List of practice Questions

A bar magnet is initially at right angles to a uniform magnetic field. The magnet is rotated till the torque acting on it becomes one-half of its initial value. The angle through which the bar magnet is rotated is:

Match the following:

List - I	List - II
A) Morphine	IV) Pain killer
B) Cannabinoids	V) Dopamine
C) Cocaine	I) Cardiovascular system
D) Benzodiazepines	II) Tranquilizers

Find the zeroes of the polynomial: \[ q(x) = 8x^2 - 2x - 3 \] Hence, find a polynomial whose zeroes are 2 less than the zeroes of $q(x)$

The number of four digit even numbers that can be formed using the digits 0, 1, 2 and 3 without repetition is:

A conductor of length $ l $ is connected across an ideal cell of emf E. Keeping the cell connected, the length of the conductor is increased to $ 2l $ by gradually stretching it. If R and $ R' $ are initial and final values of resistance and $ v_d $ and $ v_d' $ are initial and final values of drift velocity, find the relation between:
$ R' $ and $ R $
$ R' = 4R $

In a diffraction experiment, the slit is illuminated by light of wavelength 600 nm. The first minimum of the pattern falls at $ \theta = 30^\circ $. Calculate the width of the slit.

Evaluate the integral: ∫ log((2 + x)^{2 + x}) dx

An electric field $ \vec{E} $ is given by:
\[ \vec{E} = \begin{cases} +100\, \hat{i} \dfrac{\text{N}}{\text{C}} & \text{for } x>0 \\ -100\, \hat{i} \dfrac{\text{N}}{\text{C}} & \text{for } x<0 \end{cases} \] A right circular cylinder of length $ 10\, \text{cm} $ and radius $ 2\, \text{cm} $, is placed such that its axis coincides with the x-axis and its two faces are at $ x = -5\, \text{cm} $ and $ x = 5\, \text{cm} $. Calculate: (a) the net outward flux through the cylinder, and (b) the net charge inside the cylinder.

The Debt Equity Ratio of Manak Enterprises is 2.5 : 1. Which of the following transaction will result in increase in this ratio?
(A) Purchase of goods on credit ₹ 2,00,000.
(B) Payment to creditors ₹ 3,00,000.
(C) Issue of debentures ₹ 6,00,000.
(D) Sale of furniture of the book value of ₹ 4,00,000 at a profit of 10%.

A metal crystallizes in simple cubic lattice. The volume of one unit cell is $ 6.4 \times 10^{-7} \, \text{pm}^3 $. What is the radius of the metal atom in pm?

The figure shows an opamp circuit with a 5.1 V Zener diode in the feedback loop. The opamp runs from $ \pm 15 \, {V} $ supplies. If a $ +1 \, {V} $ signal is applied at the input, the output voltage (rounded off to one decimal place) is:

Explain valence bond theory in coordination compounds.

If the silver coating around the centre of a concave mirror is removed, will the mirror still form the image of an object? Justify your answer.

Which fiber is known for its excellent moisture-wicking properties, making it ideal for active wear?

On prolonged heating with HI, glucose gives a compound 'C', which can be obtained by Wurtz reaction using sodium metal and compound 'D'. Identify 'D'

Find the image $ A' $ of the point $ A(2,1,2) $ in the line \[ l: \mathbf{r} = 4\hat{i} + 2\hat{j} + 2\hat{k} + \lambda (\hat{i} - \hat{j} - \hat{k}). \] Also, find the equation of the line joining $ A A' $. Find the foot of the perpendicular from point $ A $ on the line $ l $.

A double convex lens of glass has both faces of the same radius of curvature 17 cm. Find its focal length if it is immersed in water. The refractive indices of glass and water are 1.5 and 1.33 respectively.

The integrating factor of the differential equation \[ e^{-\frac{2x}{\sqrt{x}}} \, \frac{dy}{dx} = 1 \] is:

Name the method by which Amoeba and Leishmania reproduce. Write a major difference in the way they divide to produce new individuals.

The magnetic moment of $ \text{Mn}^{3+} $ is:

For a first-order reaction, the slope of the graph between $\log[A]$ vs time is equal to:

What is the correct order of thermal stability of the following carbonates?
BaCO$_3$, MgCO$_3$, SrCO$_3$, CaCO$_3$

A charge of 2 $\mu C$ is placed in an electric field of intensity $ 4 \times 10^3 \, \text{N/C} $. What is the force experienced by the charge?

If the volume of the tetrahedron, whose vertices are $ A(1, 2, 3), B(-3, -1, 1), C(2, 1, 3) $ and $ D(-1, 2, x) $, is $ \frac{11}{6} $ cubic units, then the value of $ x $ is:

If $ f : \mathbb{R} \to \mathbb{R} $ and $ g : \mathbb{R} \to \mathbb{R} $ are two functions defined by $ f(x) = 2x - 3 $ and $ g(x) = 5x^2 - 2 $, then the least value of the function $(g \circ f)(x)$ is: