List of practice Questions

Two silicon diodes are connected to a battery and two resistors as shown in the figure. The current through the battery is __________ A (rounded off to two decimal places).
Two silicon diodes are connected to a battery and two resistors
Given: The forward voltage drop across each diode = 0.7 V
At the planar interface of two dielectrics, which of the following statements related to the electric field (\(\vec{𝐸}\) ), electric displacement (\(\vec{D}\)) and polarization (\(\vec{P}\) ) is true ?
The absolute error in the value of sin𝜃 if approximated up to two terms in the Taylor’s series for 𝜃 = 60∘ is ___________ (rounded off to three decimal places).
A single pendulum hanging vertically in an elevator has a time period 𝑇0 when the elevator is stationary. If the elevator moves upward with an acceleration of 𝑎 = 0.2𝑔, the time period of oscillations is 𝑇1. Here 𝑔 is the acceleration due to gravity. The ratio\( \frac{𝑇_0}{ 𝑇_1}\) is (rounded off to two decimal places).
A spacecraft has speed 𝑣𝑠=𝑓𝑐 with respect to the earth, where 𝑐 is the speed of light in vacuum. An observer in the spacecraft measures the time of one complete rotation of the earth to be 48 hours. The value of 𝑓 is (rounded off to two decimal places).
The sum of the x-components of unit vectors 𝑟̂ ̇ and 𝜃̂̇ for a particle moving with angular speed 2 rad s -1 at angle 𝜃 = 215° is__________ (rounded off to two decimal places)
Consider a spring mass system with mass 0.5 kg and spring constant 𝑘 = 2 Nm-1 in a viscous medium with drag coefficient 𝑏 = 3 kg s -1 . The additional mass required so that the motion becomes critically damped is _______ kg (rounded off to three decimal places)
Unit vector normal to the equipotential surface of 𝑉(𝑥, 𝑦, 𝑧) =4𝑥2+𝑦2 + 𝑧 at (1,2,1) is given by (𝑎𝑖̂+ 𝑏𝑗̂+ 𝑐𝑘̂). The value of |𝑏| is (rounded off to two decimal places).
For the Maxwell-Boltzmann speed distribution, the ratio of the root-mean-square speed (vrms) and the most probable speed (vmax) is
Given : Maxwell-Boltzmann speed distribution function for a collection of particles of mass m is
\(f(v)=(\frac{m}{2\pi k_BT})^{3/2}4\pi v^2\text{exp}(-\frac{mv^2}{2k_BT})\)
where, v is the speed and kBT is the thermal energy.
A rectangular pulse of width 0.5 cm is travelling to the right on a taut string (shown by full line in the figure) that has mass per unit length 𝜇1. The string is attached to another taut string (shown by dashed line) of mass per unit length 𝜇2. If the tension in both the strings is the same, and the transmitted pulse has width 0.7 cm, the ratio 𝜇1⁄𝜇2 is _______(rounded off to two decimal places)
A rectangular pulse of width 0.5 cm is travelling to the right on a taut string
An α particle with energy of 3 MeV is moving towards a nucleus of 50Sn. Its minimum distance of approach to the nucleus is 𝑓×10−14 m. The value of 𝑓 is ________ (rounded off to one decimal place).
An enzyme (E) catalyzes the biochemical reaction \(A \rightarrow B\) with \(k_{\text{cat}}=500~\text{s}^{-1}\). If the initial reaction velocity \((V_0)\) is \(10~\mu\text{M}\cdot\text{s}^{-1}\) at the total enzyme concentration \([E_t]=30~\text{nM}\) and substrate concentration \([A]=40~\mu\text{M}\), the value of \(K_m\) (in \(\mu\text{M}\)) is ________________.
In a X-Ray tube operating at 20 kV, the ratio of the de-Broglie wavelength of the incident electrons to the shortest wavelength of the generated X-rays is ________ (rounded off to two decimal places).
Given: e/m ratio for an electron = 1.76×1011 Ckg-1 and the speed of light in vacuum is 3×108 ms -1
A point source emitting photons of 2 eV energy and 1 W of power is kept at a distance of 1m from a small piece of a photoelectric material of area 10-4 m2 . If the efficiency of generation of photoelectrons is 10%, then the number of photoelectrons generated are 𝑓×1012 per second. The value of 𝑓 is __________ (rounded off to two decimal places).
Given: 1eV = 1.6 × 10−19 J
photoelectrons
Consider the 𝛼-decay 90𝑇ℎ 232→88𝑅𝑎 228 . In an experiment with one gram of 90𝑇ℎ 232, the average count rate (integrated over the entire volume) measured by the 𝛼-detector is 3000 counts s -1 . If the half life of 90𝑇ℎ 232 is given as 4.4 × 1017 s, then the efficiency of the 𝛼-detector is ______(rounded off to two decimal places).
Given: Avogadro’s number = 6.023 × 1023 mol−1
Let 𝑋1,𝑋2, … , 𝑋𝑛 be a random sample from a population having the probability density function
\(f(x;μ) =\begin{cases} \frac{1}{2}e-(\frac{x-2μ}{2}), & \quad \text{if }0>2μ,\\ 0, & \quad Otherwise \end{cases}\)
where −∞ < 𝜇 < ∞. For estimating 𝜇, consider estimators
\(T_1=\frac{\overline{X}-2}{2}\) and  \(T_2=\frac{nX_{(1)}-2}{2n}\)
where 𝑋̅ =\(\frac{1 }{𝑛} ∑^n_{i=1} x_i\) and Xi and X(i)=min{𝑋1, 𝑋2, … , 𝑋𝑛}. Then, which one of the following statements is TRUE?
Let 𝑋1,𝑋2, … , 𝑋𝑛 be a random sample from a \(u(θ +\frac{σ}{\sqrt3},θ+\sqrt3σ)\) distribution, where 𝜃 ∈ ℝ and 𝜎>0 are unknown parameters. Let 𝑋̅ =\(\frac{ 1}{ 𝑛} ∑^n _{i=1}X_i\) and \(𝑆 =\sqrt \frac{1}{n} ∑^n_{i=1}(X_i-\overline{X})^2\) Let \(\^θ\) and \(\^σ\) be the method of moment estimators of 𝜃 and 𝜎 ,respectively. Then, which one of the following statements is FALSE?

विशिष्ट-विभक्तेः उपयोगं कृत्वा वाक्यनिर्माणं कुरुत। (4 तः 2)
कृते
 

विशिष्ट-विभक्तेः उपयोगं कृत्वा वाक्यनिर्माणं कुरुत। (4 तः 2)
स्निह् (4 प.प.)
 

विशिष्ट-विभक्तेः उपयोगं कृत्वा वाक्यनिर्माणं कुरुत। (4 तः 2)
अलम्
 

विशिष्ट-विभक्तेः उपयोगं कृत्वा वाक्यनिर्माणं कुरुत। (4 तः 2)
कथ् (10 उ.प.)
 

योग्यं पर्यायं चिनुत। (3 तः 2)
वानराः फलानि खादन्ति। \(\underline{\hspace{1cm}}\) (मधुराणि/मधुराः)
 

The values of x and y, if (x 567)8+ (2yx5)8 = (71yx)8

योग्यं पर्यायं चिनुत। (3 तः 2)
त्वं द्रष्टुं \(\underline{\hspace{1cm}}\) । (शक्नोषि/शक्नोति)
 

योग्यं पर्यायं चिनुत। (3 तः 2)
पृथुभूपेन धनुः सज्जीकृतम् । (कर्तृवाच्यम्/कर्मवाच्यम्)