JEE Main 2022 (Online) 25th July Evening Shift

The number of real values of \(\lambda\), such that the system of linear equations
2x \(-\) 3y + 5z = 9
x + 3y \(-\) z = \(-\)18
3x \(-\) y + (\(\lambda\)2 \(-\) | \(\lambda\) |)z = 16
has no solutions, is

Let $$A=\left[\begin{array}{lll} 1 & a & a \\ 0 & 1 & b \\ 0 & 0 & 1 \end{array}\right], a, b \in \mathbb{R}$$. If for some $$n \in \mathbb{N}, A^{n}=\left[\begin{array}{ccc} 1 & 48 & 2160 \\ 0 & 1 & 96 \\ 0 & 0 & 1 \end{array}\right] $$ th...

The tangents at the points \(A(1,3)\) and \(B(1,-1)\) on the parabola \(y^{2}-2 x-2 y=1\) meet at the point \(P\). Then the area (in unit \({ }^{2}\) ) of the triangle \(P A B\) is :

If \(A\) and \(B\) are two events such that \(P(A)=\frac{1}{3}, P(B)=\frac{1}{5}\) and \(P(A \cup B)=\frac{1}{2}\), then \(P\left(A \mid B^{\prime}\right)+P\left(B \mid A^{\prime}\right)\) is equal to :

The sum \(\sum\limits_{n = 1}^{21} {{3 \over {(4n - 1)(4n + 3)}}}\) is equal to

Let \(A=\{1,2,3,4,5,6,7\}\). Define \(B=\{T \subseteq A\) : either \(1 \notin T\) or \(2 \in T\}\) and \(C=\{T \subseteq A: T\) the sum of all the elements of \(T\) is a prime number \(\}\). Then the number of elements in the set $$B \cup C...

If the mean deviation about median for the numbers 3, 5, 7, 2k, 12, 16, 21, 24, arranged in the ascending order, is 6 then the median is :

Let the point \(P(\alpha, \beta)\) be at a unit distance from each of the two lines \(L_{1}: 3 x-4 y+12=0\), and \(L_{2}: 8 x+6 y+11=0\). If \(P\) lies below \(L_{1}\) and above \({ }{L_{2}}\), then \(100(\alpha+\beta)\) is equal to :

\(2 \sin \left(\frac{\pi}{22}\right) \sin \left(\frac{3 \pi}{22}\right) \sin \left(\frac{5 \pi}{22}\right) \sin \left(\frac{7 \pi}{22}\right) \sin \left(\frac{9 \pi}{22}\right)\) is equal to :

Let \(\vec{a}=\hat{i}-\hat{j}+2 \hat{k}\) and let \(\vec{b}\) be a vector such that \(\vec{a} \times \vec{b}=2 \hat{i}-\hat{k}\) and \(\vec{a} \cdot \vec{b}=3\). Then the projection of \(\vec{b}\) on the vector \(\vec{a}-\vec{b}\) is :

When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on :

Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength \(\lambda\). The value of principal quantum number '\(n\)' of the excited state will be : (\(\mathrm{R}:\) Rydberg constant)

\({x \over {x + 4}}\) is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its
(i) third permitted energy level to the second level and
(ii) the highest permitted energy level to the second per...

Capacitance of an isolated conducting sphere of radius R1 becomes n times when it is enclosed by a concentric conducting sphere of radius R2 connected to earth. The ratio of their radii \(\left( {{{{R_2}} \over {{R_1}}}} \right)\) is :

Two parallel plate capacitors of capacity C and 3C are connected in parallel combination and charged to a potential difference 18 V. The battery is then disconnected and the space between the plates of the capacitor of capacity C is complet...

Two billiard balls of mass 0.05 kg each moving in opposite directions with 10 ms\(-\)1 collide and rebound with the same speed. If the time duration of contact is t = 0.005 s, then what is the force exerted on the ball due to each other?

Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3 m each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of positi...

In AM modulation, a signal is modulated on a carrier wave such that maximum and minimum amplitudes are found to be 6 V and 2 V respectively. The modulation index is :

A current of 15 mA flows in the circuit as shown in figure. The value of potential difference between the points A and B will be:

In a potentiometer arrangement, a cell of emf 1.20 V gives a balance point at 36 cm length of wire. This cell is now replaced by another cell of emf 1.80 V. The difference in balancing length of potentiometer wire in above conditions will b...

The ratio of wavelengths of proton and deuteron accelerated by potential Vp and Vd is 1 : \(\sqrt2\). Then the ratio of Vp to Vd will be :

The electric current in a circular coil of 2 turns produces a magnetic induction B1 at its centre. The coil is unwound and in rewound into a circular coil of 5 tuns and the same current produces a magnetic induction B2 at its centre. The ra...

Magnetic flux (in weber) in a closed circuit of resistance 20 \(\Omega\) varies with time t(s) at \(\phi\) = 8t2 \(-\) 9t + 5. The magnitude of the induced current at t = 0.25 s will be ____________ mA.

Light wave travelling in air along x-direction is given by \({E_y} = 540\sin \pi \times {10^4}(x - ct)\,V{m^{ - 1}}\). Then, the peak value of magnetic field of wave will be (Given c = 3 \(\times\) 108 ms\(-\)1)

Two ideal diodes are connected in the network as shown in figure. The equivalent resistance between A and B is __________ \(\Omega\).

For an object placed at a distance 2.4 m from a lens, a sharp focused image is observed on a screen placed at a distance 12 cm from the lens. A glass plate of refractive index 1.5 and thickness 1 cm is introduced between lens and screen suc...

A convex lens of focal length 20 cm is placed in front of a convex mirror with principal axis coinciding each other. The distance between the lens and mirror is 10 cm. A point object is placed on principal axis at a distance of 60 cm from t...

The length of a seconds pendulum at a height h = 2R from earth surface will be:
(Given R = Radius of earth and acceleration due to gravity at the surface of earth, g = \(\pi\)2 ms\(-\)2)

An object is taken to a height above the surface of earth at a distance \({5 \over 4}\) R from the centre of the earth. Where radius of earth, R = 6400 km. The percentage decrease in the weight of the object will be :

Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is \(\sqrt2\) times the speed of sound, then the value of n will be :

Let \(\eta_{1}\) is the efficiency of an engine at \(T_{1}=447^{\circ} \mathrm{C}\) and \(\mathrm{T}_{2}=147^{\circ} \mathrm{C}\) while \(\eta_{2}\) is the efficiency at \(\mathrm{T}_{1}=947^{\circ} \mathrm{C}\) and $$\mathrm{T}_{2}=47^{\ci...

A block of ice of mass 120 g at temperature 0\(^\circ\)C is put in 300 g of water at 25\(^\circ\)C. The x g of ice melts as the temperature of the water reaches 0\(^\circ\)C. The value of x is _____________.
[Use specific heat capacity of w...

For a free body diagram shown in the figure, the four forces are applied in the 'x' and 'y' directions. What additional force must be applied and at what angle with positive x-axis so that the net acceleration of body is zero?

An electron with energy 0.1 keV moves at right angle to the earth's magnetic field of 1 \(\times\) 10\(-\)4 Wbm\(-\)2. The frequency of revolution of the electron will be :
(Take mass of electron = 9.0 \(\times\) 10\(-\)31 kg)

A ball is projected from the ground with a speed 15 ms\(-\)1 at an angle \(\theta\) with horizontal so that its range and maximum height are equal, then 'tan \(\theta\)' will be equal to :

A particle is moving in a straight line such that its velocity is increasing at 5 ms\(-\)1 per meter. The acceleration of the particle is _____________ ms\(-\)2 at a point where its velocity is 20 ms\(-\)1.

A drop of liquid of density \(\rho\) is floating half immersed in a liquid of density \({\sigma}\) and surface tension \(7.5 \times 10^{-4}\) Ncm\(-\)1. The radius of drop in \(\mathrm{cm}\) will be :
(g = 10 ms\(-\)2)

The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are \(1 \%, 2 \%\) and \(3 \%\) respectively. The
maximum percentage error in the detection of the dissipated heat will be...

Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the \(\sqrt3\) times of amplitude of individual motions. The phase differen...

A bag of sand of mass 9.8 kg is suspended by a rope. A bullet of 200 g travelling with speed 10 ms\(-\)1 gets embedded in it, then loss of kinetic energy will be :