List of practice Questions

If the Earth loses its gravity, then for a body
The law which states that within elastic limits strain produced is proportional to the stress producing it is known as
The slope of the stress-strain curve in the elastic deformation region is
Hess’s law states that a chemical reaction is independent of the route by which chemical reactions take place while keeping the same
A boy of mass 50kg is standing on a frictionless surface. He throws a ball of mass 2kg away from him with a speed of 10m/s. Find the final speed of the centre of mass.
Point, where the total volume of the body is assumed to be concentrated is
The displacement of the body is given to be proportional to the cube of time elapsed. The magnitude of acceleration of body is
What may the cross product of two vectors be used for?
The inherent property, with which a body resists any change in its state of motion is known as
A bus that is travelling straight makes an abrupt right turn. What will happen to those who are on board the bus?
What is the unit of measurement of solid angles?
A particle is moving with a constant speed along a straight-line path. A force is not required to
Evaluate the limit: $$ \lim_{x \to 1} \frac{x + x^2 + x^3 + \dots + x^n - n}{x - 1}. $$ 
If $$ y = (1 + a + a^2 + \dots)e^{nx} $$ then the relative error in $y$ is:
If the extremities of the latus recta having positive ordinate of the ellipse $$ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \quad (a > b) $$ lie on the parabola $$ x^2 + 2ay - 4 = 0, $$ then the points $(a, b)$ lie on the curve:
The Laplace transform of a signal $X(t)$ is $$ X(s) = \frac{4s + 1}{s^2 + 6s + 3}. $$ The initial value $X(0)$ is:
If $$ \int \frac{1}{x^4 + 8x^2 + 9} \, dx = \frac{1}{k} \left[ \frac{1}{\sqrt{14}} \tan^{-1} (f(x)) - \frac{1}{\sqrt{2}} \tan^{-1} (g(x)) \right] + c, $$ then $$ \frac{k}{\sqrt{2}} + f(\sqrt{3}) + g(1) = $$ 
The angle between the lines $$ \frac{x-1}{2} = \frac{2y+3}{4} = \frac{z+5}{-2} \quad \text{and} \quad \frac{x-3}{4} = \frac{y+1}{-4} = \frac{z+3}{-4} $$ is equal to 
The domain of the real-valued function $$ f(x) = \sin^{-1} \left( \log_2 \left( \frac{x^2}{2} \right) \right) $$ is:
If $$ f(x) = \min \{ x, x^2 \} $$ Which of the following is true? 
Identify the correct statements from the following:
I. For spontaneous reaction, $ \Delta S_{\text{total}} < 0 $ and $ \Delta H > 0 $
II. Pressure is an intensive property
III. Bomb calorimeter works at constant volume
The number of multipliers and delay elements required in the direct form II realization of $$ H(z) = \frac{1 + 0.5z^{-1} - 2z^{-2}}{1 + z^{-1} - 2z^{-2}} $$ 

If the curves $$ 2x^2 + ky^2 = 30 \quad \text{and} \quad 3y^2 = 28x $$ cut each other orthogonally, then \( k = \) 

The value of $ \frac{1}{1 + p^{(y-z)} + p^{(x-z)}} + \frac{1}{1 + p^{(x-y)} + p^{(z-y)}} + \frac{1}{1 + p^{(y-x)} + p^{(z-x)}}, $ is:

If the function

$ f(x) = \begin{cases} \frac{\cos ax - \cos 9x}{x^2}, & \text{if } x \neq 0 \\ 16, & \text{if } x = 0 \end{cases} $

is continuous at $ x = 0 $, then $ a = ? $