List of practice Questions

Probability of getting positive integral roots of the equation x$^2$ - n = 0 for the integer n, 1 $\le$ n $\le$ 40 is

Solution of the differential equation $xdy - ydx - \sqrt{x^{2}+y^{2}}dx = 0$ is

The simplified expression of sin ($tan^{-1} x$), for any real number $x$ is given by

The center and radius of the sphere $x^2 + y^2 + z^2 + 3x - 4z + 1 = 0$ are

What is the temperature at which the kinetic energy of $0.3$ moles of helium is equal to the kinetic energy of $0.4$ moles of argon -at $400\, K$ ?

In the adiabatic compression, the decrease in volume is associated with

Identify $A$ and $B$ in the following reaction $CH _{3}- CH _{3} \stackrel{B}{\leftarrow}{B} CH _{3} COOH \xrightarrow{A} CH _{3} CH _{2} OH$

If $A$ and $B$ are independent events of a random experiment such that $P(A \cap B) = \frac{1}{6} $ and $P(A \cap B) = \frac{1}{3}$, then $P(A)$ is equal to (Here, $E$ is the complement of the event $E$)

A pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve $x^2 + y^2 = 4$ with $x + y = a$. The set containing the value of '$a$' is

If the lines $2x - 3y = 5$ and $3x - 4y = 7$ are two diameters of a circle of radius $7$, then the equation of the circle is

If $f(2) = 4$ and $f'(2) = 1$, then $\displaystyle\lim_{x \to 2} \frac{xf (2) - 2 f (x) }{x -2}$ is equal to

The velocities of two particles $A$ and $B$ are $0.05$ and $0.02\, ms^{-1}$ respectively. The mass of $B$ is five times the mass of $A$. The ratio of their de- Broglie's wavelength is

Two particles $A$ and $B$ initially at rest, move towards each other, under mutual force of attraction. At an instance when the speed of $A$ is $v$ and speed of $B$ is $2v$, the speed of center of mass $(CM)$ is

Which of the following statements are correct for alkali metal compounds? (i) Superoxides are paramagnetic in nature. (ii) The basic strengths of hydroxides increases down the group. (iii) The conductivity of chlorides in their aqueous solutions decreases down the group. (iv) The basic nature of carbonates in aqueous solutions is due to cationic hydrolysis.

In $\triangle A B C$ the mid points of the sides $A B, B C$ and $C A$ are respectively $(1,0,0),(0$, $m , 0)$ and $(0,0, n )$. Then, $\frac{A B^{2}+B C^{2}+C A^{2}}{l^{2}+m^{2}+n^{2}}$ is equal to

In a certain code ROAD is written as URDG. How is SWAN written in that code?

Which of the following will come in place of the question mark(?) in the following sequence?
6C7,8FIO, 11J14, 15019,?

Ram walks 10m South from his house, turns left and walks 23 m, again turns left and walks 40 m, then turns right and walks 5 m to reach his school. In which direction is the school from his house?

If table is called chair, chair is called cot, cot is called pot and pot is calledfilter, where does a person sit?

Off-hand is related to PERFUNCTORY, in the same way as above, Board is related to

In a class of 35 students, Kiran is placed 7th from the bottom whereas Mohan is placed 9th from the top. Sohan is placed exactly in between Kiran and Mohan. What is Kiran's position from Sohan?

Pointing to a photograph Arun said, 'She is the mother of my brother's son's wife's daughter.' How is Arun related to the lady?

Which one is different from the remaining three?

ABCD is related to OPQR in the same way as WXYZ is related to

The letters skipped between adjacent letters are the order of . . Which altemative follows this rule?