List of practice Questions

In a Doppler effect experiment, initially an observer and the source are moving towards each other with equal speeds. The observed frequency in this case is found to be $ f_0 $. The observed frequency once they cross each other is found to be $ f' $. If $ f $ is the frequency at the source, $ f' $ is equal to:

1 gm of ice at 0°C is mixed with 1 gm of water at 100°C. At thermal equilibrium, the temperature of the mixture will be:

Consider two radioactive materials A and B. When A decays into 6.25 percent of its original amount, B decays into 25 percent of its original amount. The ratio of their decay constants $ \lambda_A $ and $ \lambda_B $ is:

In the uranium radioactive series the initial nucleus is $^{238}U$ and the final nucleus is $^{206}Pb$. When the uranium nucleus decays to lead, the number of $\alpha$-particles and $\beta$-particles emitted respectively are:

The ratio of specific heats $ \frac{C_P}{C_V} $ in terms of degrees of freedom (n) is given by:

A transverse wave is described by the equation $ y = A \sin \left( 2 \pi \left( \frac{r}{\lambda} - \frac{t}{T} \right) \right) $. The maximum particle velocity is equal to four times the wave velocity if:

A series R-C combination is connected to an AC voltage of angular frequency $ \omega = 1000 $ rad/s. If the impedance of the RC circuit is $ R/\sqrt{2} $, the time constant (in milliseconds) of the circuit is:

A block of mass 300 g is kept stationary on a smooth inclined plane by applying a minimum horizontal force $ F = \sqrt{a} \, N $ as shown in the figure. The value of $ a $ is (Take $ g = 10 \, \text{m/s}^2 $):

A piece of copper and another of germanium are cooled from room temperature to 100K. The resistance of

Convert the sentence into INDIRECT SPEECH: She said, "I will visit my grandmother tomorrow."

Function of oligodendrocytes is:

If $ A = (1,2,3), B = (3,4,7) $ and $ C = (-3,-2,-5) $ are three points then the ratio in which the point C divides AB externally is

Find the general solution of the differential equation: $$ (xy + y^2)dx - (x^2 - 2xy)dy = 0. $$ is

Which of the following causal analog transfer functions is used to design causal IIR digital filter with transfer function? $$ H(z) = \frac{0.05z}{z-e^{-0.42}} + \frac{0.05z}{z-e^{-0.2}} $$ Assume impulse invariance transformation with $ T = 0.1 \, \text{s} $.

If the lines $ \frac{x-1}{2} = \frac{y-2}{\alpha} = \frac{z-3}{2} $ and $ \frac{x-1}{2} = \frac{y-2}{1} = \frac{z-3}{-2} $ are perpendicular, then the value of $ \alpha $ is:

The inverse Laplace transform of $$ \frac{1}{2s^2 + 3s + 1} $$

If a real-valued function $$ f(x) = \begin{cases} \frac{2x^2 + k(2x) + 9}{3x^2 - 7x - 6}, & \text{for } x \neq 3, \\ l, & \text{for } x = 3 \end{cases} $$ is continuous at $ x = 3 $ and $ l $ is a finite value, then $ l - k = $:

The general solution of the differential equation $$ (y^2 + x + 1) \, dy = (y + 1) \, dx $$ is:

If the differential equation $$ x \, dy + (y + y^2 x) \, dx = 0 $$ with condition $ y = 1 $ at $ x = 1 $, then the solution is:

If the circles $ S = x^2 + y^2 - 14x + 6y + 33 = 0 $ and $ S' = x^2 + y^2 - a^2 = 0 $ (where $ a \in \mathbb{N} $) have 4 common tangents, then the possible number of values of $ a $ is:

If $$ y = 1 + x + x^2 + x^3 + \dots \quad \text{and} \quad |x| < 1, \text{ then } y'' = $$

Evaluate the limit: $$ \lim_{x \to 4} \left( \frac{1}{x - 4} - \frac{5}{x^2 - 3x - 4} \right) $$ is equal to

If the equation of the circle whose radius is 3 units and which touches internally the circle $$ x^2 + y^2 - 4x - 6y - 12 = 0 $$ at the point $(-1, -1)$ is $$ x^2 + y^2 + px + qy + r = 0, $$ then $p + q - r$ is:

In a combustion reaction, heat change during the formation of 40 g of carbon dioxide from carbon and dioxygen gas is (Enthalpy of combustion of carbon = -396 kJ mol$^1$)

Assertion (A): Root pressure does not play a major role in water movement in tall trees.
Reason (R): Root pressure is responsible for pushing up water to small heights in stem.