List of practice Questions

If the sum of the first \(n\) terms of an A.P. is \(3n^2 + 5n\), then the 10th term is:
A stone is dropped from a height of 80 m. At the same instant, another stone is projected vertically upwards from the ground with a speed of 40 m/s. The time after which they meet is (\(g = 10\ \text{m/s}^2\)):
The potential energy of a particle of mass 2 kg moving along x-axis is given by \(U = (x^2 - 4x)\) J. The force acting on it at \(x = 3\) m is:
Light of wavelength 600 nm is incident on a metal surface with work function 2 eV. The maximum kinetic energy of photoelectrons is:
A transformer has 500 turns in primary and 100 turns in secondary. If input voltage is 220 V AC, the output voltage is:
If the roots of the equation \(x^3-6x^2+11x-6=0\) are in A.P., the common difference is:
The value of \(\displaystyle \int_{-\infty}^{\infty} e^{-x^2}\,dx\) is:
The angle between the planes \(2x-y+z=6\) and \(x+y+2z=7\) is:
Complete the series: \(7,\,10,\,16,\,25,\,37,\,?\)
A uniform rod of length \(L\) and mass \(M\) is pivoted at one end and displaced by a small angle \(\theta\) from vertical. The time period of small oscillations is:
A charged particle enters a uniform magnetic field perpendicular to its velocity. If the field is suddenly doubled, the radius of its path becomes:
In a series LCR circuit at resonance, the voltage across the inductor is 100 V and across the capacitor is 100 V. The voltage across the resistor is:
The de Broglie wavelength of an electron accelerated through 100 V is approximately:
The probability of getting exactly 2 heads in 4 tosses of a fair coin is:
A man is 4 times as old as his son. After 5 years, he will be 3 times as old as his son. The present age of the son is:
The solution of the equation \(\sin x + \cos x = 0\) in \([0,2\pi]\) is:
The value of \(\lim_{x\to0}\frac{\sin 3x}{x}\) is:
If the matrix \(\begin{bmatrix}1 & 2\\ 3 & 4\end{bmatrix}\) has determinant \(k\), then the determinant of its adjoint is:
The work done by a conservative force in a closed path is:
A particle moves with uniform acceleration along a straight line. The average velocity over an interval is equal to the instantaneous velocity at:
The unit of electric field intensity is:
In a p-n junction diode, the reverse saturation current doubles for every rise in temperature of:
The number of terms in the expansion of \((a+b+c)^5\) is:
The differential equation \(\frac{dy}{dx}=\frac{y}{x}\) represents:
If the vectors \(2\hat{i}+3\hat{j}+\hat{k}\) and \(4\hat{i}-\hat{j}+2\hat{k}\) are perpendicular, the value of \(\lambda\) in \(\lambda\hat{i}+2\hat{j}+3\hat{k}\) is: