List of practice Questions

The motion of a particle is given by $X = a \cos t$, $Y = a \sin t$ and $Z = t$. The trajectory traced by the particle as a function of time is:

When is the Earth Day celebrated every year?

A basket contains 12 apples in which 3 are rotten. If 3 apples are drawn at random simultaneously from it, then the probability of getting at most one rotten apple is:

If \[ \int \log \left( 6\sin^2x + 17\sin x + 12 \right)^{\cos x} \, dx = f(x) + c \] then, \[ f\left(\frac{\pi}{2}\right) = \]

The angle between the line with the direction ratios $ (2, 5, 1) $ and the plane $ 8x + 2y - z = 4 $ is given by

If the roots of $\sqrt{\frac{1 - y}{y}} + \sqrt{\frac{y}{1 - y}} = \frac{5}{2}$ are $\alpha$ and $\beta$ ($\beta > \alpha$) and the equation $(\alpha + \beta)x^4 - 25\alpha \beta x^2 + (\gamma + \beta - \alpha) = 0$ has real roots, then a possible value of $y$ is:

The number of subsets of the set A = {p,q} is

A capacitor of capacitance $ C $ and potential $ V $ has energy $ E $. It is connected to another capacitor of capacitance $ 2C $ and potential $ 2V $. Then the loss of energy is $ \frac{x}{3} E $, where $ x $ is $ \_\_\_\_ $.

The atoms of $^ {6}C^{13}$ and $^ {7}N^{14}$ are considered as:

Predict the type of cubic lattice of a solid element having edge length of 400 pm and density of 6.25 g/ml.
(Atomic mass of element = 60)

Starting from $ x_0 = 1 $, one step Newton-Raphson method in solving the equation $ x^3 + 3x - 7 = 0 $ gives the next value as

A body is thrown with a velocity $ (5\hat{i} + 6\hat{j}) \, \text{m/s} $. Its maximum height is (given that acceleration due to gravity = $ 10 \, \text{m/s}^2 $):

Peritectic reaction among the following is

In QAM, both ______ of a carrier frequency are varied.