List of practice Questions

0.1 M solution of KI reacts with excess of $ \text{H}_2\text{SO}_4 $ and KIO$_3$, according to the equation: \[ 5I^- + 6H^+ \rightarrow 3I_2 + 3H_2O \]

Identify the correct statements:

(A) 200 mL KI solution reacts with 0.004 mol of KIO₃
(B) 200 mL KI solution reacts with 0.006 mol of H₂SO₄
(3) 0.5 L KI solution produced 0.005 mol of I₂
(4) Equivalent weight of KIO₃ is equal to Molecular weight / 5

O$_2$ gas will be evolved as a product of electrolysis of:
(A) an aqueous solution of AgNO3 using silver electrodes.
(B) an aqueous solution of AgNO3 using platinum electrodes.
(C) a dilute solution of H2SO4 using platinum electrodes.
(D) a high concentration solution of H2SO4 using platinum electrodes.
Choose the correct answer from the options given below :

Let a line pass through two distinct points $ P(-2, -1, 3) $ and $ Q $, and be parallel to the vector $ 3\hat{i} + 2\hat{j} + 2\hat{k} $. If the distance of the point $ Q $ from the point $ R(1, 3, 3) $ is 5, then the square of the area of $ \triangle PQR $ is equal to:

Given below are two statements:
Statement (I): $\textit{An element in the extreme left of the periodic table forms acidic oxides.}$
Statement (II):$ \textit{Acid is formed during the reaction between water and oxide of a reactive element present in the extreme right of the periodic table.} In the light of the above statements, choose the correct answer from the options given below:$

A ring and a solid sphere are released from rest from the same height on enough rough inclined surface. The ratio of their speed when they reach the bottom is $ \sqrt{\frac{7}{x}} $ m/s, then $ x $ is ______.

In a resonance tube closed at one end. Resonance is obtained at lengths $ l_1 = 120 \, \text{cm} $ and $ l_2 = 200 \, \text{cm} $. If $ v_s = 340 \, \text{m/s} $, find the frequency of sound.

The sum of squares of roots of $ |x - 2|^2 - |x - 2| - 2 = 0 $ and $ x^2 - 2|x - 3| - 5 = 0 $ equals to:

Let the area of the bounded region $ \{(x, y) : 0 \leq 9x \leq y^2, y \geq 3x - 6 \ be $ A $. Then 6A is equal to:

Two balls with the same mass and initial velocity are projected at different angles in such a way that the maximum height reached by the first ball is 8 times higher than that of the second ball. $ T_1 $ and $ T_2 $ are the total flying times of the first and second ball, respectively, then the ratio of $ T_1 $ and $ T_2 $ is:

Which of the following binary mixture does not show the behavior of minimum boiling azeotropes?

A metal complex with a formula MC$\ell_4$3NH$_3$ is involved in sp$^3$d$^2$ hybridisation. It upon reaction with excess of AgNO$_3$ solution gives ‘x’ moles of AgCl. Consider ‘x’ is equal to the number of lone pairs of electron present in central atom of BrF$_5$. Then the number of geometrical isomers exhibited by the complex is ________

If the number of seven-digit numbers, such that the sum of their digits is even, is $ m \cdot n \cdot 10^a $; $ m, n \in \{1, 2, 3, ..., 9\} $, then $ m + n $ is equal to

If $\lim_{x \to 1} \frac{(x-1)(6+\lambda \cos(x-1)) + \mu \sin(1-x)}{(x-1)^3} = -1$, where $\lambda, \mu \in \mathbb{R}$, then $\lambda + \mu$ is equal to

The pH of a 0.01 M weak acid $\mathrm{HX}\left(\mathrm{K}_{\mathrm{a}}=4 \times 10^{-10}\right)$ is found to be 5 . Now the acid solution is diluted with excess of water so that the pH of the solution changes to 6 . The new concentration of the diluted weak acid is given as $\mathrm{x} \times 10^{-4} \mathrm{M}$. The value of x is _______ (nearest integer).

For $ \alpha, \beta, \gamma \in \mathbb{R} $, if \[ \lim_{x \to 0} \frac{x^2 \sin(\alpha x) + (\gamma - 1)e^{x^2}}{\sin(2x - \beta x)} = 3, \] then $ \beta + \gamma - \alpha $ is equal to:

Consider the above reaction, what mass of CaCl₂ will be formed if 250 ml of 0.76 M HCl reacts with 1000 g of CaCO₃?

A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the x-direction in 0.3 sec. The crest P is at $ x = 0 $ at $ t = 0 $ sec and maximum displacement of the wave is 2 cm. Which equation correctly represents this wave?

Consider a circular loop that is uniformly charged and has a radius $ \sqrt{2} $. Find the position along the positive $ z $-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in the $ xy $-plane at the origin:

Given below are some nitrogen containing compounds:
Each of them is treated with HCl separately. 1.0 g of the most basic compound will consume ...... mg of HCl.
(Given Molar mass in g mol$^{-1}$: C = 12, H = 1, O = 16, Cl = 35.5.)

Solve the inequality: $ \log_2(x^2 - 5x + 6) >1 $

A coil of resistance 10 $ \Omega $ is connected to a battery of 12 V. If the current flowing through the coil is 2 A, what is the power dissipated in the coil?

A proton and an $ \alpha $-particle are accelerated by the same potential difference. Find out the ratio of their de Broglie wavelengths.

Find: \[ \int \frac{\cos x \, dx}{1 + \cos x + \sin x}. \]

Let A be a 3 × 3 matrix such that $\text{det}(A) = 5$. If $\text{det}(3 \, \text{adj}(2A)) = 2^{\alpha \cdot 3^{\beta} \cdot 5^{\gamma}}$, then $ (\alpha + \beta + \gamma) $ is equal to:

In a family consisting of four living generations (excluding married daughters), the wife is always three years younger than her husband. The siblings in the family have an age gap of three years and there are 2 siblings in the youngest generation. Each father is thirty years older than his eldest child. The present age of the youngest daughter is six years and her father has no siblings. Based on this information, what is the age difference between the youngest child and her grandmother?