List of practice Questions

For $x \, \in \, R , x \neq 0, x \neq 1,$ let $f_0(x) = \frac{1}{1-x}$ and $f_{n+1} (x) | = f_0 (f_n(x)), n = 0 , 1 , 2 , ...$ Then the value of $f_{100}(3) + f_1 \left(\frac{2}{3} \right) + f_2 \left( \frac{3}{2} \right)$ is equal to :

The mean of $5$ observations is $5$ and their variance is $124$. If three of the observations are $1, 2$ and $6$ ; then the mean deviation from the mean of the data is :

Let $P = \{ \theta : \sin \theta - \cos \theta = \sqrt{2} \cos \theta \}$ and $Q = \{\theta : \sin \theta + \cos \theta = \sqrt{2} \sin \theta \}$ be two sets. Then :

The sum of all real values of $x$ satisfying the equation $(x^2 - 5x + 5)^{x^2 + 4x -60} = 1 $ is

$CO$ is a stronger ligand than $Cl^-$ because

The sulphur compound in which the sulphur atom has octet configuration in its valence shell among the following is

The hypothetical complex chloropentaamminecobalt (III) chloride can be represented as

Which of the following compound has all the four types $\left(1^{\circ}, 2^{\circ}, 3^{\circ}\right.$ and $\left.4^{\circ}\right)$ of carbon atoms?

A compound of Xe and F is found to have 53.5% of Xe. What is oxidation number of Xe in this compound ?

All the words that can be formed using alphabets $A, H, L, U$ and $R$ are written as in a dictionary (no alphabet is repeated). Rank of the word RAHUL is

Nucleotides are joined together by between $ 5' $ and $ 3' $ carbon atoms of pentose sugar

The normality of $26\%$ (wt/vol) solution of ammonia (density $= 0.855$ ) is approximately :

$1.25\, g$ of a sample of $Na _{2} CO _{3}$ and $Na _{2} SO _{4}$ is dissolved in $250\, ml$ solution. $25 ml$ of this solution neutralises $20\, ml$ of $0.1\, N\, H _{2} SO _{4}$. The $\%$ of $Na _{2} CO _{3}$ in this sample is

At what temperature, the rate of effusion of $N_2$ would be $1.625$ times than that of $SO_2$ at $50^{\circ} C$ ?

Block $A$ of mass $m$ and block $B$ of mass $2 m$ are placed on a fixed triangular wedge by means of a massless, inextensible string and a frictionless pulley as shown in figure. The wedge is inclined at $45^{\circ}$ to the horizontal on both the sides. If the coefficient of friction between the block $A$ and the wedge is $2 / 3$ and that between the block $B$ and the wedge is $1 / 3$ and both the blocks $A$ and $B$ are released from rest, the acceleration of $A$ will be

Consider the following statements in respect of the function $f(x)=x^{3}-1, x \in[-1,1]$ I. $f(x)$ is increasing in $[-1,1]$ II. $f(x)$ has no root in $(-1,1)$. Which of the statements given above is/are correct?

For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index :

Formation of polyethylene from calcium carbide takes place as follows $ CaC _{2}+2 H _{2} O \longrightarrow Ca ( OH )_{2}+ C _{2} H _{2}$ $C _{2} H _{2}+ H _{2} \longrightarrow C _{2} H _{4} $ $ nC _{2} H _{4} \longrightarrow\left(- CH _{2}- CH _{2}-\right) n$ The amount of polyethylene obtained from $64.1\, kg$ of $CaC _{2}$ is

If $\log a, \log b$, and $\log c$ are in A.P. and also $\log a-\log 2 b, \log 2 b-\log 3 c, \log 3 c-\log a$ are in A.P., then

If $\sin^{-1} \left(\frac{2a}{1+a^{2}}\right) -\cos^{-1} \left(\frac{1-b^{2}}{1+b^{2}}\right) = \tan^{-1} \left(\frac{2x}{1-x^{2}}\right) , $ then what is the value of x?

If three vertices of a regular hexagon are chosen at random, then the chance that they form an equilateral triangle is :

The degree of dissociation of $P C l_{5}(\alpha)$ obeying the equilibrium $PCl _{5} \rightleftharpoons PCl _{3}+ Cl _{2}$ is related to the equilibrium pressure by

The number of values of $r$ satisfying the equation $^{39}C_{3r-1} - ^{39}C_{r^{2}} = ^{39}C_{r^{2}-1} - ^{39}C_{3r} $ is

Two spheres of different materials one with double the radius and one-fourth wall thickness of the other are filled with ice. If the time taken for complete melting of ice in the larger sphere is $25$ minute and for smaller one is $16$ minute, the ratio of thermal conductivities of the materials of larger spheres to that of smaller sphere is

Two wires are made of the same material and have the same volume. However wire $1$ has cross sectional area A and wire $2$ has cross-sectional area $3A$. If the length of wire $1$ increases by $\Delta x$ on applying force $F$, how much force is needed to stretch wire $2$ by the same amount?