List of practice Questions

The heat of solution of anhydrous CuSO$_4$ and CuSO$_4\cdot$5H$_2$O are $-70$ kJ mol$^{-1}$ and $+12$ kJ mol$^{-1}$ respectively. The heat of hydration of CuSO$_4$ to CuSO$_4\cdot$5H$_2$O is $-x$ kJ. The value of $x$ is _____.

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Both rhombic and monoclinic sulphur exist as S$_8$ while oxygen exists as O$_2$.
{Reason (R): Oxygen forms $p\pi$-$p\pi$ multiple bonds with itself and other elements having small size and high electronegativity like C, N, which is not possible for sulphur.
In the light of the above statements, choose the most appropriate answer from the options given below:

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The total number of geometrical isomers shown by [Co(en)$_2$Cl$_2$]$^+$ complex ion is three.
Reason (R): [Co(en)$_2$Cl$_2$]$^+$ complex ion has an octahedral geometry.
In the light of the above statements, choose the most appropriate answer from the options given below:

Identify major product "X" formed in the following reaction :

The electronic configuration of Cu(II) is 3d⁹ whereas that of Cu(I) is 3d¹⁰. Which of the following is correct ?

What is the structure of C ?

Given below are two statements:
Statement (I): The oxidation state of an element in a particular compound is the charge acquired by its atom on the basis of electron gain enthalpy consideration from other atoms in the molecule.
Statement (II): $p\pi$-$p\pi$ bond formation is more prevalent in second period elements over other periods.
In the light of the above statements, choose the {most appropriate answer from the options given below:

In which one of the following pairs the central atoms exhibit sp$^2$ hybridization?

The F$^-$ ions make the enamel on teeth much harder by converting hydroxyapatite (the enamel on the surface of teeth) into much harder fluoroapatite having the formula:

In the following sequence of reaction, the major products B and C respectively are :

Methods used for purification of organic compounds are based on :

The molar conductivity for electrolytes A and B are plotted against C^1/2 as shown below. Electrolytes A and B respectively are :

Let \( f(x) = ax^3 + bx^2 + ex + 41 \) be such that \( f(1) = 40 \), \( f'(1) = 2 \) and \( f''(1) = 4 \). Then \( a^2 + b^2 + c^2 \) is equal to:

The shortest distance between the line:
\[ \frac{x-3}{4} = \frac{y+7}{-11} = \frac{z-1}{5} \] and \[ \frac{x-5}{3} = \frac{y-9}{-6} = \frac{z+2}{1} \] is:

If the domain of the function \(f(x) = \sin^{-1}\left( \frac{x - 1}{2x + 3} \right)\) is \(\mathbb{R} - (\alpha, \beta)\), then \(12 \alpha \beta\) is equal to:

Let \[ \left| \cos \theta \cos (60^\circ - \theta) \cos (60^\circ - \theta) \right| \leq \frac{1}{8}, \quad \theta \in [0, 2\pi] \] Then, the sum of all \( \theta \in [0, 2\pi] \), where \( \cos 3\theta \) attains its maximum value, is:

Let \(\overrightarrow{OA} = 2\vec{a}\), \(\overrightarrow{OB} = 6\vec{a} + 5\vec{b}\), and \(\overrightarrow{OC} = 3\vec{b}\), where \(O\) is the origin. If the area of the parallelogram with adjacent sides \(\overrightarrow{OA}\) and \(\overrightarrow{OC}\) is 15 sq. units, then the area (in sq. units) of the quadrilateral \(OABC\) is equal to:

A ray of light coming from the point \( P(1, 2) \) gets reflected from the point \( Q \) on the x-axis and then passes through the point \( R(4, 3) \). If the point \( S(h, k) \) is such that \( PQRS \) is a parallelogram, then \( hk^2 \) is equal to:

Let \( \int \frac{2 - \tan x}{3 + \tan x} \, dx = \frac{1}{2} \left( \alpha x + \log_e \lvert \beta \sin x + \gamma \cos x \rvert \right) + C \), where \( C \) is the constant of integration.

The solution curve, of the differential equation \( 2y \frac{dy}{dx} + 3 = 5 \frac{dy}{dx} \), passing through the point \( (0, 1) \), is a conic, whose vertex lies on the line:

The parabola \( y^2 = 4x \) divides the area of the circle \( x^2 + y^2 = 5 \) in two parts. The area of the smaller part is equal to:

In given circuit, reading of voltmeter is 1 V, then resistance of

The approximate total cross sectional areas of various types of blood vessels are given below. It was estimated that the velocity of blood in the aorta is 30 cms^-1. The time it will take for the blood to travel through a capillary of length 0.5 mm is_______ seconds. Give your answer rounded off to two decimal places.

Vessel Type	Approximate total cross sectional area (cm2)
Aorta	4.5
Artery	20
Arteriole	400
Capillary	4500
Venule	40
Vein	15

Two point charges of charge \( +q \) each are placed a distance \( 2d \) apart. A grounded solid conducting sphere of radius \( a \) is placed midway between them. Assume \( a^2 \ll d^2 \). Which of the following statements is/are true?

If the mirror image of the point \(P(3,4,9)\) in the Line 
\(\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-2}{1}\) is \((α,β,γ)\) then find \(14(a+ẞ+y)\) is: