List of practice Questions

The function \(f(x)=xe^{x(1-x)}\),x∈R is

An acidified manganate solution undergoes disproportionation reaction. The spin-only magnetic moment value of the product having manganese in higher oxidation state is ____ B.M. (Nearest integer)

In the above reaction ‘A’ is

Consider the ions/molecules \(O^{2+}, O_2, O_2^-, O_2^{2-}\)For increasing bond order the correct option is

Consider the above reaction sequence and identify the product B.

The formulas of A and B for the following reaction sequence are

Match List I with List II.

List I Pollutant	List II Source
A. Microorganisms	I. Strip mining
B. Plant nutrients	II. Domestic sewage
C. Toxic heavy metals	III. Chemical fertilizer
D. Sediment	IV. Chemical factory

Choose the correct answer from the options given below:

For a real gas at 25°C temperature and high pressure (99 bar) the value of the compressibility factor is 2, so the value of van der Waal’s constant ‘b’ should be ______ × 10^–2 L mol^–1 (Nearest integer).
(Given R=0.083 L bar K-1 mol-1)

The spin only magnetic moment of the complex present in Fehling’s reagent is_____ B.M. (Nearest integer).

The first ionization enthalpy of Na, Mg and Si, respectively, are : 496, 737 and 786 kJ mol^–1. The first ionization enthalpy (kJ mol^–1) of Al is:

The mean and variance of 10 observation were calculated as 15 and 15 respectively by a student who took by mistake 25 instead of 15 for one observation. Then, the correct standard deviation is ________.

Let the line
\(\frac{x - 3}{7} = \frac{y - 2}{-1} = \frac{z - 3}{-4}\)
intersect the plane containing the lines
\(\frac{x - 4}{1} = \frac{y + 1}{-2} = \frac{z}{1}\) and \(4ax-y+5z-7a = 0 = 2x-5y-z-3, a∈R\)
at the point P(α, β, γ). Then the value of α + β + γ equals _____.

Let
\(f(x) = 2x^2 - x - 1\ and\ S = \{ n \in \mathbb{Z} : |f(n)| \leq 800 \}\)
Then, the value of ∑_n∈S f(n) is equal to ________.

Leaching of gold with dilute aqueous solution of NaCN in presence of oxygen gives complex [A], which on reaction with zinc forms the elemental gold and another complex [B]. [A] and [B], respectively are :

An organic compound ‘A’ on reaction with NH₃ followed by heating gives compound B. Which on further strong heating gives compound C(C₈H₅NO₂). Compound C on sequential reaction with ethanolic KOH, alkyl chloride and hydrolysis with alkali gives a primary amine. The compound A is :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : At 10°C, the density of a 5 M solution of KCl [atomic masses of K & Cl are 39 & 35.5 g \(mol^{–1}\) respectively], is ‘x’ g \(ml^{–1}\). The solution is cooled to –21°C. The molality of the solution will remain unchanged.
Reason (R) : The molality of a solution does not change with temperature as mass remains unaffected with temperature.
In the light of the above statements, choose the correct answer from the options given below.

A radioactive nucleus can decay by two different processes. Half-life for the first process is 3.0 hours while it is 4.5 hours for the second process. The effective half-life of the nucleus will be:

Let the solution curve of the differential equation \(x\frac{dy}{dx}-y=\sqrt{y^2+16x^2},\) y(1) = 3 be y = y(x). Then y(2) is equal to

Consider a cuboid of sides 2x, 4x and 5x and a closed hemisphere of radius r. If the sum of their surface areas is a constant k, then the ratio x : r, for which the sum of their volumes is maximum, is

Let
\(\stackrel{→}{a} = \hat{i} + \hat{j} + \hat{2k}, \stackrel{→}{b} = \hat{2i} - \hat{3j} + \hat{k}\)
and
\(\stackrel{→}{c}= \hat{i} - \hat{j} + \hat{k}\)
be three given vectors.
Let \(\stackrel{→}{v}\) be a vector in the plane of \(\stackrel{→}{a}\) and \(\stackrel{→}{b}\) whose projection on \(\stackrel{→}{c}\) is \(\frac{2}{\sqrt3}\).
If \(\stackrel{→}{v}.\hat{j}\) = 7 , then \(\stackrel{→}{v}.(\hat{i}+\hat{k})\) is equal to :

Which of the following can be used to prevent the decomposition of \(H_2O_2\)?

The current in a coil of self inductance \(2.0\ H\) is increasing according to \(I = 2\ sin(t^2)\ A\). The amount of energy spent during the period when current changes from 0 to \(2\ A\) is _______ \(J\).

Nitrogen gas is obtained by thermal decomposition of

For

\(z=a^2x^3y^{\frac{1}{2}}\)

where ‘a‘ is a constant. If percentage error in measurement of ‘x‘ and ‘y’ are 4% and 12%, respectively, then the percentage error for ‘z‘ will be ____ %.

Two 10 cm long, straight wires, each carrying a current of 5 A are kept parallel to each other. If each wire experienced a force of 10^–5 N, then separation between the wires is _____ cm.