JEE Main 2023 (Online) 6th April Morning Shift

The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is ___________.

A pair of dice is thrown 5 times. For each throw, a total of 5 is considered a success. If the probability of at least 4 successes is \(\frac{k}{3^{11}}\), then \(k\) is equal to :

Let \(A = \{ x \in R:[x + 3] + [x + 4] \le 3\} ,\)
\(B = \left\{ {x \in R:{3^x}{{\left( {\sum\limits_{r = 1}^\infty {{3 \over {{{10}^r}}}} } \right)}^{x - 3}} < {3^{ - 3x}}} \right\},\) where [t] denotes greatest integer function. Then,

The sum of all the roots of the equation \(\left|x^{2}-8 x+15\right|-2 x+7=0\) is :

The sum of the first \(20\) terms of the series \(5+11+19+29+41+\ldots\) is :

Let \(\mathrm{A}=\{1,2,3,4, \ldots ., 10\}\) and \(\mathrm{B}=\{0,1,2,3,4\}\). The number of elements in the relation \(R=\left\{(a, b) \in A \times A: 2(a-b)^{2}+3(a-b) \in B\right\}\) is ___________.

The mean and variance of a set of 15 numbers are 12 and 14 respectively. The mean and variance of another set of 15 numbers are 14 and \(\sigma^{2}\) respectively. If the variance of all the 30 numbers in the two sets is 13 , then $$\sigma^...

The straight lines \(\mathrm{l_{1}}\) and \(\mathrm{l_{2}}\) pass through the origin and trisect the line segment of the line L : \(9 x+5 y=45\) between the axes. If \(\mathrm{m}_{1}\) and \(\mathrm{m}_{2}\) are the slopes of the lines $$\m...

Let the position vectors of the points A, B, C and D be
\(5 \hat{i}+5 \hat{j}+2 \lambda \hat{k}, \hat{i}+2 \hat{j}+3 \hat{k},-2 \hat{i}+\lambda \hat{j}+4 \hat{k}\) and \(-\hat{i}+5 \hat{j}+6 \hat{k}\). Let the set $$S=\{\lambda \in \mathbb{...

Let \(\vec{a}=2 \hat{i}+3 \hat{j}+4 \hat{k}, \vec{b}=\hat{i}-2 \hat{j}-2 \hat{k}\) and \(\vec{c}=-\hat{i}+4 \hat{j}+3 \hat{k}\).

If \(\vec{d}\) is a vector perpendicular to both \(\vec{b}\) and \(\vec{c}\), and \(\vec{a} \cdot \vec{d}=18\)...

An ideal transformer with purely resistive load operates at \(12 ~\mathrm{kV}\) on the primary side. It supplies electrical energy to a number of nearby houses at \(120 \mathrm{~V}\). The average rate of energy consumption in the houses ser...

The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is :

The radius of fifth orbit of the \(\mathrm{Li}^{++}\) is __________ \(\times 10^{-12} \mathrm{~m}\).
Take: radius of hydrogen atom \(= 0.51\,\mathop A\limits^o\)

A parallel plate capacitor with plate area \(\mathrm{A}\) and plate separation \(\mathrm{d}\) is filled with a dielectric material of dielectric constant \(K=4\). The thickness of the dielectric material is \(x\), where \(x < d\).

Let $$\m...

A particle is moving with constant speed in a circular path. When the particle turns by an angle \(90^{\circ}\), the ratio of instantaneous velocity to its average velocity is \(\pi: x \sqrt{2}\). The value of \(x\) will be -

A small block of mass \(100 \mathrm{~g}\) is tied to a spring of spring constant \(7.5 \mathrm{~N} / \mathrm{m}\) and length \(20 \mathrm{~cm}\). The other end of spring is fixed at a particular point A. If the block moves in a circular pat...

By what percentage will the transmission range of a TV tower be affected when the height of the tower is increased by \(21 \%\) ?

The length of a metallic wire is increased by \(20 \%\) and its area of cross section is reduced by \(4 \%\). The percentage change in resistance of the metallic wire is __________.

The kinetic energy of an electron, \(\alpha\)-particle and a proton are given as \(4 \mathrm{~K}, 2 \mathrm{~K}\) and \(\mathrm{K}\) respectively. The de-Broglie wavelength associated with electron \((\lambda \mathrm{e}), \alpha\)-particle ...

The induced emf can be produced in a coil by
A. moving the coil with uniform speed inside uniform magnetic field
B. moving the coil with non uniform speed inside uniform magnetic field
C. rotating the coil inside the uniform magnetic field
...

For the plane electromagnetic wave given by \(E=E_{0} \sin (\omega t-k x)\) and \(B=B_{0} \sin (\omega t-k x)\), the ratio of average electric energy density to average magnetic energy density is

Name the logic gate equivalent to the diagram attached

The resistivity \((\rho)\) of semiconductor varies with temperature. Which of the following curve represents the correct behaviour :

For a uniformly charged thin spherical shell, the electric potential (V) radially away from the centre (O) of shell can be graphically represented as -

A monochromatic light wave with wavelength \(\lambda_{1}\) and frequency \(v_{1}\) in air enters another medium. If the angle of incidence and angle of refraction at the interface are \(45^{\circ}\) and \(30^{\circ}\) respectively, then the...

A pole is vertically submerged in swimming pool, such that it gives a length of shadow \(2.15 \mathrm{~m}\) within water when sunlight is incident at angle of \(30^{\circ}\) with the surface of water. If swimming pool is filled to a height ...

Given below are two statements : one is labelled as Assertion \(\mathbf{A}\) and the other is labelled as Reason \(\mathbf{R}\).
Assertion A : Earth has atmosphere whereas moon doesn't have any atmosphere.
Reason R : The escape velocity on ...

A planet has double the mass of the earth. Its average density is equal to that of the earth. An object weighing \(\mathrm{W}\) on earth will weigh on that planet:

A source supplies heat to a system at the rate of \(1000 \mathrm{~W}\). If the system performs work at a rate of \(200 \mathrm{~W}\). The rate at which internal energy of the system increases is

The number of air molecules per cm\(^3\) increased from \(3\times10^{19}\) to \(12\times10^{19}\). The ratio of collision frequency of air molecules before and after the increase in number respectively is:

A long straight wire of circular cross-section (radius a) is carrying steady current I. The current I is uniformly distributed across this cross-section. The magnetic field is

Two identical circular wires of radius \(20 \mathrm{~cm}\) and carrying current \(\sqrt{2} \mathrm{~A}\) are placed in perpendicular planes as shown in figure. The net magnetic field at the centre of the circular wires is __________ $$\time...

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : When a body is projected at an angle \(45^{\circ}\), it's range is maximum.
Reason R : For maximum range, the value of $$\si...

A small ball of mass \(\mathrm{M}\) and density \(\rho\) is dropped in a viscous liquid of density \(\rho_{0}\). After some time, the ball falls with a constant velocity. What is the viscous force on the ball ?

A steel rod has a radius of \(20 \mathrm{~mm}\) and a length of \(2.0 \mathrm{~m}\). A force of \(62.8 ~\mathrm{kN}\) stretches it along its length. Young's modulus of steel is \(2.0 \times 10^{11} \mathrm{~N} / \mathrm{m}^{2}\). The longit...

Two identical solid spheres each of mass \(2 \mathrm{~kg}\) and radii \(10 \mathrm{~cm}\) are fixed at the ends of a light rod. The separation between the centres of the spheres is \(40 \mathrm{~cm}\). The moment of inertia of the system ab...

A mass \(m\) is attached to two strings as shown in figure. The spring constants of two springs are \(\mathrm{K}_{1}\) and \(\mathrm{K}_{2}\). For the frictionless surface, the time period of oscillation of mass \(m\) is :

Two resistances are given as \(\mathrm{R}_{1}=(10 \pm 0.5) \Omega\) and \(\mathrm{R}_{2}=(15 \pm 0.5) \Omega\). The percentage error in the measurement of equivalent resistance when they are connected in parallel is -

A person driving car at a constant speed of \(15 \mathrm{~m} / \mathrm{s}\) is approaching a vertical wall. The person notices a change of \(40 \mathrm{~Hz}\) in the frequency of his car's horn upon reflection from the wall. The frequency o...

A particle of mass \(10 \mathrm{~g}\) moves in a straight line with retardation \(2 x\), where \(x\) is the displacement in SI units. Its loss of kinetic energy for above displacement is \(\left(\frac{10}{x}\right)^{-n}\) J. The value of $$...