List of practice Questions

If the number of electron-hole pairs per cm\(^3\) of an intrinsic Si wafer at temperature 300 K is \(1.1 \times 10^{10}\) and the mobilities of electrons and holes at 300 K are 1500 and 500 cm\(^2\) per volt, second, respectively, then the conductivity of the Si wafer at this temperature (in \(\mu\)mho cm\(^{-1}\)) is nearly:
In a radioactive sample \( 2 \times 10^8 \) nuclei reduce to \( 10^8 \) nuclei in 15 minutes, then the half-life of the sample in minutes is:

Let \( I = \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{\tan^2 x}{1+5^x} \, dx \). Then:

Which of the following statement is correct?
If \( z = x + iy \) and the point \( P \) represents \( z \) in the Argand plane. If the amplitude of \( \frac{2z-i}{z+2i} \) is \( \frac{\pi}{4} \), then the equation of the locus of \( P \) is:
In \( \triangle ABC \), if \( (r_2 - r_1)(r_3 - r_1) = 2r_2r_3 \), then \( 2(r + R) = \):
If 35 is removed from the data 30, 34, 35, 36, 37, 38, 39, 40, then the median increases by
If \(\cos x + \cos y = \tfrac{2}{3}\) and \(\sin x - \sin y = \tfrac{3}{4}\), then \[ \sin(x - y) \;+\; \cos(x - y) \;=\;? \]
If R is the resistance of a conductor of length l, then
Among the oxides SiO\(_2\), SO\(_2\), Al\(_2\)O\(_3\), and P\(_2\)O\(_5\), the correct order of acidic strength is:
The power of a lens of focal length 20 cm is
Given below are two statements
Statement - I: For isothermal irreversible change of an ideal gas, \[ q = -w = P_{\text{ext}}(V_{\text{final}} - V_{\text{initial}}) \] Statement - II: For adiabatic change, \[ \Delta U = W_{\text{adiabatic}} \] The correct answer is:
The common ratio of a G.P. is \( \frac{1}{2} \). If the product of the first three terms is 64, then the sum of the first 10 terms is:
If the ratio of the absolute temperature of the sink and source of a Carnot engine is changed from 2:3 to 3:4, the efficiency of the engine changes by:

The focus of the parabola \(y^2 + 4y - 8x + 20 = 0\) is at the point:

Compound ‘X’ (C\(_6\)H\(_6\)O) reacts with aqueous NaOH to give compound ‘Y’. ‘Y’ reacts with CO\(_2\) followed by acidification to give compound ‘Z’. The compounds X, Y and Z are respectively

If three numbers are randomly selected from the set \( \{1,2,3,\dots,50\} \), then the probability that they are in arithmetic progression is: 

An ink mark is made on a piece of paper and a glass slab of thickness $t$ and refractive index $\mu$ is placed on it. If the image of the ink mark appears to be at a distance of $x$ from the top surface of the slab, then the value of $x$ is
The symmetric equation of the straight line passing through the points \( (-1, 4, 2) \) and \( (-3, 0, 5) \) is
A rectangular tank of depth 4 m is full of water of refractive index \(\frac 43\). When viewed from the top, the bottom of the tank is seen at a depth of
If \(v_1\) and \(v_2\) are the speeds of light in the two media of refractive indices \(n_1\) and \(n_2\) respectively, then
The pair of linear equations \(a_1x+b_1y+c_1=0\) and \(a_2x+b_2y+c_2=0\) has a unique solution, then
If a body is taken above the surface of the Earth, it loses its weight by 20% at a height of \( h = \frac{\sqrt{5}}{2} R \), where \( R \) is the radius of the Earth, then:
In the following OP-AMP circuit, 𝑣𝑖𝑛 and 𝑣𝑜𝑢𝑡 represent the input and output signals, respectively.
OP-AMP circuit
Choose the correct statement(s):
When two spheres of radii $r$ and $\frac{r}{2}$ are brought in contact, the gravitational force of attraction between them is proportional to