List of practice Questions

The vernier scale of travelling microscope has 50 divisions which coincides with 49 main scale division. If each main scale division is 0.5 mm, then the least count of the microscope is

The forbidden energy gap for 'Ge' crystal at '0' K is
The resistivity of semiconductor at room temperature is between

Which of the following radiations is deflected by electric field?

The radius of hydrogen atom in the ground state is 0.53 Å .After collision with an electron it is found to have a radius of 2.1 Å, the principal quantum number 'n' of the state of the atom is 

A satellite is revolving around the Earth in a closed orbit. The height of the satellite above Earth's surface at perigee and apogee are 2500 km and 4500 km, respectively. Consider the radius of the Earth to be 6500 km. The eccentricity of the satellite's orbit is ________ (Round off to 1 decimal place).
Potential energy as a function of \(r\) is given by \( U = \frac{A}{r^{10}} - \frac{B}{r^5} \), where \(r\) is the interatomic distance, \(A\) and \(B\) are positive constants. The equilibrium distance between the two atoms will be:

Let,
\(\vec{a}=a\hat{i}+2\hat{j}−\hat{k}\) and \(\vec{b}=−2\hat{i}+α\hat{j}+\hat{k}\)
, where α ∈ R. If the area of the parallelogram whose adjacent sides are represented by the vectors 
\(\vec{a}\) and \(\vec{b}\) is \(\sqrt{15(α^2+4)}\) , then the value of \(2|\vec{a}|^2+(\vec{a}⋅\vec{b})|\vec{b}|^2 \)
is equal to :

4.0 L of an ideal gas is allowed to expand isothermally into vacuum until the total volume is 20 L. The amount of heat absorbed in this expansion is ____ L atm.
Forty three persons went to a canteen which sold cold drink 'Maaza' and 'Pepsi'. If 18 persons took Maaza only, 8 took Pepsi only and 5 took nothing, find how many took both the drinks
Let arg(z) represent the principal argument of the complex number z. Then, |z| = 3 and arg(z – 1) – arg(z + 1) = π/4 intersect

Let f,g : R → R be functions defined by*
\(f(x) = \begin{cases}   [x], &  x < 0 \\   |1 - x|, &  x \geq 0 \end{cases}\)
and \(g(x) = \begin{cases}   e^x - x, &  x < 0 \\   {(x - 1)^2 - 1}, &  x \geq 0 \end{cases}\)
Where [x] denotes the greatest integer less than or equal to x. Then, the function fog is discontinuous at exactly:

At the time of admission of partner if goodwill exist in the books of account it will be written off among:
Assuming 1μg of trace radioactive element X with a half life of 30 years is absorbed by a growing tree. The amount of X remaining in the tree after 100 years is ______ × 10–1μg.
[Given : ln 10 = 2.303; log 2 = 0.30]
Select the most appropriate pair of words to fill in the blanks in the same order to make the sentence meaningfully complete :
The _________ imposed was too ______ to yield any result.
If \( \alpha \) be a root of the equation \( 4x^2 + 2x - 1 = 0 \), then the other root of the equation is
If \( A = \{ x : x { is a multiple of 4} \} \) and \( B = \{ x : x { is a multiple of 6} \} \), then \( A \cap B \) consists of multiples of:
If \( |w| = 2 \), then the set of points \( z = w - \frac{1}{w} \) is contained in or equal to the set of points \( z \) satisfying:

The value of \[ \lim_{x \to 0} \frac{1 - \cos(1 - \cos x)}{x^4} \] is:

Let \( a_1, a_2, \dots, a_{40} \) be in AP and \( h_1, h_2, \dots, h_{10} \) be in HP. If \( a_1 = h_1 = 2 \) and \( a_{10} = h_{10} = 3 \), then \( a_4 h_7 \) is:
The number of terms in the expansion of \( (1 + 5\sqrt{2}x)^9 + (1 - 5\sqrt{2}x)^9 \) is:
The number of different seven-digit numbers that can be written using only the digits 1, 2, and 3 with the condition that the digit 2 occurs twice in each number is:

Given \[ 2x - y + 2z = 2, \quad x - 2y + z = -4, \quad x + y + \lambda z = 4, \] then the value of  \( \lambda \) such that the given system of equations has no solution is:

Let \[ A = \begin{pmatrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{pmatrix}, \quad 10B = \begin{pmatrix} 4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3 \end{pmatrix} \] If \( B \) is the inverse of \( A \), then the value of \( \alpha \) is:

If \( x \in \left( 0, \frac{\pi}{2} \right) \), then the value of \( \cos^{-1} \left( \frac{7}{2} (1 + \cos 2x) + \sqrt{(\sin^2 x - 48\cos^2 x)\sin x} \right) \) is equal to: