List of practice Questions

An endothermic reaction, $A \to B$ has an activation energy as $x\, kJ/mol$. If the energy change of the reaction is $y\, kJ$, the activation energy of the reverse reaction is
$\int^{\frac{\pi}{2}}_0 \log(\tan\,x)dx=$
Consider an experiment $E$ in which a box contains $10$ identical tickets numbered $1$ to $10$ and $2$ tickets are drawn at random from the box. What is the probability that both the tickets have even numbers on them?
If the coefficients of $x^5$ and $x^6$ in $\left(2+\frac{x}{3}\right)^{n}$ are equal, then $n$ is
Let $x$ be a number which exceeds its square by the greatest possible quantity, then $x$ =
The value of $\int^2_{-2}(ax^3+bx +c)dx$ depends on the
The value of $\frac{\tan 330^{\circ} \sec 420^{\circ} \sin 300^{\circ}}{\tan 135^{\circ} \sin 210^{\circ} \sec 315^{\circ} } $ is equal to
A hospital uses an ultrasonic scanner to locate tumors in a tissue. The operating frequency of the scanner is $4.2 \, MHz$. The speed of sound in a tissue is $1.7 \, km \, s^{-1}$. The wavelength of sound in the tissue
A policeman on duty detects a drop of $15 \%$ in the pitch of the horn of a motor car as it crosses him. If the velocity of sound is $330 \, m \, s^{-1}$ , calculate the speed of the car.
The $TV$ signals have a bandwidth of $3.7\, MHz$. The number of $TV$ channels that can be accommodated with a band of $3700 \,GHz$ is
Two boys are standing at ends $A$ and $B$ of a ground where $AB = 200\, m$. The boy at B starts running in a direction perpendicular to $AB$ with a speed of $6\, m \,s^{-1}$? The boy at A starts simultaneously with a velocity of $10 \, m \, s^{-1}$ and catches the other at time t where the time $t$ is
A pump on the ground floor of a building can pump up water to fill the tank of $30\, m^3$ in $15\,min$. If the tank is $40\,m$ above the ground, and the efficiency of the pump is $30\,%$, the power consumed by the pump is $(g = 10 \, m \, s^{-2})$
The increase in the height of the tower of height $200\,m$ to get its coverage range tripled is
Let $E _{1}( r ), E _{2}( r )$ and $E _{3}( r )$ be the respective electric fields at a distance $r$ from a point charge $Q , an$ infinitely long wire with constant linear charge density $\lambda$, and an infinite plane with uniform surface charge density $\sigma$. If $E_{1}\left(r_{0}\right)=E_{2}\left(r_{0}\right)=E_{3}\left(r_{0}\right)$ at a given distance $r_{0}$, then
If the focal length of objective lens is increased then magnifying power of
Two cities are $150\, km$ apart. Electric power is sent from one city to another city through copper wires. The fall of potential per km is $8\, volt$ and the average resistance per km is $0.5\, \Omega$. The power loss in the wire is
Hydrogen atom in ground state is excited by a monochromatic radiation of $\lambda$ = 975 $\mathring{A}$. Number of spectral lines in the resulting spectrum emitted will be
A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth (mass $= 5.98 \times 10^{24} \, kg$) have to be compressed to be a black hole?
An analysis of chromosomal DNA using the Southern hybridization technique does not use
Light with an energy flux of $ 25 \times 10^4 W m^{-2} $ falls on a perfectly reflecting surface at normal incidence. If the surface area is $ 15 c m^2 $, the average force exerted on the surface is
A projectile is fired from the surface of the earth with a velocity of $5\, m s^{- 1}$ and angle $\theta$ with the horizontal. Another projectile fired from another planet with a velocity of $3\,ms^{ - 1}$ at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in $ms^{ - 2}$ ) is (Given $g= 9.8 \,ms^{ - 2}$)
Five kingdom system of classification suggested by R.H. Whittaker is not based on
Which of the following organic compounds has same hybridisation as its combustion (CO$_2$) product?
Among the following sets of reactants which one produces anisole?
A monoatomic gas at a pressure $P$, having a volume $V$ expands isothermally to a volume $2V$ and then adiabatically to a volume $16\,V$. The final pressure of the gas is (Take $\gamma =5/3 )$