List of practice Questions

If $ y = \tan^{-1}\left(\frac{2x}{1 - x^2}\right) $, then $ \frac{dy}{dx} $ is:
If the roots of the quadratic equation $ x^2 + 4x + k = 0 $ are real and equal, then the value of $ k $ is:
If $ f(x) = x^2 + 3x $, then $ f'(x) $ is:
Find the slope of the line passing through the points $ (1, 2) $ and $ (3, 6) $:
If a force of $ 10 \, \text{N} $ displaces a body by $ 5 \, \text{m} $ in the direction of the force, the work done is:
A block of mass $ 5\, \text{kg} $ is placed on a rough horizontal surface. A horizontal force of $ 25\, \text{N} $ is applied. If the coefficient of friction is $ 0.4 $, what is the acceleration of the block? (Take $ g = 10\, \text{m/s}^2 $)
Three resistors of $ 2\, \Omega $, $ 3\, \Omega $, and $ 6\, \Omega $ are connected in parallel. What is the equivalent resistance of the combination?
How many moles are present in $ 22\, \text{g} $ of carbon dioxide (CO$_2$)? (Molar mass of CO$_2$ = $ 44\, \text{g/mol} $)
Which of the following elements has the highest electronegativity?
Which of the following molecules has a linear shape?
Which of the following is a strong acid?
Which of the following is an alkene?
Evaluate: \[ \lim_{x \to 0} \frac{\sin 3x - 3 \sin x}{x^3} \]
Two circles with centers $O_1$ and $O_2$ touch externally. The radius of the first circle is 4 cm and the second is 9 cm. The distance between their centers is 13 cm. Find the length of the direct common tangent.
From a group of 10 men and 8 women, a committee of 5 is to be formed such that it contains at least 3 women. How many such committees are possible?
Find the number of integers \(n\) such that \(1 \leq n \leq 100\) and \(n^2 + 3n + 2\) is divisible by 5.
If \( z = 2(\cos 60^\circ + i \sin 60^\circ) \), find the value of \( z^3 \).
Find the coordinates of the point which divides the line segment joining \((2, -3)\) and \((7, 9)\) in the ratio \(3:2\).
How many 4-digit numbers can be formed using the digits 1, 2, 3, 4, 5 without repetition such that the number is divisible by 5?
For the reaction \( \mathrm{N_2} + 3\mathrm{H_2} \rightleftharpoons 2\mathrm{NH_3} \), the equilibrium constant \(K_c\) is 0.5 at a certain temperature. If initially, 1 mole of \(\mathrm{N_2}\) and 3 moles of \(\mathrm{H_2}\) are placed in a 1 L container, what is the equilibrium concentration of \(\mathrm{NH_3}\)?
The standard reduction potentials are: \[ \mathrm{Cu^{2+} + 2e^- \rightarrow Cu} \quad E^\circ = +0.34\,V \] \[ \mathrm{Zn^{2+} + 2e^- \rightarrow Zn} \quad E^\circ = -0.76\,V \] Calculate the standard cell potential for the reaction: \[ \mathrm{Zn + Cu^{2+} \rightarrow Zn^{2+} + Cu} \]
Which of the following reagents can convert an aldehyde to a primary alcohol?
An ideal gas expands from 2 L to 6 L at a constant temperature of 300 K. Calculate the work done by the gas if pressure remains constant at 2 atm. (1 atm = $1.013 \times 10^5$ Pa)
A light wave of wavelength 600 nm passes from air into a medium with refractive index 1.5. What is the wavelength of light in the medium?
A wire of length 0.5 m carrying a current of 3 A is placed in a magnetic field of 2 T perpendicular to the wire. What is the force on the wire?