List of top Questions asked in JEE Main, KCET

A solid sphere (A) of mass \(5m\) and a spherical shell (B) of mass \(m\), both having the same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of \(A\) and \(B\), they start rolling without slipping with accelerations \(a_A\) and \(a_B\) respectively. The ratio of \(a_A\) and \(a_B\) is _____.

Match List-I with List-II.

Choose the correct answer.

The percentage error in the calculated volume of a sphere, if there is \(2%\) error in its diameter measurement, is _____.

Which of the following is NOT a physical or chemical characteristic of interstitial compounds?

Correct statements from the following are:
A. Nitrogen in oxidation states from \(+1\) to \(+4\) disproportionates in acid medium.
B. Nitrogen has the ability to form \(d\pi - p\pi\) multiple bonds with itself and other elements with small size and high electronegativity.
C. N-N single bond is stronger than P-P single bond.
D. Nitrogen has highest density in its group due to small size.
E. The maximum covalency of nitrogen is four since it has only four valence orbitals for bonding.

Given below are two statements:
Statement I: The correct order of electronegativity of fluorine, oxygen and nitrogen is \(F>O>N\).
Statement II: The oxidation state of oxygen in \(OF_2\) is \(+2\) and in \(Na_2O\) is \(-2\).

Arrange the following resultant mixtures in increasing order of their pH values}
A. \(10 \text{ mL } 0.2 \text{ M Ca(OH)}_2 + 25 \text{ mL } 0.1 \text{ M HCl}\)
B. \(10 \text{ mL } 0.01 \text{ M H}_2\text{SO}_4 + 10 \text{ mL } 0.01 \text{ M Ca(OH)}_2\)
C. \(10 \text{ mL } 0.1 \text{ M H}_2\text{SO}_4 + 10 \text{ mL } 0.1 \text{ M KOH}\)

\(M_3A_2\) is a sparingly soluble salt of molar mass \(y \text{ g mol}^{-1}\) and solubility \(x \text{ g L}^{-1}\). The ratio of the molar concentration of the anion (\(A^{3-}\)) to the solubility product (\(K_{sp}\)) of the salt is:

Identify the correct statements from the following :}
A. Heisenberg uncertainty principle is applicable to electrons.
B. The size of \(2p_x\) orbital is less than the size of \(3p_x\) orbital.
C. The energy of \(2s\) orbital of H atom is equal to the energy of \(2s\) orbital of Li.
D. The electronic configuration of Cr is \([Ar] 3d^5 4s^1\)

Arrange the following atomic orbitals of multi electron atoms in order of increasing energy.
A. \(n=3, l=2, m=+1\)
B. \(n=4, l=0, m=0\)
C. \(n=6, l=1, m=0\)
D. \(n=5, l=1, m=+1\)
E. \(n=2, l=1, m=+1\)

How many grams of residue is obtained by heating \(2.76 \text{ g}\) of silver carbonate? (Given : Molar mass of C, O and Ag are 12, 16 and \(108 \text{ g mol}^{-1}\) respectively)

In the given circuit below inductance values of \(L_1, L_2\) and \(L_3\) are same. The magnetic energy stored in the entire circuit is \((U_t)\) and that stored in the \(L_2\) inductor is \((U_j)\). \(U_t / U_j\) is ____. (Ignore the mutual inductance if any).

The charged particle moving in a uniform magnetic field of \((3\hat{i} + 2\hat{j}) \text{ T}\) has an acceleration \((4\hat{i} - \frac{x}{2}\hat{j}) \text{ m/s}^2\). The value of \(x\) is ____.

A transverse wave on a string is described by \(y = 3\sin(36t + 0.018x + \pi/4)\), where \(x, y\) are in cm and \(t\) in seconds. The least distance between the two successive crests in the wave is ____ \text{cm}. (Nearest integer) (\(\pi = 3.14\))}

From \(18 \text{ m}\) height above the ground a ball is dropped from rest. The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is ____ \text{m}. (Take \(g = 10 \text{ m/s}^2\) and neglect air resistance)}

A cube has side length \(5 \text{ cm}\) and modulus of rigidity \(10^5 \text{ N/m}^2\). The displacement produced by a force of \(10 \text{ N}\) in the upper face of the cube is ____ \text{mm}.

For the given logic circuit, which of the following inputs combination will make both LED-1 and LED-2 to glow?}

An a.c. source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current is observed as $I$. Now the frequency of the source is changed to $\omega/4$, (keeping the voltage unchanged) the current is found to be $I/3$. The ratio of resistance to reactance at frequency $\omega$ is:

Two wires as shown in the figure below, made of steel and have breaking stress of $12 \times 10^8 \text{ N/m}^2$. Area of cross-section of upper wire is $0.008 \text{ cm}^2$ and of lower wire is $0.004 \text{ cm}^2$. The maximum mass that can be added to pan without breaking any wire is _________ kg. (take $g = 10 \text{ m/s}^2$)}

A compound microscope is designed with two symmetric biconvex lenses. The objective lens is cut vertically, creating two identical plano-convex lenses. One of them is used in place of original objective lens. To retain same magnification keeping the object distance unchanged, the tube length has to be:

Light source having wavelength 331 nm is used to generate photo-electrons whose stopping potential is 0.2 V. The work function of the used metal in the experiment is $\alpha \times 10^{-19} \text{ J}$. The value of $\alpha$ is ______. ($h = 6.62 \times 10^{-34} \text{ Js}, e = 1.6 \times 10^{-19} \text{ C and } c = 3 \times 10^8 \text{ m/s}$)

A ray of light passing through an equilateral prism is having velocity $2.12 \times 10^8 \text{ m/s}$ in the prism material, then the minimum angle of deviation is _______ degrees.

In Young's double slit experiment, the fringe width of the interference pattern produced on the screen is $2.4 \mu \text{m}$. If the experiment is carried out in another medium having refractive index 1.2, the fringe width will be _______ $\mu \text{m}$.

Refer to the figure given below, current between terminals $A$ and $B$ is _____}

A displacement current of 4.0 A can be set up in the space between two parallel plates of $6 \mu \text{F}$ capacitor. The rate of change of potential difference across the plates of the capacitor is nearly $\alpha \times 10^6 \text{ V/s}$. The value of $\alpha$ is _________.