List of practice Questions

Method used for separation of mixture of products (B and C) obtained in the following reaction is:

The moment of inertia of a square loop made of four uniform solid cylinders, each having radius R and length L ($R \le L$) about an axis passing through the mid points of opposite sides, is (Take the mass of the entire loop as M) :

Which of the following best represents the temperature versus heat supplied graph for water, in the range of $-20^\circ\text{C}$ to $120^\circ\text{C}$?

When a part of a straight capillary tube is placed vertically in a liquid, the liquid rises upto certain height $ h $. If the inner radius of the capillary tube, density of the liquid and surface tension of the liquid decrease by $1%$ each, then the height of the liquid in the tube will change by ________ %.

A gas of certain mass filled in a closed cylinder at a pressure of $3.23\,\text{kPa}$ has temperature $50^\circ$C. The gas is now heated to double its temperature. The modified pressure is ___ Pa.

Let the circle $x^2+y^2=4$ intersect the $x$-axis at points $A(a,0)$ and $B(b,0)$. Let $P(2\cos\alpha,2\sin\alpha)$, $0<\alpha<\frac{\pi}{2}$, and $Q(2\cos\beta,2\sin\beta)$ be two points on the circle such that $(\alpha-\beta)=\frac{\pi}{2}$. Then the point of intersection of lines $AQ$ and $BP$ lies on:

When a light of a given wavelength falls on a metallic surface the stopping potential for photoelectrons is $3.2\ \text{V}$. If a second light having wavelength twice of the first light is used, the stopping potential drops to $0.7\ \text{V}$. The wavelength of the first light is ________ m.

An infinitely long straight wire carrying current $I$ is bent in a planar shape as shown in the diagram. The radius of the circular part is $r$. The magnetic field at the centre $O$ of the circular loop is :

Identify the correct statements: The presence of –NO$_2$ group in benzene ring A. activates the ring towards electrophilic substitutions. B. deactivates the ring towards electrophilic substitutions. C. activates the ring towards nucleophilic substitutions. D. deactivates the ring towards nucleophilic substitutions. Choose the correct answer from the options given below:

If the distances of the point $ (1,2,a) $ from the line \[ \frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1} \] along the lines \[ L_1:\ \frac{x-1}{3}=\frac{y-2}{4}=\frac{z-a}{b} \quad \text{and} \quad L_2:\ \frac{x-1}{1}=\frac{y-2}{4}=\frac{z-a}{c} \] are equal, then $ a+b+c $ is equal to:

Two circular discs of radius $10$ cm each are joined at their centres by a rod, as shown in the figure. The length of the rod is $30$ cm and its mass is $600$ g. The mass of each disc is also $600$ g. If the applied torque between the two discs is $43\times10^{-7}$ dyne·cm, then the angular acceleration of the system about the given axis $AB$ is ________ rad s$^{-2}$.

In an experiment, a set of readings are obtained as follows: \[ 1.24~\text{mm},\ 1.25~\text{mm},\ 1.23~\text{mm},\ 1.21~\text{mm}. \] The expected least count of the instrument used in recording these readings is _______ mm.

The number of numbers greater than $5000$, less than $9000$ and divisible by $3$, that can be formed using the digits $0,1,2,5,9$, if repetition of digits is allowed, is

Two point charges of $1\,\text{nC}$ and $2\,\text{nC}$ are placed at two corners of an equilateral triangle of side $3$ cm. The work done in bringing a charge of $3\,\text{nC}$ from infinity to the third corner of the triangle is ________ $\mu\text{J}$. \[ \left(\frac{1}{4\pi\varepsilon_0}=9\times10^9\,\text{N m}^2\text{C}^{-2}\right) \]

Evaluate: \[ \frac{6}{3^{26}}+\frac{10\cdot1}{3^{25}}+\frac{10\cdot2}{3^{24}}+\frac{10\cdot2^{2}}{3^{23}}+\cdots+\frac{10\cdot2^{24}}{3}. \]

If the coefficient of $ x $ in the expansion of \[ (ax^2 + bx + c)(1 - 2x)^{26} \] is $-56$ and the coefficients of $ x^2 $ and $ x^3 $ are both zero, then $ a + b + c $ is equal to

The equivalent resistance between the points $A$ and $B$ in the given circuit is \[ \frac{x}{5}\,\Omega. \] Find the value of $x$.

Consider light travelling from a medium A to medium B separated by a plane interface. If the light undergoes total internal reflection during its travel from medium A to B and the speed of light in media A and B are $2.4 \times 10^8$ m/s and $2.7 \times 10^8$ m/s, respectively, then the value of critical angle is :

In the following $p\text{–}V$ diagram, the equation of state along the curved path is given by \[ (V-2)^2 = 4ap, \] where $a$ is a constant. The total work done in the closed path is: