Consider a titration of potassium dichromate solution with acidified Mohr's salt solution using diphenylamine as indicator. The number of moles of Mohr's salt required per mole of dichromate is

Paragraph: When potassium iodide is added to an aqueous solution of potassium ferricyanide, a reversible reaction is observed in which a complex \(\mathrm{P}\) is formed. In a strong acidic medium, the equilibrium shifts completely towards \(\mathrm{P}\). Addition of zinc chloride to \(\mathrm{P}\) in a slightly acidic medium results in a sparingly soluble complex Q.
Question: The number of moles of potassium iodide required to produce two moles of \(\mathbf{P}\) is

The correct stability order for the following species is

The $1^{\mathrm{st}}$, $2^{\mathrm{nd}}$ and the $3^{\mathrm{rd}}$ ionization enthalpies, ${\mathrm{I}}_1, {\mathrm{I}}_2$ and ${\mathrm{I}}_3$, of four atoms with atomic numbers $\mathrm{n}, \mathrm{n}+1, \mathrm{n}+2,$ and $\mathrm{n}+3,$ where $\mathrm{n}<10,$ are tabulated below. What is the value of $\mathrm{n}$?

Atomic number	Ionization Enthalpy (kJ/mol)
	${\mathrm{I}}_1$	${\mathrm{I}}_2$	${\mathrm{I}}_3$
$\mathrm{n}$	$1681$	$3374$	$6050$
$\mathrm{n}+1$	$2081$	$3952$	$6122$
$\mathrm{n}+2$	$496$	$4562$	$6910$
$\mathrm{n}+3$	$738$	$1451$	$7733$

In a metal deficient oxide sample, \(\mathbf{M}_{\mathbf{x}} \mathbf{Y}_2 \mathbf{O}_4\) ( \(\mathbf{M}\) and \(\mathbf{Y}\) are metals), \(\mathbf{M}\) is present in both +2 and +3 oxidation states and \(\mathbf{Y}\) is in +3 oxidation state. If the fraction of \(\mathbf{M}^{2+}\) ions present in \(\mathbf{M}\) is \(\frac{1}{3}\), the value of \(\mathbf{X}\) is ________.

In thermodynamics, the $\mathrm{P}-\mathrm{V}$ work done is given by $\mathrm{w}=-\int {\mathrm{dVP}}_{\mathrm{ext}}$. For a system undergoing a particular process, the work done is,
$\mathrm{w}=-\int \mathrm{dV}\left(\frac{\mathrm{RT}}{\mathrm{V}-\mathrm{b}}-\frac{\mathrm{a}}{{\mathrm{V}}^2}\right)$. This equation is applicable to a

Benzene and naphthalene form an ideal solution at room temperature. For this process, the true statement(s) is (are)

Paragraph:
Let \(A, B, C\) be three sets of complex numbers as defined below.
\(A=\{z ; \operatorname{lm} z \geq 1\} ; B=\{z:|z-2-i|=3\} ;\) \(C=\{z: \operatorname{Re}((1-i) z)=\sqrt{2}\}\).
Question:
Let \(z\) be any point in \(A \cap B \cap C\). The \(|z+1-i|^2+|z-5-i|^2\) lies between

Electrolysis of dilute aq. \(\mathrm{NaCl}\) solution was carried out by passing \(10 \mathrm{~mA}\) current. The time required to liberate \(0.01\) mole of \(\mathrm{H}_2\) gas at the cathode is (1 Faraday \(=96500 \mathrm{C} \mathrm{mol}^{-1}\) )

The freezing point (in \({ }^{\circ} \mathrm{C}\) ) of solution containing \(0.1 \mathrm{~g}\) of \(\mathrm{K}_3\left[\mathrm{Fe}(\mathrm{CN})_6\right]\) (molecular weight 329\()\) in \(100 \mathrm{~g}\) of water \(\left(K_f=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)\) is

Let \(k \in \mathbb{R}\). If \(\lim _{x \rightarrow 0^+}(\sin (\sin k x)+\cos x+x)^{\frac{2}{x}}=e^6\), then the value of \(k\) is

Let $P$ be a point on the parabola $y^2=4ax$, where $a>0$. The normal to the parabola at $P$ meets the $x$-axis at a point $Q$. The area of the triangle $PFQ$, where $F$ is the focus of the parabola, is $120$. If the slope $m$ of the normal and $a$ are both positive integers, then the pair $\left(a, m\right)$ is

Paragraph:

In a thin rectangular metallic strip a constant current \(I\) flows along the positive \(x\)-direction, as shown in the figure. The length, width and thickness of the strip are \(l, w\) and \(d\), respectively.

A uniform magnetic field \(\vec{B}\) is applied on the strip along the positive \(y\)-direction. Due to this, the charge carriers experience a net deflection along the \(z\)-direction. This results in accumulation of charge carriers on the surface \(P Q R S\) and appearance of equal and opposite charges on the face opposite to \(P Q R S\). A potential difference along the \(z\)-direction is thus developed. Charge accumulation continues until the magnetic force is balanced by the electric force. The current is assumed to be uniformly distributed on the cross section of the strip and carried by electrons.






Question:

Consider two different metallic strips (\(1\) and \(2\)) of same dimensions (length \(l\), width \(w\) and thickness \(d\) ) with carrier densities \(n_{1}\) and \(n_{2}\), respectively. Strip \(1\) is placed in magnetic field \(B_{1}\) and strip \(2\) is placed in magnetic field \(B_{2}\), both along positive \(y\)-directions. Then \(V_{1}\) and \(V_{2}\) are the potential differences developed between \(K\) and \(M\) in strips \(1\) and \(2\), respectively. Assuming that the current \(I\) is the same for both the strips, the correct option(s) is(are)