JEE Main 2024 (Online) 8th April Evening Shift

The number of distinct real roots of the equation \(|x+1||x+3|-4|x+2|+5=0\), is _______

In an increasing geometric progression of positive terms, the sum of the second and sixth terms is \(\frac{70}{3}\) and the product of the third and fifth terms is 49. Then the sum of the \(4^{\text {th }}, 6^{\text {th }}\) and $$8^{\text ...

An arithmetic progression is written in the following way

The sum of all the terms of the 10th row is _________.

Let \(A=\{2,3,6,8,9,11\}\) and \(B=\{1,4,5,10,15\}\). Let \(R\) be a relation on \(A \times B\) defined by
\((a, b) R(c, d)\) if and only if \(3 a d-7 b c\) is an even integer. Then the relation \(R\) is

Let \(\mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathbf{N}\) and \(\mathrm{a}< \mathrm{b}< \mathrm{c}\). Let the mean, the mean deviation about the mean and the variance of the 5 observations \(9,25, a, b, c\) be 18, 4 and \(\frac{136}{5}\), r...

If the line segment joining the points \((5,2)\) and \((2, a)\) subtends an angle \(\frac{\pi}{4}\) at the origin, then the absolute value of the product of all possible values of $a$ is :

Let a ray of light passing through the point \((3,10)\) reflects on the line \(2 x+y=6\) and the reflected ray passes through the point \((7,2)\). If the equation of the incident ray is \(a x+b y+1=0\), then \(a^2+b^2+3 a b\) is equal to __...

If the value of \(\frac{3 \cos 36^{\circ}+5 \sin 18^{\circ}}{5 \cos 36^{\circ}-3 \sin 18^{\circ}}\) is \(\frac{a \sqrt{5}-b}{c}\), where \(a, b, c\) are natural numbers and \(\operatorname{gcd}(a, c)=1\), then \(a+b+c\) is equal to :

Let \(\overrightarrow{\mathrm{a}}=\hat{i}+2 \hat{j}+3 \hat{k}, \overrightarrow{\mathrm{b}}=2 \hat{i}+3 \hat{j}-5 \hat{k}\) and \(\overrightarrow{\mathrm{c}}=3 \hat{i}-\hat{j}+\lambda \hat{k}\) be three vectors. Let $$\overrightarrow{\mathrm...

Let \(\overrightarrow{\mathrm{a}}=4 \hat{i}-\hat{j}+\hat{k}, \overrightarrow{\mathrm{b}}=11 \hat{i}-\hat{j}+\hat{k}\) and \(\overrightarrow{\mathrm{c}}\) be a vector such that $$(\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}) \tim...

A coil of negligible resistance is connected in series with \(90 \Omega\) resistor across \(120 \mathrm{~V}, 60 \mathrm{~Hz}\) supply. A voltmeter reads \(36 \mathrm{~V}\) across resistance. Inductance of the coil is :

An alternating emf \(\mathrm{E}=110 \sqrt{2} \sin 100 \mathrm{t}\) volt is applied to a capacitor of \(2 \mu \mathrm{F}\), the rms value of current in the circuit is ________ \(\mathrm{mA}\).

If \(M_0\) is the mass of isotope \({ }_5^{12} B, M_p\) and \(M_n\) are the masses of proton and neutron, then nuclear binding energy of isotope is:

In a hypothetical fission reaction
\({ }_{92} X^{236} \rightarrow{ }_{56} \mathrm{Y}^{141}+{ }_{36} Z^{92}+3 R\)
The identity of emitted particles (R) is :

A capacitor has air as dielectric medium and two conducting plates of area \(12 \mathrm{~cm}^2\) and they are \(0.6 \mathrm{~cm}\) apart. When a slab of dielectric having area \(12 \mathrm{~cm}^2\) and \(0.6 \mathrm{~cm}\) thickness is inse...

Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating element should be _________ to __________ times of its initial length if the water is to be boiled in 15 minutes.

A heater is designed to operate with a power of \(1000 \mathrm{~W}\) in a \(100 \mathrm{~V}\) line. It is connected in combination with a resistance of \(10 \Omega\) and a resistance \(R\), to a \(100 \mathrm{~V}\) mains as shown in figure....

A proton and an electron have the same de Broglie wavelength. If \(\mathrm{K}_{\mathrm{p}}\) and \(\mathrm{K}_{\mathrm{e}}\) be the kinetic energies of proton and electron respectively, then choose the correct relation :

A potential divider circuit is connected with a dc source of \(20 \mathrm{~V}\), a light emitting diode of glow in voltage \(1.8 \mathrm{~V}\) and a zener diode of breakdown voltage of \(3.2 \mathrm{~V}\). The length (PR) of the resistive w...

If the net electric field at point \(\mathrm{P}\) along \(\mathrm{Y}\) axis is zero, then the ratio of \(\left|\frac{q_2}{q_3}\right|\) is \(\frac{8}{5 \sqrt{x}}\), where \(x=\) ________.

The position of the image formed by the combination of lenses is :

Two satellite A and B go round a planet in circular orbits having radii 4R and R respectively. If the speed of \(\mathrm{A}\) is \(3 v\), the speed of \(\mathrm{B}\) will be :

Given below are two statements :
Statement (I) : The mean free path of gas molecules is inversely proportional to square of molecular diameter.
Statement (II) : Average kinetic energy of gas molecules is directly proportional to absolute te...

A diatomic gas \((\gamma=1.4)\) does \(100 \mathrm{~J}\) of work in an isobaric expansion. The heat given to the gas is :

A given object takes \(\mathrm{n}\) times the time to slide down \(45^{\circ}\) rough inclined plane as it takes the time to slide down an identical perfectly smooth \(45^{\circ}\) inclined plane. The coefficient of kinetic friction between...

The coercivity of a magnet is \(5 \times 10^3 \mathrm{~A} / \mathrm{m}\). The amount of current required to be passed in a solenoid of length \(30 \mathrm{~cm}\) and the number of turns 150, so that the magnet gets demagnetised when inside ...

A long straight wire of radius a carries a steady current I. The current is uniformly distributed across its cross section. The ratio of the magnetic field at \(\frac{a}{2}\) and \(2 a\) from axis of the wire is :

The angle of projection for a projectile to have same horizontal range and maximum height is :

A body of mass M thrown horizontally with velocity v from the top of the tower of height H touches the ground at a distance of \(100 \mathrm{~m}\) from the foot of the tower. A body of mass \(2 \mathrm{~M}\) thrown at a velocity $$\frac{v}{...

Small water droplets of radius \(0.01 \mathrm{~mm}\) are formed in the upper atmosphere and falling with a terminal velocity of \(10 \mathrm{~cm} / \mathrm{s}\). Due to condensation, if 8 such droplets are coalesced and formed a larger drop...

A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil (specific gravity of Kerosene oil = 0.8, specific gravity of ice = 0.9):

A thin circular disc of mass \(\mathrm{M}\) and radius \(\mathrm{R}\) is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity \(\omega\). If another disc of same dimens...

A circular table is rotating with an angular velocity of \(\omega \mathrm{~rad} / \mathrm{s}\) about its axis (see figure). There is a smooth groove along a radial direction on the table. A steel ball is gently placed at a distance of $$1 \...

An object of mass \(0.2 \mathrm{~kg}\) executes simple harmonic motion along \(x\) axis with frequency of \(\left(\frac{25}{\pi}\right) \mathrm{Hz}\). At the position \(x=0.04 \mathrm{~m}\) the object has kinetic energy \(0.5 \mathrm{~J}\) ...

If \(\epsilon_{\mathrm{o}}\) is the permittivity of free space and \(\mathrm{E}\) is the electric field, then \(\epsilon_{\mathrm{o}} \mathrm{E}^2\) has the dimensions :

There are 100 divisions on the circular scale of a screw gauge of pitch \(1 \mathrm{~mm}\). With no measuring quantity in between the jaws, the zero of the circular scale lies 5 divisions below the reference line. The diameter of a wire is ...

Least count of a vernier caliper is \(\frac{1}{20 \mathrm{~N}} \mathrm{~cm}\). The value of one division on the main scale is \(1 \mathrm{~mm}\). Then the number of divisions of main scale that coincide with \(\mathrm{N}\) divisions of vern...

Two slits are \(1 \mathrm{~mm}\) apart and the screen is located \(1 \mathrm{~m}\) away from the slits. A light of wavelength \(500 \mathrm{~nm}\) is used. The width of each slit to obtain 10 maxima of the double slit pattern within the cen...

A plane progressive wave is given by \(y=2 \cos 2 \pi(330 \mathrm{t}-x) \mathrm{m}\). The frequency of the wave is :

A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is :