List of practice Questions

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 :

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)?

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

speeds of $20\, m/s$ and $15\, m/s$ relative to the ground. The first train sounds a whistle of frequency $600\, Hz$. The frequency of the whistle heard by a passenger in the second train before the train meets, is (the speed of sound in air is 340 m/s)

General formula of solid in zinc blende structure is:

What is the slope of the normal at the point (at, 2at) of the parabola y = 4ax ?

In the reaction $2 PCl _{5} \rightleftharpoons PCl _{4}^{+}+ PCl _{6}^{-}$, the change in hybridisation is from

The coefficient of $x^2$ term in the binomial expansion of $\left(\frac{1}{3}x^{1/2}+x^{-1/4}\right)^{10}$ is :

With the usual notation $\displaystyle \int_1^2 ([x^2]-[x]^2)dx$ is equal to

For the following feasible region, the linear constraints are

Water is flowing through a horizontal tube having cross-sectional areas of its two ends beings $A$ and $A$' such that the ratio $A/A$' is $5$. If the pressure difference of water between the two ends is $3 \times 10^5\, N m^{-2}$, the velocity of water with which it enters the tube will be (neglect gravity effects)

Volume of blood that flows per unit time per unit volume of the tissue is :

In Dumas method one gram of carbon compound gives $50 \,mL$ of $N _{2}$ at $300\, K$ and $740 \,mm\, Hg$ pressure. If the aqueous tension at $300\, K$ is $15\, mm\, Hg$, what is the percentage of nitrogen in it?

Write the IUPAC name of the following