List of practice Questions

In the given figure, two equal positive point charges $ q_1 = q_2 = 2.0 \mu C $ interact with a third point charge $ Q = 4.0 \mu C $. The magnitude and direction of the net force on $ Q $ is:
\includegraphics[width=0.5\linewidth]{35.png}

Which of the following cannot be made by using Williamson's synthesis?

$ P_A $ and $ P_B $ are the vapor pressures of pure liquid components A and B, respectively, in an ideal binary solution. If $ X_A $ represents the mole fraction of component A, the total pressure of the solution will be:

In which of the following situations Indian Penal Code, 1860 may not apply?
i. An offence committed by Indians outside India.
ii. An offence committed by any person on any ship registered in India.
iii. Any person committing offence targeting computer resources located in any country.

Which one of the following curves represents the variation of impedance $ (Z) $ with frequency $ f $ in a series LCR circuit?

A convex lens has power $ P $. It is cut into two halves along its principal axis. Further, one piece (out of the two halves) is cut into two halves perpendicular to the principal axis (as shown in figure). Choose the incorrect option for the reported pieces.
\includegraphics[width=0.5\linewidth]{27.png}

A Carnot engine takes $ 3 \times 10^6 $ cal of heat from a reservoir at $ 627^\circ C $, and gives it to a sink at $ 27^\circ C $. The work done by the engine is:

Assertion :
The binding energy of the nucleus increases with the increase in atomic number.
Reason :
Heavier elements have a greater number of non-radioactive isotopes than radioactive isotopes.

Two identical blocks A and B, each of mass 'm' resting on a smooth floor are connected by a light spring of natural length L and spring constant K, with the spring at its natural length. A third identical block 'C' (mass m) moving with a speed v along the line joining A and B collides with A. the maximum compression in the spring is

Light of wavelength $ \lambda_A $ and $ \lambda_B $ falls on two identical metal plates A and B respectively. The maximum kinetic energy of photoelectrons is $ K_A $ and $ K_B $ respectively. Given that $ \lambda_A = 2\lambda_B $, which one of the following relations is true?

Let $P(S)$ denote the power set of $S = \{1, 2, 3, \ldots, 10\}$. Define the relations $R_1$ and $R_2$ on $P(S)$ as $A R_1 B$ if \[(A \cap B^c) \cup (B \cap A^c) = ,\]and $A R_2 B$ if\[A \cup B^c = B \cup A^c,\]for all $A, B \in P(S)$. Then:

If $P$ is a $3 \times 3$ real matrix such that $P^T=a P+(a-1) I$, where $a>$, then

The distance of the point $(6,-2 \sqrt{2})$ from the common tangent $y=m x+c, m>$, of the curves $x=2 y^2$ and $x=1+y^2$ is :

The shortest distance between the lines $ x = y + 2 = 6z - 6 $ and $ x + 1 = 2y = -12z $ is:

If the foot of the perpendicular drawn from $(1,9,7)$ to the line passing through the point $(3,2,1)$ and parallel to the planes $x+2 y+z=0$ and $3 y-z=3$ is $(\alpha, \beta, \gamma)$, then $\alpha+\beta+\gamma$ is equal to

A rectangle is drawn by lines x=0, x=2, y=0 and y=5. Points A and B lie on coordinate axes. If line AB divides the area of rectangle in 4:1, then the locus of mid-point of AB is?

Let $𝑆={𝑤_1,𝑤_2,…….}$ be the sample space associated to a random experiment. Let $𝑃(𝑤_𝑛)= \frac{𝑃(𝑤_{𝑛−1})}{2} ,𝑛≥2.$ Let 𝐴=${(2𝑘+3𝑙:k,𝑙∈ℕ)}$ and $𝐵={𝑤_𝑛:𝑛∈𝐴}$. Then 𝑃( 𝐵) is equal to

What is the approximate percentage increase in the production of Monopoly from 1993 to 1995?

If equation of the plane that contains the point $(-2,3,5)$ and is perpendicular to each of the planes $ 2x + 4y + 5z = 8 $ and $ 3x - 2y + 3z = 5 $, is $ \alpha x + \beta y + \gamma z = 97 $, then $ \alpha + \beta + \gamma $ is:

Which of the following is material for deciding the jurisdiction of the Civil Court in the light of the Code of Civil Procedure, 1908?

The molar conductivities at infinite dilution for Na₂SO₄,K₂S0_4,KCl, HCl and HCOONa at 300K are 260, 308, 150, 426, and 105 S cm² mol^-1, respectively. What will be A⁺m for formic acid in the same unit?

A disc is rolling without slipping on a surface. The radius of the disc is $ R $. At $ t = 0 $, the topmost point on the disc is $ A $ as shown in the figure. When the disc completes half of its rotation, the displacement of point $ A $ from its initial position is: