List of practice Questions

What is the ratio of maximum shear stress to average shear stress for a circular section?
In the simple bending theory, the stress distribution assumed across the cross-section of a beam is
A steel column has a length of 4 meters and a square cross-section with moment of inertia $1.6 \times 10^{-4} \text{ m}^4$. If the column is pinned at both ends and the modulus of elasticity of steel is 200 GPa, what is the critical buckling load? (take $\pi^2$ value as 10)
The real part of an analytic function \( f(z) = u + iv \), where \( v(x, y) = \left( \frac{e^{-y} - e^y}{2} \right) \sin x \), is:
If the probability density function of a continuous random variable \( X \) is \( f(x) \), \( -\infty<x<\infty \), and if the median of \( X \) is \( M \), then:
A card is drawn from a pack of cards successively 5 times by replacing the card drawn in the pack of cards. What is the mean of the number of red cards drawn?
When the IVP \( \frac{dy}{dx} = y + x,\; y(0) = 1 \) is solved by Rung–Kutta fourth order method to find \( y(0.2) \), the approximate value of \( y(0.2) \) by taking step size \( h = 0.2 \) is:
A man weighing \( W \) newtons entered a lift which moves with an acceleration of \( a \, \text{m/s}^2 \). When the lift is moving downward, the force exerted by the man on the floor of the lift is:
The magnitude of the resultant of two equal forces each of magnitude \( F \) is \( \sqrt{2}F \). Then the angle between their line of action is:
The equation of motion of a particle starting from rest along a straight line is \( x = t^3 - 3t^2 + 5 \). The ratio of the accelerations after 5 s and 3 s will be:
If \( E \) is the region bounded by a closed curve \( C \) in the \( xy \)-plane, then \( \iint_E dx\,dy = \)
The maximum value of \( f(x, y) = x^2 y^3 (1 - x - y) \) is:
The substitution which reduces the differential equation \( t^2 \frac{d^2y}{dt^2} + 5t \frac{dy}{dt} + 7y = 0 \) to \( \frac{d^2y}{dx^2} + 4 \frac{dy}{dx} + 7y = 0 \) is:
If \( \mathcal{L}(f(t)) = F(s) \), then \( \mathcal{L}((\cosh 2t)f(t)) \) is:
How many countries are currently members of the United Nations?
A gold ring is 58.33% pure, its purity can be alternatively shown as ________ .
Which one of the following is not a member of the Quad group of nations?
Which of the following lens are used in the microscope?
The Nobel Prize was awarded for the first time in ________ .
“Channel Tunnel” is an undersea rail tunnel that links ________ .
One nautical mile is equal to ________ .
Copyright day is celebrated on ________ .
Currently, how many countries are the members of the North Atlantic Treaty Organization (NATO)?
Buddhism is the world’s fourth-largest religion. It is believed to have originated in ________ .
Which city is called the Silicon Valley of India?