List of practice Questions

In a flowering plant, a cross is made between a homozygous dominant tall plant (TT) and a homozygous recessive dwarf plant (tt). What is the phenotypic ratio of the F1 generation?

Which of the following enzymes is responsible for breaking down starch into maltose during digestion in humans?

The wavelength of the light emitted by a hydrogen atom during a transition from \( n = 3 \) to \( n = 2 \) is \( 656.3 \, \text{nm} \). What is the energy of the photon emitted during this transition?

In the reaction \( 2 \, \text{H}_2 + \text{O}_2 \rightarrow 2 \, \text{H}_2\text{O} \), how many moles of water are produced when 4 moles of hydrogen react with excess oxygen?

A gas absorbs \( 100 \, \text{J} \) of heat while performing \( 40 \, \text{J} \) of work on its surroundings. Calculate the change in internal energy of the gas.

A cylindrical pipe has a radius of \( 0.1 \, \text{m} \). If the speed of water flowing through the pipe is \( 2 \, \text{m/s} \), calculate the volume flow rate of water through the pipe.

For a reaction, the rate law is given by \( \text{rate} = k[A]^2[B] \). If the concentration of \( A \) is doubled and the concentration of \( B \) is halved, how will the rate of the reaction change?

A gas in a cylinder is compressed from an initial volume of \( 5 \, \text{m}^3 \) to a final volume of \( 2 \, \text{m}^3 \) while maintaining a constant pressure of \( 1 \times 10^5 \, \text{Pa} \). Calculate the work done by the gas during the compression.

A long straight wire carries a current of 10 A. A proton moves parallel to the wire at a distance of 0.05 m with a velocity of \( 2 \times 10^5 \, \text{m/s} \) in the same direction as the current. Find the magnitude of the magnetic force acting on the proton. (Given: Charge of proton \( q = 1.6 \times 10^{-19} \, \text{C} \), permeability of free space \( \mu_0 = 4\pi \times 10^{-7} \, \text{Tm/A} \)).

A ball is thrown vertically upward with an initial velocity of \( 20 \, \text{m/s} \). Calculate the time taken for the ball to reach its maximum height.

The switch (S) closes at \( t = 0 \) sec. The time, in sec, the capacitor takes to charge to 50 V is _________ (round off to one decimal place).

The op-amps in the following circuit are ideal. The voltage gain of the circuit is __________(round off to the nearest integer).

Let \( C \) be a clockwise oriented closed curve in the complex plane defined by \( |z| = 1 \). Further, let \( f(z) = jz \) be a complex function, where \( j = \sqrt{-1} \). Then, \[ \oint_C f(z)\, dz = \underline{2cm} \quad \text{(round off to the nearest integer)}. \]

Let \( (x, y) \in \mathbb{R}^2 \). The rate of change of the real-valued function \[ V(x, y) = x^2 + x + y^2 + 1 \] at the origin in the direction of the point \( (1, 2) \) is __________ (round off to the nearest integer).

Consider ordinary differential equations given by \[ \frac{dx_1(t)}{dt} = 2x_2(t), \quad \frac{dx_2(t)}{dt} = r(t) \] with initial conditions \( x_1(0) = 1 \) and \( x_2(0) = 0 \). If \[ r(t) = \begin{cases} 1, & t \geq 0 \\ 0, & t < 0 \end{cases} \] then at \( t = 1 \), \( x_1(t) = \underline{2cm} \) (round off to the nearest integer).

Let \( \mathbf{a}_R \) be the unit radial vector in the spherical coordinate system. For which of the following value(s) of \( n \), the divergence of the radial vector field \( \mathbf{f}(R) = \mathbf{a}_R \frac{1}{R^n} \) is independent of \( R \)?

An air filled cylindrical capacitor (capacitance \( C_0 \)) of length \( L \), with \( a \) and \( b \) as its inner and outer radii, respectively, consists of two coaxial conducting surfaces. Its cross-sectional view is shown in Fig. (i). In order to increase the capacitance, a dielectric material of relative permittivity \( \varepsilon_r \) is inserted inside 50% of the annular region as shown in Fig. (ii). The value of \( \varepsilon_r \) for which the capacitance of the capacitor in Fig. (ii), becomes \( 5C_0 \) is

In the system shown below, the generator was initially supplying power to the grid. A temporary LLLG bolted fault occurs at \( F \) very close to circuit breaker 1. The circuit breakers open to isolate the line. The fault self-clears. The circuit breakers reclose and restore the line. Which one of the following diagrams best indicates the rotor accelerating and decelerating areas?

In the following circuit, the average voltage \[ V_o = 400 \left(1 + \frac{\cos \alpha}{3} \right) {V}, \] where \( \alpha \) is the firing angle. If the power dissipated in the resistor is 64 W, then the closest value of \( \alpha \) in degrees is:

An ideal sinusoidal voltage source \( v(t) = 230\sqrt{2} \sin(2\pi \times 50t) \, \text{V} \) feeds an ideal inductor \( L \) through an ideal SCR with firing angle \( \alpha = 0^\circ \). If \( L = 100 \, \text{mH} \), then the peak of the inductor current, in ampere, is closest to:

The 3-phase modulating waveforms \( v_a(t), v_b(t), v_c(t) \), used in sinusoidal PWM in a Voltage Source Inverter (VSI) are given as: \[ v_a(t) = 0.8 \sin(\omega t) \quad v_b(t) = 0.8 \sin\left(\omega t - \frac{2\pi}{3}\right) \quad v_c(t) = 0.8 \sin\left(\omega t + \frac{2\pi}{3}\right) \] where \( \omega = 2\pi \times 40 \, {rad/s} \) is the fundamental frequency. The modulating waveforms are compared with a 10 kHz triangular carrier whose magnitude varies between +1 and -1. The VSI has a DC link voltage of 600 V and feeds a star connected motor. The per phase fundamental RMS motor voltage, in volts, is closest to:

A DC series motor with negligible series resistance is running at a certain speed driving a load, where the load torque varies as cube of the speed. The motor is fed from a 400 V DC source and draws 40 A armature current. Assume linear magnetic circuit. The external resistance, in \( \Omega \), that must be connected in series with the armature to reduce the speed of the motor by half, is closest to:

The transformer connection given in the figure is part of a balanced 3-phase circuit where the phase sequence is “abc”. The primary to secondary turns ratio is 2:1. If \( I_a + I_b + I_c = 0 \), then the relationship between \( I_A \) and \( I_{ad} \) will be:

The continuous-time unit impulse signal is applied as an input to a continuous-time linear time-invariant system \( \mathcal{S} \). The output is observed to be the continuous-time unit step signal \( u(t) \). Which one of the following statements is true?

Let \( G(s) = \frac{1}{(s+1)(s+2)} \). Then the closed-loop system shown in the figure below is: