List of practice Questions

The de Broglie wavelength of a proton is twice the de Broglie wavelength of an alpha particle. The ratio of the kinetic energies of the proton and the alpha particle is:
Suppose an Indian company borrowed 300 dollars from a foreign bank at the beginning of the year and repaid it in dollars along with the agreed interest rate of 12 percent per annum. At the time of borrowing, the exchange rate was Rs. 70 per dollar. Assuming zero inflation rate in both the countries, the real cost of borrowing will be zero if the exchange rate is Rs. per dollar at the time of repayment (rounded off to one decimal place).
The degree of the differential equation \( (y^m)^2 + (\sin y')^4 + y = 0 \) is:
The general solution of \( \frac{dy}{dx} + y = 5 \) is:
The differential equation \( \frac{dy}{dx} + x = A \) (where A is constant) represents:
Find the area of the smaller segment cut-off from the circle \( x^2 + y^2 = 25 \) by \( x = 3 \):
Find the area bounded by the curves \( y = 2x \) and \( y = x^2 \):
Evaluate \( \int_{-\pi/2}^{\pi/2} \sin^9 x \cos^2 x \, dx \):
Evaluate \( \int_0^1 \log \left( \frac{1}{x - 1} \right) \, dx \):
Evaluate \( \int \frac{dx}{x^2 (x^4 + 1)^{3/4}} \):
Evaluate \( \int x e^{x^2} \, dx \):
Evaluate \( \int x \cos x \, dx \):
The integral \( \int \frac{dx}{1 + e^x} \) is:
The limit \( \lim_{x \to 10} \frac{x - 10}{\sqrt{x + 6} - 4} \) is equal to:
The maximum value of \( y = 12 - |x - 12| \) in the range \( -11 \leq x \leq 11 \) is:
The function \( f(x) = 2x^3 + 9x^2 + 12x - 1 \) is decreasing in the interval:
If \( y = \frac{x^2}{x - 1} \), then \( \frac{dy}{dx} \) at \( x = -1 \) is:
If \( y = \tan^{-1} \left( \frac{\cos x - \sin x}{\cos x + \sin x} \right) \), \( \frac{-\pi}{2}<x<\frac{\pi}{2} \), then \( \frac{dy}{dx} \) is:
If \( f(x) = \sin^{-1}(\cos x) \), then \( \frac{d^2 y}{dx^2} \) at \( x = \frac{\pi}{4} \) is:
If \( f(x) = \cos x - \sin x \), and \( x \in \left( \frac{\pi}{4}, \frac{\pi}{2} \right) \), then \( f' \left( \frac{\pi}{3} \right) \) is equal to:
Let \( f(x) = x - \lfloor x \rfloor \), where \( \lfloor \cdot \rfloor \) denotes the greatest integer function and \( x \in (-1, 2) \). The number of points at which the function is not continuous is:
If \( f(x) = \left\{ \begin{array}{ll} mx + 1, & \text{when } x \leq \frac{\pi}{2} \\ \sin x + n, & \text{when } x > \frac{\pi}{2} \end{array} \right. \) is continuous at \( x = \frac{\pi}{2} \), then the values of \( m \) and \( n \) are:
Evaluate \( \lim_{x \to 0} \frac{\sin 2x + \sin 5x}{\sin 4x + \sin 6x} \):
If \( g(x) = -\sqrt{25 - x^2} \), then \( g'(1) \) is:
The mean deviation of the numbers 3, 10, 10, 4, 7, 10 and 5 from the mean is: