JEE Main 2023 (Online) 29th January Morning Shift

Five digit numbers are formed using the digits 1, 2, 3, 5, 7 with repetitions and are written in descending order with serial numbers. For example, the number 77777 has serial number 1. Then the serial number of 35337 is ____________.

Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at least 3 players pick the correct T-shirt is :

Let \(\lambda \ne 0\) be a real number. Let \(\alpha,\beta\) be the roots of the equation \(14{x^2} - 31x + 3\lambda = 0\) and \(\alpha,\gamma\) be the roots of the equation \(35{x^2} - 53x + 4\lambda = 0\). Then $${{3\alpha } \over \bet...

Let \(a_1,a_2,a_3,...\) be a \(GP\) of increasing positive numbers. If the product of fourth and sixth terms is 9 and the sum of fifth and seventh terms is 24, then \(a_1a_9+a_2a_4a_9+a_5+a_7\) is equal to __________.

Three rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable X denote the number of rotten apples. If \(\mu\) and \(\sigma^2\) represent mean and variance ...

Let \(B\) and \(C\) be the two points on the line \(y+x=0\) such that \(B\) and \(C\) are symmetric with respect to the origin. Suppose \(A\) is a point on \(y-2 x=2\) such that \(\triangle A B C\) is an equilateral triangle. Then, the area...

A light ray emits from the origin making an angle 30\(^\circ\) with the positive \(x\)-axis. After getting reflected by the line \(x+y=1\), if this ray intersects \(x\)-axis at Q, then the abscissa of Q is :

Let \(f(\theta ) = 3\left( {{{\sin }^4}\left( {{{3\pi } \over 2} - \theta } \right) + {{\sin }^4}(3\pi + \theta )} \right) - 2(1 - {\sin ^2}2\theta )\) and $$S = \left\{ {\theta \in [0,\pi ]:f'(\theta ) = - {{\sqrt 3 } \over 2}} \right\}...

If the vectors \(\overrightarrow a = \lambda \widehat i + \mu \widehat j + 4\widehat k\), \(\overrightarrow b = - 2\widehat i + 4\widehat j - 2\widehat k\) and \(\overrightarrow c = 2\widehat i + 3\widehat j + \widehat k\) are coplanar ...

Let \(\overrightarrow a\), \(\overrightarrow b\) and \(\overrightarrow c\) be three non-zero non-coplanar vectors. Let the position vectors of four points \(A,B,C\) and \(D\) be $$\overrightarrow a - \overrightarrow b + \overrightarrow...

If a radioactive element having half-life of \(30 \mathrm{~min}\) is undergoing beta decay, the fraction of radioactive element remains undecayed after \(90 \mathrm{~min}\). will be

A radioactive element \(_{92}^{242}\)X emits two \(\alpha\)-particles, one electron and two positrons. The product nucleus is represented by \(_{\mathrm{P}}^{234}\)Y. The value of P is __________.

A car is moving on a horizontal curved road with radius 50 m. The approximate maximum speed of car will be, if friction between tyres and road is 0.34. [take g = 10 ms\(^{-2}\)]

If the height of transmitting and receiving antennas are 80 m each, the maximum line of sight distance will be:
Given : Earth's radius \(=6.4\times10^6\) m

Ratio of thermal energy released in two resistors R and 3R connected in parallel in an electric circuit is :

In a metre bridge experiment the balance point is obtained if the gaps are closed by 2\(\Omega\) and 3\(\Omega\). A shunt of X \(\Omega\) is added to 3\(\Omega\) resistor to shift the balancing point by 22.5 cm. The value of X is __________...

The threshold wavelength for photoelectric emission from a material is 5500 \(\mathop A\limits^o\). Photoelectrons will be emitted, when this material is illuminated with monochromatic radiation from a
A. 75 W infra-red lamp
B. 10 W infra-...

Find the mutual inductance in the arrangement, when a small circular loop of wire of radius '\(R\)' is placed inside a large square loop of wire of side \(L\) \((L \gg R)\). The loops are coplanar and their centres coincide :

A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field B = 0.8 T. When released the radius of the loop starts shrinking at a constant rate of 2 cms$$^{...

Which of the following are true?
A. Speed of light in vacuum is dependent on the direction of propagation.
B. Speed of light in a medium is independent of the wavelength of light.
C. The speed of light is independent of the motion of the so...

Which one of the following statement is not correct in the case of light emitting diodes?
A. It is a heavily doped p-n junction.
B. It emits light only when it is forward biased.
C. It emits light only when it is reverse biased.
D. The ene...

In a cuboid of dimension \(2 \mathrm{~L} \times 2 \mathrm{~L} \times \mathrm{L}\), a charge \(q\) is placed at the center of the surface '\(\mathrm{S}\)' having area of \(4 \mathrm{~L}^{2}\). The flux through the opposite surface to '$$\mat...

A point charge \(q_1=4q_0\) is placed at origin. Another point charge \(q_2=-q_0\) is placed at \(x=12\) cm. Charge of proton is \(q_0\). The proton is placed on \(x\) axis so that the electrostatic force on the proton is zero. In this situ...

Two particles of equal mass '\(m\)' move in a circle of radius '\(r\)' under the action of their mutual gravitational attraction. The speed of each particle will be :

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: If \(d Q\) and \(d W\) represent the heat supplied to the system and the work done on the system respectively. Then according...

A block of mass $m$ slides down the plane inclined at angle \(30^{\circ}\) with an acceleration \(\frac{g}{4}\). The value of coefficient of kinetic friction will be:

The magnitude of magnetic induction at mid point \(\mathrm{O}\) due to current arrangement as shown in Fig will be

A single current carrying loop of wire carrying current I flowing in anticlockwise direction seen from +ve \(\mathrm{z}\) direction and lying in \(x y\) plane is shown in figure. The plot of \(\hat{j}\) component of magnetic field (By) at a...

A tennis ball is dropped on to the floor from a height of 9.8 m. It rebounds to a height 5.0 m. Ball comes in contact with the floor for 0.2s. The average acceleration during contact is ___________ ms\(^{-2}\).
(Given g = 10 ms\(^{-2}\))

Surface tension of a soap bubble is \(2.0 \times 10^{-2} \mathrm{Nm}^{-1}\). Work done to increase the radius of soap bubble from \(3.5 \mathrm{~cm}\) to \(7 \mathrm{~cm}\) will be:
Take \(\left[\pi=\frac{22}{7}\right]\)

A bicycle tyre is filled with air having pressure of \(270 ~\mathrm{kPa}\) at \(27^{\circ} \mathrm{C}\). The approximate pressure of the air in the tyre when the temperature increases to \(36^{\circ} \mathrm{C}\) is

A body cools from 60\(^\circ\)C to 40\(^\circ\)C in 6 minutes. If, temperature of surroundings is 10\(^\circ\)C. Then, after the next 6 minutes, its temperature will be ____________\(^\circ\)C.

A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J. The velocity of centre of mass of the sphere will be _______ ms\(^{-1}\).

Match List I with List II :

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In a Young's double slit experiment, two slits are illuminated with a light of wavelength \(800 \mathrm{~nm}\). The line joining \(A_{1} P\) is perpendicular to \(A_{1} A_{2}\) as shown in the figure. If the first minimum is detected at $$P...

As shown in the figure, three identical polaroids P\(_1\), P\(_2\) and P\(_3\) are placed one after another. The pass axis of P\(_2\) and P\(_3\) are inclined at angle of 60\(^\circ\) and 90\(^\circ\) with respect to axis of P\(_1\). The so...

A person observes two moving trains, 'A' reaching the station and 'B' leaving the station with equal speed of \(30 \mathrm{~m} / \mathrm{s}\). If both trains emit sounds with frequency \(300 \mathrm{~Hz}\), (Speed of sound: $$330 \mathrm{~m...

Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm. The phase difference between the individual waves is _________ degree.

A stone is projected at angle \(30^{\circ}\) to the horizontal. The ratio of kinetic energy of the stone at point of projection to its kinetic energy at the highest point of flight will be -

A 0.4 kg mass takes 8s to reach ground when dropped from a certain height 'P' above surface of earth. The loss of potential energy in the last second of fall is __________ J.
(Take g = 10 m/s\(^2\))