List of practice Questions

The area of the region enclosed between the curve \( y = |x| \), x-axis, \( x = -2 \)} and \( x = 2 \) is:

The integral \[ \int \sqrt{1 + \sin x} \, dx \] is equal to:
The slope of the curve \( y = -x^3 + 3x^2 + 8x - 20 \) is maximum at:
If \[ \begin{bmatrix} 4 + x & x - 1 \\ -2 & 3 \end{bmatrix} \] is a singular matrix, then the value of \( x \) is:
If \( f(x) = \lfloor x \rfloor \) is the greatest integer function, then the correct statement is:
The principal value of \( \cot^{-1} \left( -\frac{1}{\sqrt{3}} \right) \) is:
If \[ A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & -2 \end{bmatrix}, \] then \( |A| \) is:
If \[ \left| \frac{2x}{5} \right| = \left| \frac{6 - 5}{4} \right|, \quad \text{then the value of } x \text{ is:} \]
If \[ f(x) = \begin{cases} \frac{\sin^2(ax)}{x^2}, & x \neq 0 \\ 1, & x = 0 \end{cases} \] is continuous at \( x = 0 \), then the value of \( a \) is:

If \( P(A \cup B) = 0.9 \) and} \( P(A \cap B) = 0.4 \), then \( P(A) + P(B) \) is:

If \[ A = \begin{bmatrix} 1 & 2 & 3 \\ -4 & 3 & 7 \end{bmatrix}, \quad B = \begin{bmatrix} 4 & 3 \\ -1 & 2 \\ 0 & 5 \end{bmatrix}, \] then the correct statement is:
A project requires 12 workers to complete in 20 days. If 4 workers leave after 8 days, how many additional days will the remaining workers take to finish the project?
Suppose that the number of terms in an A.P. is \( 2k, k \in \mathbb{N} \). If the sum of all odd terms of the A.P. is 40, the sum of all even terms is 55, and the last term of the A.P. exceeds the first term by 27, then \( k \) is equal to:
What is the sum of interior angles of a polygon with 10 sides?
If $ 0 \le x \le 3,\ 0 \le y \le 3 $, then the number of solutions $(x, y)$ for the equation: $$ \left( \sqrt{\sin^2 x - \sin x + \frac{1}{2}} \right)^{\sec^2 y} = 1 $$
What color does Silver Chloride (AgCl) turn upon exposure to sunlight?
In case of association, abnormal molar mass of solute will:
The current through an inductor is uniformly increased from zero to 2 A in 40 s. An emf of 5 mV is induced during this period. Find the flux linked with the inductor at t = 10 s.
Find the next number in the series: 2, 6, 12, 20, 30, ?
Two coherent light waves, each having amplitude ‘a’, superpose to produce an interference pattern on a screen. The intensity of light as seen on the screen varies between:
Which of the following electromagnetic waves has photons of largest momentum?
Which of the following rays coming from the Sun plays an important role in maintaining the Earth’s warmth?
The magnetic flux linked with a coil changes with time \( t \) as \( \phi = (8t^2 + 5t + 7) \), where \( t \) is in seconds and \( \phi \) is in Wb. The value of emf induced in the coil at \( t = 4 \) s is:
The electric field at a point in a region is given by \( \vec{E} = \alpha \frac{\hat{r}}{r^3} \), where \( \alpha \) is a constant and \( r \) is the distance of the point from the origin. The magnitude of potential of the point is:
A charged particle gains a speed of \(10^6 \, \text{ms}^{-1}\) when accelerated from rest through a potential difference of 10 kV. It enters a region of magnetic field of 0.4 T such that \( \vec{v} \perp \vec{B} \). The radius of the circular path described by it is: