity of light, then the ratio of K.E. of electron and K.E. of photon will be:

Match List I with List II

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...

A square loop of side \(10 \mathrm{~cm}\) and resistance \(0.7 \Omega\) is placed vertically in east-west plane. A uniform magnetic field of \(0.20 T\) is set up across the plane in north east direction. The magnetic field is decreased to z...

In the given circuit, the breakdown voltage of the Zener diode is \(3.0 \mathrm{~V}\). What is the value of \(\mathrm{I}_{\mathrm{z}}\) ?

Two charges of \(5 Q\) and \(-2 Q\) are situated at the points \((3 a, 0)\) and \((-5 a, 0)\) respectively. The electric flux through a sphere of radius '\(4 a\)' having center at origin is :

An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet \(\mathrm{S}\) having surface charge density \(+\sigma\). The electron at \(t=0\) is at a distance of \(1 \mathrm{~m}\) from \(S\) a...

A convex mirror of radius of curvature \(30 \mathrm{~cm}\) forms an image that is half the size of the object. The object distance is :

A biconvex lens of refractive index 1.5 has a focal length of \(20 \mathrm{~cm}\) in air. Its focal length when immersed in a liquid of refractive index 1.6 will be:

At what distance above and below the surface of the earth a body will have same weight. (take radius of earth as \(R\).)

A thermodynamic system is taken from an original state \(\mathrm{A}\) to an intermediate state \(B\) by a linear process as shown in the figure. It's volume is then reduced to the original value from \(\mathrm{B}\) to \(\mathrm{C}\) by an i...

Two vessels \(A\) and \(B\) are of the same size and are at same temperature. A contains \(1 \mathrm{~g}\) of hydrogen and \(B\) contains \(1 \mathrm{~g}\) of oxygen. \(\mathrm{P}_{\mathrm{A}}\) and \(\mathrm{P}_{\mathrm{B}}\) are the press...

The magnetic potential due to a magnetic dipole at a point on its axis situated at a distance of \(20 \mathrm{~cm}\) from its center is \(1.5 \times 10^{-5} \mathrm{~T} \mathrm{~m}\). The magnetic moment of the dipole is _________ $$A \math...

A ball rolls off the top of a stairway with horizontal velocity \(u\). The steps are \(0.1 \mathrm{~m}\) high and \(0.1 \mathrm{~m}\) wide. The minimum velocity \(u\) with which that ball just hits the step 5 of the stairway will be $$\sqrt...

A body starts moving from rest with constant acceleration covers displacement \(S_1\) in first \((p-1)\) seconds and \(\mathrm{S}_2\) in first \(p\) seconds. The displacement \(\mathrm{S}_1+\mathrm{S}_2\) will be made in time :

Given below are two statements:
Statement I : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water.
Statement II : If a capillary tube is immersed first in cold...

In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are \(70 \mathrm{~ms}^{-1}\) and \(65 \mathrm{~ms}^{-1}\) respectively. If the wing area is \(2 \mathrm{~m}^2\), the lift...

A cylinder is rolling down on an inclined plane of inclination \(60^{\circ}\). It's acceleration during rolling down will be \(\frac{x}{\sqrt{3}} m / s^2\), where \(x=\) ________ (use \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\)).

When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is \(\frac{x}{8}\), where \(x=\) _________.

The resistance \(R=\frac{V}{I}\) where \(\mathrm{V}=(200 \pm 5) \mathrm{V}\) and \(I=(20 \pm 0.2) \mathrm{A}\), the percentage error in the measurement of \(\mathrm{R}\) is :

In a double slit experiment shown in figure, when light of wavelength \(400 \mathrm{~nm}\) is used, dark fringe is observed at \(P\). If \(\mathrm{D}=0.2 \mathrm{~m}\), the minimum distance between the slits \(S_1\) and \(S_2\) is _________...

A block of mass \(100 \mathrm{~kg}\) slides over a distance of \(10 \mathrm{~m}\) on a horizontal surface. If the co-efficient of friction between the surfaces is 0.4, then the work done against friction \((\operatorname{in} J\)) is :

The potential energy function (in \(J\) ) of a particle in a region of space is given as \(U=\left(2 x^2+3 y^3+2 z\right)\). Here \(x, y\) and \(z\) are in meter. The magnitude of \(x\)-component of force (in \(N\) ) acting on the particle ...