List of practice Questions

An equilateral triangle ABC formed from a uniform wire has two small identical beads initially located at A. The triangle is set rotating about the vertical axis AO. Then the beads are released from rest simultaneously and allowed to slide down, one along AB and other along AC as shown. Neglecting frictional effects, the quantities that are conserved as the beads slide down are:

A gas is kept in a vessel of volume 0.2 m³ at temperature 300 K and pressure 1 bar. The molar heat capacity of gas at constant volume is 5 cal/mol K. The heat (kcal) required to raise the temperature to 400 K is ______.

In Young's double-slit experiment with slit separation $0.1$ mm, one observes a bright fringe at angle $\frac{1}{4^{\circ }}$ rad by using the light of wavelength ${\lambda }_1$. When the light of wavelength ${\lambda }_2$ is used a bright fringe is seen at the same angle in the same setup. Given that $1$ and $2$ are in the visible range $(380nm$ to $740nm)$, their values are

Steam at ${100}^{\circ }C$ is passed into $1.1kg$ of water contained in calorimeter of water equivalent $0.02kg$ at ${15}^{\circ }C$ till the temperature of the calorimeter rises to ${80}^{0}C$. What is the mass of steam condensed?

The de Broglie wavelength of an electron moving with a velocity 1.5 × 10⁸ m/s is equal to that of a photon. The ratio of the energy of the photon to the kinetic energy of the electron is ______.

A thin concave lens is in contact with a thin convex lens. The ratio of their magnitude of the focal length is $\frac{3}{2}$ and the focal length of the combined lens is $30$ cm. The focal lengths of the individual lenses are

A wave on a string is described by $u(x,t)=0.005 \sin (6.28x-314t)$ in which all quantities are in SI units. It's wavelength is _______.

Let $f,g:[-1,2]\to R$ be continuous functions which are twice differentiable on the interval (-1,2). Let the values of $f$ and $g$ at the points -1,0 and 2 be as given in the following table:$\begin{array}{|llll|}\hline e& x=-1& x=0& x=2\\ f(x)& 3& 6& 0\\ g(x)& 0& 1& -1\\ \hline\end{array}$In each of the intervals (-1,0) and (0,2) the function $(f-3g)$ never vanishes. Then the correct statement(s) is (are):

At a hydroelectric power plant, the water pressure head is at a height of $300m$ and the water flow available is $100m^3{s}^{-1}$. If the turbine generator efficiency is $60\mathrm{\%}$, estimate the electric power available from the plant. $($Given $g=9.8{ms}^{-2})$

A short linear object of length b lies along the axis of a concave mirror of focal length $\mathrm{f}$ at a distance $\mathrm{u}$ from the pole of the mirror. The size of the image is approximately equal to:

At ${90}^{\circ }C$, pure water has $\left[H_3{O}^{+}\right]={10}^{-6}m$ on the value of $k_w$ at this temperature is:

Which of the following have undistorted octahedral structures?
1. $S{F}_6$
2. $P{F}_6^{-}$
3. $Si{F}_6^{2-}$
4. $Xe{F}_6$
Select the correct answer using the codes given below:

An aromatic compound 'A' C7H6Cl2  gives white precipitate on boiling with AgNO3 solution and yields C7H7OCl on treatment with NaOH.  'A' on oxidation gives a monochloro benzoic acid which affords only one mononitroderivative.  The compound A is:

If the ionisation potential of the hydrogen atom is $13.6\mathrm{eV}$, then what will be the longest wavelength needed to remove an electron from the $1^{\text{st }}$ Bohr's orbit of ${\mathrm{He}}^{+}$ ion?

In the reaction:$BC{l}_3+P{H}_3\rightleftharpoons C{l}_{3}B·P{H}_3$ Lewis base is:

The atomic masses of He and Ne are $4$ and $20$ a.m.u., respectively. The value of the de-Broglie wavelength of He gas at $-{73}^{\circ }C$ is "M" times that of the de-Broglie wavelength of $Ne$ at ${727}^{\circ }C.M$ is

$2$ g of a base whose equivalent weight is $40$ reacts with $3g$ of an acid. The equivalent weight of the acid is:

Bond dissociation energy of $XY,X_2$, and $Y_2$ (all diatomic molecules) are in the ratio of $1:1:0.5$ and $\mathrm{\Delta }{H}_f$ of $XY$ is $-100kJ{mol}^{-1}$. The bond dissociation energy of $X_2$ is $100x.$ The value of $x$ is

The $\mathrm{pH}$ value of $0.1\mathrm{M}$ solution of anilinium chloride is:$(K_a$ of $C_6{H}_{5}N{H}_3^{+}={10}^{-6})$

The conductivity of $0.02\mathrm{N}$ solution of a cell of $\mathrm{KCl}$ at ${25}^{\circ }\mathrm{C}$ is $2.765\times {10}^{-3}S{\mathrm{cm}}^{-1}$. If the resistance of a cell containing this solution is $4\times {10}^3$ ohm, what will be the cell constant?

' $n$ ' polarizing sheets are arranged such that each makes an angle $45^{\circ}$ with the preceeding sheet An unpolarized light of intensity I is incident into this arrangement The output intensity is found to be $I / 64$ The value of $n$ will be:

A mercury drop of radius $10^{-3} m$ is broken into $125$ equal size droplets Surface tension of mercury is $045\, Nm ^{-1}$ The gain in surface energy is:

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of $\lambda$ An alpha particle having certain kinetic energy has the same de-Brogle wavelength $\lambda$ The ratio of kinetic energy of proton and that of alpha particle is:

Match List I with List II:

List I		List II
A	Intrinsic Semiconductor	I	Fermi-level near the conduction band
B	n-type semiconductor	II	Fermi-level in the middle of valence and conduction band
C	p-type semiconductor	III	Fermi-level near the valence band
D	Metals	IV	Fermi-level inside the conduction band

Choose the correct answer from the options given below:

Let $\sigma$ be the uniform surface charge density of two infinite thin plane sheets shown in figure Then the electric fields in three different region $E_I, E_{I I}$ and $E_{I I I}$ are: