List of practice Questions

Find the dimensions of $ \frac{B}{\mu_0} $

Consider the following elements In, Tl, Al, Pb, and Ge. The most stable oxidation states of elements with highest and lowest first ionisation enthalpies, respectively, are:

Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag 2. A ball is then drawn randomly from Bag 2. If the probability that the ball drawn is white is $\frac{29}{45}$, then n is equal to:

A cup of coffee cools from 90°C to 80°C in $ t $ minutes when the room temperature is 20°C. The time taken by the similar cup of coffee to cool from 80°C to 60°C at the same room temperature is:

Given below are two statements:
Statement (I): In partition chromatography, the stationary phase is a thin film of liquid present in the inert support.
Statement (II): In paper chromatography, the material of paper acts as a stationary phase.
In light of the above statements, choose the correct answer from the options given below:

Total number of non-bonded electrons present in $ \text{NO}_2 $; ion based on Lewis theory is:

Let the distance between two parallel lines be 5 units and a point $ P $ lies between the lines at a unit distance from one of them. An equilateral triangle $ POR $ is formed such that $ Q $ lies on one of the parallel lines, while $ R $ lies on the other. Then $ (QR)^2 $ is equal to _______.

If \[ \sum_{r=1}^{30} r^2 \left( \binom{30}{r} \right)^2 = \alpha \times 2^{29}, \] then $ \alpha $ is equal to _______.

Number of solutions in the interval $ [-2\pi, 2\pi] $ for the equation: \[ 2\sqrt{2} \cos^2 \theta + (2 - \sqrt{6}) \cos \theta - \sqrt{3} = 0 \]

The distance of the point $ (7, 10, 11) $ from the line $ \frac{x-9}{2} = \frac{y-13}{3} = \frac{z-17}{6} $ along the line is:

Two plane polarized light waves combine at a certain point, whose "E" components are: \[ E_1 = E_0 \sin \omega t, \quad E_2 = E_0 \sin \left( \omega t + \frac{\pi}{3} \right) \] Find the amplitude of the resultant wave.

\[ \int_9^{10} \frac{\sqrt{1 + x^2 + x}}{\sqrt{1 + x^2 - x}} \, dx = \frac{1}{m} \left[ \left( \sqrt{1 + x^2 + x} + x \right)^n \left( n \sqrt{1 + x^2 - x} - x \right) \right] + c \] where $ c $ is the constant of integration and $ m, n \in \mathbb{N} $, then $ m + n $ is ______.

Atomic number of element with lowest first ionisation enthalpy is:

Let the ellipse $ 3x^2 + py^2 = 4 $ pass through the centre $ C $ of the circle $ x^2 + y^2 - 2x - 4y - 11 = 0 $ of radius $ r $. Let $ f_1, f_2 $ be the focal distances of the point $ C $ on the ellipse. Then $ 6f_1 f_2 - r $ is equal to

Two strings with circular cross section and made of same material are stretched to have same amount of tension. A transverse wave is then made to pass through the strings. The velocity of the wave in the first string having the radius of cross section $ R $ is $ v_1 $, and that in the other string having radius of cross section $ R/2 $ is $ v_2 $. Then, $ \frac{v_2}{v_1} $ is:

A sample of a liquid is kept at 1 atm. It is compressed to 5 atm which leads to change of volume of 0.8 cm$^3$. If the bulk modulus of the liquid is 2 GPa, the initial volume of the liquid was ______ litre. (Take 1 atm = $10^5$ Pa)

Given below are two statements:
Statement I: A homoleptic octahedral complex, formed using monodentate ligands, will not show stereoisomerism
Statement II: cis- and trans-platin are heteroleptic complexes of Pd.
In the light of the above statements, choose the correct answer from the options given below

Given below are two statements:
Statement (I): Alcohols are formed when alkyl chlorides are treated with aqueous potassium hydroxide by elimination reaction.
Statement (II): In alcoholic potassium hydroxide, alkyl chlorides form alkenes by abstracting the hydrogen from the $ \beta $-carbon.
In the light of the above statements, choose the most appropriate answer from the options given below:

Given below are two statements:
Statement (I): The first ionisation enthalpy of group 14 elements is higher than the corresponding elements of group 13.
Statement (II): Melting points and boiling points of group 13 elements are in general much higher than those of the corresponding elements of group 14. Choose the most appropriate answer from the options given below:

Let $ y = y(x) $ be the solution curve of the differential equation $ x(x^2 + e^x) \, dy + \left( e^x(x - 2) y - x^3 \right) \, dx = 0, \quad x>0, $ passing through the point $ (1, 0) $. Then $ y(2) $ is equal to:

A cubic block of mass $ m $ is sliding down on an inclined plane at $ 60^\circ $ with an acceleration of $ \frac{g}{2} $, the value of coefficient of kinetic friction is:

The percentage dissociation of a salt (MX$_3$) solution at a given temperature (van't Hoff factor $i = 2$) is .................. % (Nearest integer)

Given below are two statements:
Statement I : The N-N single bond is weaker and longer than that of P-P single bond
Statement II : Compounds of group 15 elements in +3 oxidation states readily undergo disproportionation reactions.
In the light of above statements, choose the correct answer from the options given below

Consider the following reaction:

\[ A + NaCl + H_2SO_4 \xrightarrow[\text{Little amount}]{} CrO_2Cl_2 + \text{Side products} \] \[ CrO_2Cl_2(\text{Vapour}) + NaOH \rightarrow B + NaCl + H_2O \] \[ B + H^+ \rightarrow C + H_2O \]

The number of terminal 'O' present in the compound 'C' is ________.

$\mathrm{KMnO}_{4}$ acts as an oxidising agent in acidic medium. ' X ' is the difference between the oxidation states of Mn in reactant and product. ' Y ' is the number of ' d ' electrons present in the brown red precipitate formed at the end of the acetate ion test with neutral ferric chloride. The value of $\mathrm{X}+\mathrm{Y}$ is _______ .