List of practice Questions

Consider the following changes I and II
Change I: ${O2 → O2^{2-}}$
Change II: ${O2 → O2^{-}}$
The correct statements about these changes (I) and (II) in accordance with MO theory are

The increasing order of number of lone pair electrons on the central atom of the following molecules is which of the following?
I) ${ClF3}$
II) ${XeF2}$
III) ${SF4}$
IV) ${SiH4}$

Which of the following is the correct statement for an ideal gas (constant =\( \textit{energy}\) )?

The number of primary (1$^\circ$), secondary (2$^\circ$), and tertiary (3$^\circ$) alcohols possible for the formula C$_5$H$_{12}$O respectively are:

Activation energy for the hydrolysis of sucrose by acid is X kJ mol$^{-1}$ and by sucrase is Y kJ mol$^{-1}$. X and Y respectively are

Match the following:

List-I (Atomic number, Z)	List-II (Block)
A) 112	I) \(s\)
B) 116	II) \(p\)
C) 88	III) \(d\)
D) 100	IV) \(f\)

Observe the following numbers:
I) 0.0063
II) 132.00
III) 1004
The number of significant figures in I, II and III respectively is

Observe the following reactions
I) Sucrose (aq) + H2O →[x] glucose + fructose
II) Glucose (aq) →[y] ethanol + CO2
What are $x$ and $y$ respectively? Identify the correct option from the following:

The set of all real values of $x$ such that \[ f(x) = \frac{[x] - 1}{\sqrt{[x]^2 - [x] - 6}} \] is a real valued function is

If a function $f : \mathbb{Z} \to \mathbb{Z}$ is defined by $f(x) = x - (-1)^x$, then $f(x)$ is

If \[ A = \begin{bmatrix} 1 & 2 & -2 \\ 2 & -1 & 2\\ -1 & 1 & -2 \end{bmatrix}, \] then find $A + 2A^{-1}$.

If $(3 + 4i)^{2025} = 5^{2023}(x + iy)$, then find $\sqrt{x^2 + y^2}$.

If \[ \left(\frac{\cos \theta + i \sin \theta}{\sin \theta + i \cos \theta}\right)^{2024} + \left(\frac{1 + \cos \theta + i \sin \theta}{1 - \cos \theta + i \sin \theta}\right)^{2025} = x + iy, \] and $x + y$ at $\theta = \frac{\pi}{2}$ is

The coefficient of \(x^3\) in the expansion of \(\frac{x^4 + 1}{(x^2 + 1)(x - 1)}\) when it is expressed in terms of positive integral powers of \(x\), is

If \(x\) is a real number, then the number of solutions of \(\tan^{-1}\left(\sqrt{x(x+1)}\right) + \sin^{-1}\left(\sqrt{x^2 + x + 1}\right) = \dfrac{\pi}{2}\) is

Domain of the real-valued function \(f(x) = \log(x^2 - 1) + x \, \coth^{-1}x\) is

If \(|\vec{a}| = 2, |\vec{b}| = 3, |\vec{c}| = 5, |\vec{a} + \vec{b} + \vec{c}| = \sqrt{69}\) and angle between \((\vec{a}, \vec{b}) = \dfrac{\pi}{3}\), then angle between \((\vec{c}, \vec{a}) =\)

One of the latus recta of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ subtends an angle $2 \tan^{-1} \left(\frac{3}{2}\right)$ at the centre of the hyperbola. If $b^2 = 36$ and $e$ is the eccentricity of the hyperbola, then find $\sqrt{a^2 + e^2}$.

If $L$ is the normal drawn to the parabola $y^2 = 8x$ at the point $t = \frac{1}{\sqrt{2}}$, then the foot of the perpendicular drawn from the focus of the parabola onto the normal $L$ is:

If the acute angle between the circles $S \equiv x^2 + y^2 + 2kx + 4y - 3 = 0$ and $S^1 \equiv x^2 + y^2 - 4x + 2ky + 9 = 0$ is $\cos^{-1}\left(\frac{3}{8}\right)$ and the centre of $S^1 = 0$ lies in the first quadrant, then the radical axis of $S = 0$ and $S^1 = 0$ is:

If \(\cos \alpha = \sec h \beta\), then \(\beta =\)

If \((1+x)^n = \sum_{r=0}^n \binom{n}{r} x^r\), then the value of \[ C_0 + (C_0 + C_1) + (C_0 + C_1 + C_2) + \cdots + (C_0 + C_1 + \cdots + C_n) \] is:

Consider the following statements:
Statement-I: CH$_3$NH$_2$ is more basic than NH$_3$, but C$_6$H$_5$NH$_2$ is less basic than NH$_3$.
Statement-II: The order of basic strength of amines in aqueous phase follows
(C$_2$H$_5$)$_2$NH > C$_2$H$_5$NH$_2$ > C$_6$H$_5$NH$_2$

The structure of the nitrogen-containing heterocyclic base shown below represents:

What is the drug used to control depression and hypertension?