List of practice Questions

The sum of the first n terms of the series $$ 1^2 + 2 \cdot 2^2 + 3^2 + 2 \cdot 4^2 + 5^2 + 2 \cdot 6^2 + \cdots $$ is $$ \frac{n(n + 1)^2}{2} \quad \text{when n is even. When n is odd the sum is} $$

What is the total marks obtained by Meera in all the subjects?

What is the average marks obtained by these seven students in History? (rounded off to two digits)

A series is given, with one term missing. Choose the correct alternative from the given ones that will complete the series. \[ 5, 11, 24, 51, 106, \_ ? \]

In which of the following cases it was decided that a contract with a minor is void?

A group of N people worked on a project.They finished $35\%$ of the project by working 7 hours a day for 10 days.Thereafter,10 people left the group and the remaining people finished the rest of the project in 14 days by working 10 hours a day.Then the value of N is

If$\begin{array}{l}1 + \left(2 + ^{49}C_1 + ^{49}C_2 + … ^{49}C_{49}\right) \left(^{50}C_2 + ^{50}C_4 + … ^{50}C_{50}\right) \end{array}$is equal to 2ⁿ. m, where m is odd, then n + m is equal to ______.

The terminal acceptor of electron during anaerobic respiration in $\textit{Methanococcus}$ is _________.

Molar conductance of monobromoacetic acid at infinite dilution is calculated to be $ x \times 10^{-4} \, \text{S m}^2 \, \text{mol}^{-1} $ $\text{at 25°C.} $The value of $ x $ is (round off to the nearest integer).

Consider the function $ f(z) = \frac{1}{(z+1)(z+2)(z+3)} $. The residue of $ f(z) $ at $ z = -1 $ is _________.

In the circuit shown, the load is driven by a sinusoidal ac voltage source $ V_1 = 100 \angle 0^\circ \, \text{V} $ at 50 Hz. Given $ R_1 = 20 \, \Omega $, $ C_1 = \left(\frac{1000}{\pi}\right) \, \mu\text{F} $, $ L_1 = \left(\frac{20}{\pi}\right) \, \text{mH} $, and $ R_2 = 4 \, \Omega $, the power factor is _________ (round off to one decimal place)

A capacitor is constructed using two concentric spheres and air as the dielectric medium (permittivity of air = $8.854 \times 10^{-12} \, \text{F/m}$). The radii of the inner and outer spheres are $a = 10 \, \text{cm}$ and $b = 15 \, \text{cm}$, respectively. The capacitance (in picofarads) is _________ (round off to 2 decimal places).

A 1 kHz sine-wave generator having an internal resistance of 50Ω generates an open-circuit voltage of 10 Vp-p. When a capacitor is connected across the output terminals, the voltage drops to 8 Vp-p. The capacitance of the capacitor (in microfarads) is _________.

In the circuit shown, the capacitance $ C_0 = 10 \, \mu\text{F} $ and inductance $ L_0 = 1 \, \text{mH} $ and the diode is ideal. The capacitor is initially charged to 10 V and the current in the inductor is initially zero. If the switch is closed at $ t = 0 \, \text{s} $, the voltage $ V_C(t) $ (in volts) across the capacitor at $ t = 0.5 \, \text{s} $ is _________ (round off to one decimal place)

The bridge shown is balanced when $ R_1 = 100 \, \Omega $, $ R_2 = 210 \, \Omega $, $ C_2 = 2.9 \, \mu\text{F} $, and $ R_4 = 50 \, \Omega $. The 2 kHz sine-wave generator supplies a voltage of 10 V$_\text{p-p}$. The value of $ L_3 $ (in millihenry) is _________ (round off to two decimal places)

In the circuit shown, the switch is initially closed. It is opened at $ t = 0 \, \text{s} $ and remains open thereafter. The time (in milliseconds) at which the output voltage $ V_{\text{out}} $ becomes LOW is _________ (round off to three decimal places).

In the Wheatstone bridge circuit shown, $ R_1 = 1.5 \, k\Omega $ and $ R_2 = R_3 = R_4 = 1 \, k\Omega $. The switch is initially open and the voltage between the points C and D is $ V_{CD} $. Upon closing the switch at $ t = 0 $, the resistance in the arm AD changes by an amount $ \delta R_1 $, and the voltage between C and D changes by $ \delta V_{CD} $. The sensitivity of the bridge in volt/kilohm, defined as $ \left| \frac{\delta V_{CD}}{\delta R_1} \right| $, is _________.

Monochromatic light of wavelength 532 nm is used to measure the absorption coefficient of a material in a UV-Visible Spectrophotometer. The measured light intensity after transmission through a 1 cm thick sample of the material is 0.414 mW/cm$^2$. For a sample of thickness 2 cm, the measured light intensity is 0.186 mW/cm$^2$. The absorption coefficient (in cm$^{-1}$) of the material is _________ (round off to two decimal places)

In a unity-gain feedback control system, the plant \[ P(s) = \frac{0.001}{s(2s + 1)(0.01s + 1)} \] is controlled by a lag compensator \[ C(s) = \frac{s + 10}{s + 0.1} \] The slope (in dB/decade) of the asymptotic Bode magnitude plot of the loop gain at $ \omega = 3 \, \text{rad/s} $ is _________ (in integer).

Given Circuit A with currents $I_1$ and $I_2$ as shown, the current $I_3$ in Circuit B (in amperes) is _________ (round off to one decimal place).

In the balanced three-phase circuit shown, $ C_0 = 8.2 \, \mu F $ and the line-to-line r.m.s. voltage is 440 V at 50 Hz. The reading on the wattmeter (in watts) is _________.

The circuit shown is driven by a sinusoidal input voltage, $ V_{\text{in}} $, resulting in the output voltage, $ V_{\text{out}} $. The frequency (in kilohertz) at which the voltage gain is 0 dB is _________ (round off to two decimal places)