JEE Main 2023 (Online) 30th January Morning Shift

Number of 4-digit numbers (the repetition of digits is allowed) which are made using the digits 1, 2, 3 and 5, and are divisible by 15, is equal to ___________.

If an unbiased die, marked with \(-2,-1,0,1,2,3\) on its faces, is thrown five times, then the probability that the product of the outcomes is positive, is :

A straight line cuts off the intercepts \(\mathrm{OA}=\mathrm{a}\) and \(\mathrm{OB}=\mathrm{b}\) on the positive directions of \(x\)-axis and \(y\) axis respectively. If the perpendicular from origin \(O\) to this line makes an angle of $$...

If \({a_n} = {{ - 2} \over {4{n^2} - 16n + 15}}\), then \({a_1} + {a_2}\, + \,....\, + \,{a_{25}}\) is equal to :

Let \(\sum_\limits{n=0}^{\infty} \frac{\mathrm{n}^{3}((2 \mathrm{n}) !)+(2 \mathrm{n}-1)(\mathrm{n} !)}{(\mathrm{n} !)((2 \mathrm{n}) !)}=\mathrm{ae}+\frac{\mathrm{b}}{\mathrm{e}}+\mathrm{c}\), where $$\mathrm{a}, \mathrm{b}, \mathrm{c} \in...

The minimum number of elements that must be added to the relation \(\mathrm{R}=\{(\mathrm{a}, \mathrm{b}),(\mathrm{b}, \mathrm{c})\}\) on the set \(\{a, b, c\}\) so that it becomes symmetric and transitive is :

The mean and variance of 7 observations are 8 and 16 respectively. If one observation 14 is omitted and a and b are respectively mean and variance of remaining 6 observation, then \(\mathrm{a+3 b-5}\) is equal to ___________.

If \(\tan 15^\circ + {1 \over {\tan 75^\circ }} + {1 \over {\tan 105^\circ }} + \tan 195^\circ = 2a\), then the value of \(\left( {a + {1 \over a}} \right)\) is :

If \(\overrightarrow a ,\overrightarrow b ,\overrightarrow c\) are three non-zero vectors and \(\widehat n\) is a unit vector perpendicular to \(\overrightarrow c\) such that $$\overrightarrow a = \alpha \overrightarrow b - \widehat n,(...

Let a unit vector \(\widehat{O P}\) make angles \(\alpha, \beta, \gamma\) with the positive directions of the co-ordinate axes \(\mathrm{OX}\), \(\mathrm{OY}, \mathrm{OZ}\) respectively, where \(\beta \in\left(0, \frac{\pi}{2}\right)\). If ...

In a series LR circuit with \(\mathrm{X_L=R}\), power factor P1. If a capacitor of capacitance C with \(\mathrm{X_C=X_L}\) is added to the circuit the power factor becomes P2. The ratio of P1 to P2 will be :

Speed of an electron in Bohr's \(7^{\text {th }}\) orbit for Hydrogen atom is \(3.6 \times 10^{6} \mathrm{~m} / \mathrm{s}\). The corresponding speed of the electron in \(3^{\text {rd }}\) orbit, in \(\mathrm{m} / \mathrm{s}\) is :

A capacitor of capacitance \(900 \mu \mathrm{F}\) is charged by a \(100 \mathrm{~V}\) battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor ...

As per the given figure, a small ball P slides down the quadrant of a circle and hits the other ball Q of equal mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball ...

The figure represents the momentum time (\(\mathrm{p}-\mathrm{t}\)) curve for a particle moving along an axis under the influence of the force. Identify the regions on the graph where the magnitude of the force is maximum and minimum respec...

A ball of mass \(200 \mathrm{~g}\) rests on a vertical post of height \(20 \mathrm{~m}\). A bullet of mass \(10 \mathrm{~g}\), travelling in horizontal direction, hits the centre of the ball. After collision both travels independently. The ...

A sinusoidal carrier voltage is amplitude modulated. The resultant amplitude modulated wave has maximum and minimum amplitude of \(120 \mathrm{~V}\) and \(80 \mathrm{~V}\) respectively. The amplitude of each sideband is :

The charge flowing in a conductor changes with time as \(\mathrm{Q}(\mathrm{t})=\alpha \mathrm{t}-\beta \mathrm{t}^{2}+\gamma \mathrm{t}^{3}\). Where \(\alpha, \beta\) and \(\gamma\) are constants. Minimum value of current is :

In the following circuit, the magnitude of current I1, is ___________ A.

A small object at rest, absorbs a light pulse of power \(20 \mathrm{~mW}\) and duration \(300 \mathrm{~ns}\). Assuming speed of light as \(3 \times 10^{8} \mathrm{~m} / \mathrm{s}\), the momentum of the object becomes equal to :

As per the given figure, if \(\frac{\mathrm{dI}}{\mathrm{dt}}=-1 \mathrm{~A} / s\) then the value of \(\mathrm{V}_{\mathrm{AB}}\) at this instant will be ____________ \(\mathrm{V}\).

A point source of light is placed at the centre of curvature of a hemispherical surface. The source emits a power of \(24 \mathrm{~W}\). The radius of curvature of hemisphere is \(10 \mathrm{~cm}\) and the inner surface is completely reflec...

The output waveform of the given logical circuit for the following inputs A and B as shown below, is :

Electric field in a certain region is given by \(\overrightarrow{\mathrm{E}}=\left(\frac{\mathrm{A}}{x^{2}} \hat{i}+\frac{\mathrm{B}}{y^{3}} \hat{j}\right) \text {. The } \mathrm{SI} \text { unit of } \mathrm{A} \text { and } \mathrm{B}\) a...

Two isolated metallic solid spheres of radii \(\mathrm{R}\) and \(2 \mathrm{R}\) are charged such that both have same charge density \(\sigma\). The spheres are then connected by a thin conducting wire. If the new charge density of the bigg...

A person has been using spectacles of power \(-1.0\) dioptre for distant vision and a separate reading glass of power \(2.0\) dioptres. What is the least distance of distinct vision for this person :

In an experiment for estimating the value of focal length of converging mirror, image of an object placed at \(40 \mathrm{~cm}\) from the pole of the mirror is formed at distance \(120 \mathrm{~cm}\) from the pole of the mirror. These dista...

If the gravitational field in the space is given as \(\left(-\frac{K}{r^{2}}\right)\). Taking the reference point to be at \(\mathrm{r}=2 \mathrm{~cm}\)
with gravitational potential \(\mathrm{V}=10 \mathrm{~J} / \mathrm{kg}\). Find the gra...

The pressure \((\mathrm{P})\) and temperature (\(\mathrm{T})\) relationship of an ideal gas obeys the equation

\(\mathrm{PT}^{2}=\) constant. The volume expansion coefficient of the gas will be :

Heat is given to an ideal gas in an isothermal process.
A. Internal energy of the gas will decrease.
B. Internal energy of the gas will increase.
C. Internal energy of the gas will not change.
D. The gas will do positive work.
E. The gas wi...

A massless square loop, of wire of resistance \(10 \Omega\), supporting a mass of \(1 \mathrm{~g}\), hangs vertically with one of its sides in a uniform magnetic field of \(10^{3} \mathrm{G}\), directed outwards in the shaded region. A dc v...

The magnetic moments associated with two closely wound circular coils \(\mathrm{A}\) and \(\mathrm{B}\) of radius \(\mathrm{r}_{\mathrm{A}}=10\) \(\mathrm{cm}\) and \(\mathrm{r}_{\mathrm{B}}=20 \mathrm{~cm}\) respectively are equal if : (Wh...

Match Column-I with Column-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:no...

A horse rider covers half the distance with \(5 \mathrm{~m} / \mathrm{s}\) speed. The remaining part of the distance was travelled with speed \(10 \mathrm{~m} / \mathrm{s}\) for half the time and with speed \(15 \mathrm{~m} / \mathrm{s}\) f...

The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, \(5 \mathrm{~cm}\). If the tube is dipped in a similar manner in another liquid \(\mathrm{B}\) of surface tension and density do...

Choose the correct relationship between Poisson ratio \((\sigma)\), bulk modulus (K) and modulus of rigidity \((\eta)\) of a given solid object :

A thin uniform rod of length \(2 \mathrm{~m}\), cross sectional area '\(A\)' and density '\(\mathrm{d}\)' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity \(\omega\). If value of $$\o...

The general displacement of a simple harmonic oscillator is \(x = A\sin \omega t\). Let T be its time period. The slope of its potential energy (U) - time (t) curve will be maximum when \(t = {T \over \beta }\). The value of \(\beta\) is __...

In a screw gauge, there are 100 divisions on the circular scale and the main scale moves by \(0.5 \mathrm{~mm}\) on a complete rotation of the circular scale. The zero of circular scale lies 6 divisions below the line of graduation when two...

In Young's double slit experiment, two slits \(S_{1}\) and \(S_{2}\) are '\(d\)' distance apart and the separation from slits to screen is \(\mathrm{D}\) (as shown in figure). Now if two transparent slabs of equal thickness $$0.1 \mathrm{~m...