JEE Main 2023 (Online) 10th April Evening Shift

Let a die be rolled \(n\) times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is \(\frac{k}{2^{15}}\), then $$\mathrm...

In the figure, \(\theta_{1}+\theta_{2}=\frac{\pi}{2}\) and \(\sqrt{3}(\mathrm{BE})=4(\mathrm{AB})\). If the area of \(\triangle \mathrm{CAB}\) is \(2 \sqrt{3}-3\) unit \({ }^{2}\), when \(\frac{\theta_{2}}{\theta_{1}}\) is the largest, then...

If \(\mathrm{S}_{n}=4+11+21+34+50+\ldots\) to \(n\) terms, then \(\frac{1}{60}\left(\mathrm{~S}_{29}-\mathrm{S}_{9}\right)\) is equal to :

Suppose \(a_{1}, a_{2}, 2, a_{3}, a_{4}\) be in an arithmetico-geometric progression. If the common ratio of the corresponding geometric progression is 2 and the sum of all 5 terms of the arithmetico-geometric progression is $$\frac{49}{2}$...

Let \(\mathrm{A}=\{2,3,4\}\) and \(\mathrm{B}=\{8,9,12\}\). Then the number of elements in the relation

$$\mathrm{R}=\left\{\left(\left(a_{1}, \mathrm{~b}_{1}\right),\left(a_{2}, \mathrm{~b}_{2}\right)\right) \in(A \times B, A \times B): a...

Let \(\mu\) be the mean and \(\sigma\) be the standard deviation of the distribution

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Let the equations of two adjacent sides of a parallelogram \(\mathrm{ABCD}\) be \(2 x-3 y=-23\) and \(5 x+4 y=23\). If the equation of its one diagonal \(\mathrm{AC}\) is \(3 x+7 y=23\) and the distance of A from the other diagonal is $$\ma...

Let \(S=\left\{x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right): 9^{1-\tan ^{2} x}+9^{\tan ^{2} x}=10\right\}\) and

\(\beta=\sum_\limits{x \in S} \tan ^{2}\left(\frac{x}{3}\right)\), then \(\frac{1}{6}(\beta-14)^{2}\) is equal to :

Let \(\vec{a}=2 \hat{i}+7 \hat{j}-\hat{k}, \vec{b}=3 \hat{i}+5 \hat{k}\) and \(\vec{c}=\hat{i}-\hat{j}+2 \hat{k}\). Let \(\vec{d}\) be a vector which is perpendicular to both \(\vec{a}\) and \(\vec{b}\), and \(\vec{c} \cdot \vec{d}=12\). Th...

If the points \(\mathrm{P}\) and \(\mathrm{Q}\) are respectively the circumcenter and the orthocentre of a \(\triangle \mathrm{ABC}\), then \(\overrightarrow{\mathrm{PA}}+\overrightarrow{\mathrm{PB}}+\overrightarrow{\mathrm{PC}}\) is
equal ...

The half life of a radioactive substance is T. The time taken, for disintegrating \(\frac{7}{8}\)th part of its original mass will be:

If 917 \(\mathop A\limits^o\) be the lowest wavelength of Lyman series then the lowest wavelength of Balmer series will be ___________ \(\mathop A\limits^o\).

The distance between two plates of a capacitor is \(\mathrm{d}\) and its capacitance is \(\mathrm{C}_{1}\), when air is the medium between the plates. If a metal sheet of thickness \(\frac{2 d}{3}\) and of the same area as plate is introduc...

A message signal of frequency \(3 ~\mathrm{kHz}\) is used to modulate a carrier signal of frequency \(1.5 ~\mathrm{MHz}\). The bandwidth of the amplitude modulated wave is

A rectangular parallelopiped is measured as \(1 \mathrm{~cm} \times 1 \mathrm{~cm} \times 100 \mathrm{~cm}\). If its specific resistance is \(3 \times 10^{-7} ~\Omega \mathrm{m}\), then the resistance between its two opposite rectangular fa...

The variation of stopping potential \(\left(\mathrm{V}_{0}\right)\) as a function of the frequency \((v)\) of the incident light for a metal is shown in figure. The work function of the surface is

A square loop of side \(2.0 \mathrm{~cm}\) is placed inside a long solenoid that has 50 turns per centimetre and carries a sinusoidally varying current of amplitude \(2.5 \mathrm{~A}\) and angular frequency $$700 ~\mathrm{rad} ~\mathrm{s}^{...

The amplitude of magnetic field in an electromagnetic wave propagating along y-axis is \(6.0 \times 10^{-7} \mathrm{~T}\). The maximum value of electric field in the electromagnetic wave is

If each diode has a forward bias resistance of \(25 ~\Omega\) in the below circuit,

Which of the following options is correct :

In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor

An electron revolves around an infinite cylindrical wire having uniform linear charge density \(2 \times 10^{-8} \mathrm{C} \mathrm{m}^{-1}\) in circular path under the influence of attractive electrostatic field as shown in the figure. The...

A point object, 'O' is placed in front of two thin symmetrical coaxial convex lenses \(\mathrm{L}_{1}\) and \(\mathrm{L}_{2}\) with focal length \(24 \mathrm{~cm}\) and \(9 \mathrm{~cm}\) respectively. The distance between two lenses is $$1...

The time period of a satellite, revolving above earth's surface at a height equal to \(\mathrm{R}\) will be
(Given \(g=\pi^{2} \mathrm{~m} / \mathrm{s}^{2}, \mathrm{R}=\) radius of earth)

Given below are two statements:
Statement I : Rotation of the earth shows effect on the value of acceleration due to gravity (g)
Statement II : The effect of rotation of the earth on the value of 'g' at the equator is minimum and that at th...

A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be,

A gas is compressed adiabatically, which one of the following statement is NOT true.

A bar magnet is released from rest along the axis of a very long vertical copper tube. After some time the magnet will

Given below are two statements:
Statement I : For diamagnetic substance, \(-1 \leq \chi < 0\), where \(\chi\) is the magnetic susceptibility.
Statement II : Diamagnetic substances when placed in an external magnetic field, tend to move from...

A straight wire carrying a current of \(14 \mathrm{~A}\) is bent into a semi-circular arc of radius \(2.2 \mathrm{~cm}\) as shown in the figure. The magnetic field produced by the current at the centre \((\mathrm{O})\) of the arc. is ______...

Two projectiles are projected at \(30^{\circ}\) and \(60^{\circ}\) with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:

A person travels \(x\) distance with velocity \(v_{1}\) and then \(x\) distance with velocity \(v_{2}\) in the same direction. The average velocity of the person is \(\mathrm{v}\), then the relation between \(v, v_{1}\) and \(v_{2}\) will b...

Young's moduli of the material of wires A and B are in the ratio of \(1: 4\), while its area of cross sections are in the ratio of \(1: 3\). If the same amount of load is applied to both the wires, the amount of elongation produced in the w...

Figure below shows a liquid being pushed out of the tube by a piston having area of cross section \(2.0 \mathrm{~cm}^{2}\). The area of cross section at the outlet is \(10 \mathrm{~mm}^{2}\). If the piston is pushed at a speed of $$4 \mathr...

Given below are two statements: one is labelled as Assertion \(\mathbf{A}\) and the other is labelled as Reason \(\mathbf{R}\)
Assertion A : An electric fan continues to rotate for some time after the current is switched off.
Reason R : Fan...

A force of \(-\mathrm{P} \hat{\mathrm{k}}\) acts on the origin of the coordinate system. The torque about the point \((2,-3)\) is \(\mathrm{P}(a \hat{i}+b \hat{j})\), The ratio of \(\frac{a}{b}\) is \(\frac{x}{2}\). The value of \(x\) is -

A rectangular block of mass \(5 \mathrm{~kg}\) attached to a horizontal spiral spring executes simple harmonic motion of amplitude \(1 \mathrm{~m}\) and time period \(3.14 \mathrm{~s}\). The maximum force exerted by spring on block is _____...

In an experiment with vernier callipers of least count \(0.1 \mathrm{~mm}\), when two jaws are joined together the zero of vernier scale lies right to the zero of the main scale and 6th division of vernier scale coincides with the main scal...

The ratio of intensities at two points \(\mathrm{P}\) and \(\mathrm{Q}\) on the screen in a Young's double slit experiment where phase difference between two waves of same amplitude are \(\pi / 3\) and \(\pi / 2\), respectively are

For a periodic motion represented by the equation
\(y=\sin \omega \mathrm{t}+\cos \omega \mathrm{t}\)
the amplitude of the motion is

If the maximum load carried by an elevator is \(1400 \mathrm{~kg}\) ( \(600 \mathrm{~kg}\) - Passengers + 800 \(\mathrm{kg}\) - elevator), which is moving up with a uniform speed of \(3 \mathrm{~m} \mathrm{~s}^{-1}\) and the frictional forc...