List of top Questions asked in JEE Main, KCET

The mean deviation about the mean for the data

56 is equal to:

A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the envelope just two consecutive letters AN are visible. The probability, that the letter came from ANANTPUR, is:

Let tan A, tan B, where A, B $\in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$, be the roots of the quadratic equation $x^2 - 2x - 5 = 0$. Then $20 \sin^2\left(\frac{A+B}{2}\right)$ is equal to:

The sum $\sum_{n=1}^{10} \frac{528}{n(n+1)(n+2)}$ is equal to:

Let A be a 3 x 3 matrix such that
$A^T \begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix} = \begin{pmatrix} 5 \\ 2 \\ 2 \end{pmatrix}$, $A \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} = \begin{pmatrix} 3 \\ 1 \\ 1 \end{pmatrix}$, $A \begin{pmatrix} 1 \\ 0 \\ 1 \end{pmatrix} = \begin{pmatrix} 3 \\ 4 \\ 4 \end{pmatrix}$ and $A \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix} = \begin{pmatrix} 1 \\ 3 \\ 1 \end{pmatrix}$
If det(A) = 1, then det(adj($A^2$ + A)) is equal to:

Let a, b $\in$ C. Let $\alpha, \beta$ be the roots of the equation $x^2 + ax + b = 0$. If $\beta-\alpha =\sqrt{11}$ and $\beta^2-\alpha^2 = 3i\sqrt{11}$, then $(\beta^3 - \alpha^3)^2$ is equal to:

The correct statements among the following are:
A. Mo(VI) and W(VI) are less stable than Cr(VI).
B. Ce⁴⁺ and Tb⁴⁺ are oxidant while Eu²⁺ and Yb²⁺ are reductant.
C. Cm and Am have seven unpaired electrons.
D. Actinoid contraction is greater from element to element than lanthanoid contraction.
Choose the correct answer:

Statement I: The covalency of oxygen is generally two but it can exceed up to four. The oxidation state of oxygen in SO₂ is -2 and in OF₂ it is +2.
Statement II: The anomalous behaviour of oxygen when compared to the other elements of group 16 is due to its small size and high electronegativity.
In the light of the above statements, choose the correct answer:

A monoatomic anion (A⁻) has 45 neutrons and 36 electrons. Atomic mass, group in the periodic table and physical state at room temperature of the element (A) respectively are

Consider the first order reaction R → P. The fraction of molecules decomposed in the given first order reaction can be expressed as

In order to oxidise a mixture of 1 mole each of FeC₂O₄, Fe₂(C₂O₄)₃, FeSO₄ and Fe₂(SO₄)₃ in acidic medium, the number of moles of KMnO₄ required is

At T(K), the equilibrium constant of \(A_2(g) + B_2(g) \rightleftharpoons C(g)\) is \(2.7 \times 10^{-5}\). What is the equilibrium constant for \(\frac{1}{3} A_2(g) + \frac{1}{3} B_2(g) \rightleftharpoons \frac{1}{3} C(g)\) at the same temperature?

Statement I: For an ideal gas, heat capacity at constant volume is always greater than the heat capacity at constant pressure.
Statement II: In a constant volume process, no work is produced and all the heat withdrawn goes into the chaotic motion and is reflected by a temperature increase of the ideal gas.
In the light of the above statements, choose the correct answer:

Which of the following is correct set of 4 quantum numbers of 19th electron in Chromium (Atomic number = 24) in accordance with Aufbau principle?

What is the ratio of wave number of first line (lowest energy line) of Balmer series of H atomic spectrum to first line of its Brackett series?

An inductor of 10 mH, capacitor of 0.1 µF and a resistor of 100 Ω are connected in series across an a.c power supply 220 V, 70 Hz. The power factor of the given circuit is 0.5. The difference in the inductive reactance and capacitance reactance is \(\sqrt{3} a\) Ω. The value of \(a\) is ______.

A body of mass 2 kg begins to move under the influence of time dependent force \(\vec{F} = (2t \hat{i} + 6t^2 \hat{j})\) N, where \(\hat{i}\) and \(\hat{j}\) are unit vectors along x and y-axis respectively. The power produced by the force at \(t = 2\) s is ______ W.

The velocity of a particle executing simple harmonic motion along x-axis is described as \(v^2 = 50 - x^2\), where \(x\) represents displacement. If the time period of motion is \(\pi/7\) s, the value of \(x\) is ______.

The surface tension of a soap solution is \(3.5 \times 10^{-2}\) N/m. The work required to increase the radius of a soap bubble from 1 cm to 2 cm is \(\alpha \times 10^{-6}\) J. The value of \(\alpha\) is ______. (\(\pi = 22/7\))

A 1 kg block subjected to two simultaneous forces \((2\hat{i} + 3\hat{j} + 4\hat{k})\) N and \((3\hat{i} - \hat{j} - 2\hat{k})\) N is moved a distance of 25 m along \((3\hat{i} - 4\hat{j})\) direction. The work done in this process is ______ J.

An unpolarized light is incident on the plane interface of air-dielectric medium shown in figure. If the incident angle is equal to Brewster angle, identify the expression representing reflected wave.

A telescope with objective diameter \(R\) is used to observe a distant star emitting light of wavelength 500 nm, at a resolution of \(5 \times 10^{-7}\) radian. The value of \(R\) is ________ cm.

The voltage and the current between A and B points shown in the circuit are ________.

Consider a circuit consisting of a capacitor (20 μF), resistor \((100 \Omega)\) and two identical diodes as shown in figure. The resistance of diode under forward biasing condition is 10 Ω. The time constant of the circuit is \(\alpha \times 10^{-3}\) s. The value of \(\alpha\) is ________.

An insulated wire is wound so that it forms a flat coil with \(N = 200\) turns. The radius of the innermost turn is \(r_1 = 3\) cm, and of the outermost turn \(r_2 = 6\) cm. If 20 mA current flows in it then the magnetic moment will be \(\alpha \times 10^{-2}\) A.m². The value of \(\alpha\) is ______.