List of practice Questions

For $x > 1$, if $(2x)^{2y} = 4e^{2x - 2y}$, then $\left( 1 +\log_{e} 2x\right)^{2} \frac{dy}{dx} $ is equal to :

In a class of $140$ students numbered $1$ to $140$, all even numbered students opted mathematics course, those whose number is divisible by $3$ opted Physics course and those whose number is divisible by $5$ opted Chemistry course. Then the number of students who did not opt for any of the three courses is :

Let S and S' be the foci of the ellipse and B be any one of the extremities of its minor axis. If 'S'BS is a right angled triangle with right angle at B and area ($\Delta$S'BS) = 8 s units, then the length of a latus rectum of the ellipse is :

Let $z \in C$ with Im(z) = 10 and it satisfies $\frac{2z-n}{2z+n} = 2i -1$ for some natural number $n$.Then :

The value of $\cos \frac{\pi}{2^{2}} .\cos \frac{\pi}{2^{3} } . ...... .\cos \frac{\pi}{2^{10}} .\sin \frac{\pi}{2^{10}} $ is :

The solution of the differential equation , $\frac{dy}{dx} = \left(x-y\right)^{2} , $ when $y(1) = 1$, is :

In a game, a man wins Rs. $100$ if he gets $5$ of $6$ on a throw of a fair die and loses Rs. $50$ for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/ loss (in rupees) is :

Consider a class of $5$ girls and $7$ boys. The number of different teams consisting of $2$ girls and $3$ boys that can be formed from this class, if there are two specific boys $A$ and $B$, who refuse to be the members of the same team, is :

If $m$ is chosen in the quadratic equation $(m^2 + 1) x^2 - 3x + (m^2 + 1)^2 = 0$ such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is :

If some three consecutive in the binomial expansion of $(x + 1)^n$ is powers of $x$ are in the ratio $2 : 15 : 70$, then the average of these three coefficient is :-

If $x = 3 \,tan \,t $ and $y = 3 \,sec \,t$, then the value of $\frac{d^2 y}{dx^2}$ at $t = \frac{\pi}{4}$, is :

Let $a_1, a_2 , ....... , a_{30}$ be an $A. P$., $S =\displaystyle \sum^{30}_{i=1} a_i $ and $T = \displaystyle\sum^{15}_{i=1} a_{(2i -1)}$. If $a_5 = 27$ and $S - 2T = 75, $ then $a_{10}$ is equal to :

The value of cos $^2 10^{\circ} - cos10^{\circ} cos50^{\circ} + cos^2 50^{\circ}$

Speed of particles at 3^rd and 8^th seconds are 20 m/s are zero respectively. Then average acceleration between 3^rd and 8^th second will be -

Calculate the limit of resolution of a telescope objective having a diameter of $200\, cm$, if it has to detect light of wavelength $500\, nm$ coming from a star :

Diameter of the objective lens of a telescope is $250\, cm$. For light of wavelength $600\,nm$. coming from a distant object, the limit of resolution of the telescope is close to :

Ice at $-20^{\circ} C$ os added tp $50\, g$ of water at $40^{\circ}C$. When the temperature of the mixture reaches $0^{\circ}C$, it is found that $20\, g$ of ice is still unmelted. The amount of ice added to the water was close to (Specific heat of water = $4.2 \; J/g/^{\circ}C$) Specific heat of Ice = $2.1 \; J/g/^{\circ}C$ Heat of fusion of water at $0^{\circ}C = 334 \; J/g$)

If a ball of mass 0.1 kg hits the ground from the height of 20m and bounce back to the same height then find out the force exerted on the ball if the time of impact is 0.04 sec. (g = 10 m/s)

What is the value of γ for a monoatomic gas (ideal gas):

What will be the Heat of vaporisation of 1 mole of water, when it has the entropy change (AS) of 35.2 cal/mole.deg (at 25°C)?

$aK _{2} Cr _{2} O _{7}+ bKCl + cH _{2} SO _{4} \longrightarrow xCrO _{2} Cl _{2}+ yKHSO _{4}+ zH _{2} O$ The above equation balances when

Which of the following element has the highest ionisation enthalpy?

Which of the following has zero net dipole moment?

In the clathrates of xenon with water, the nature of bonding between xenon and water molecule is

In the purification of impure nickel by Mond's process, metal is purified by: