On decreasing the $\mathrm{pH}$ from $7$ to $2$, the solubility of a sparingly soluble salt $\left(\mathrm{MX}\right)$ of a weak acid $\left(\mathrm{HX}\right)$ increased from ${10}^{-4} \mathrm{mol} {\mathrm{L}}^{-1}$ to ${10}^{-3} \mathrm{mol} {\mathrm{L}}^{-1}$. The ${\mathrm{pK}}_{\mathrm{a}}$ of $\mathrm{HX}$ is

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The concentration of potassium ions inside a biological cell is at least twenty times higher than the outside. The resulting potential difference across the cell is important in several processes such as transmission of nerve impulses and maintaining the ion balance. A simple model for such a concentration cell involving a metal \(\mathrm{M}\) is :
\(
M(s) \mid M^{+}(\alpha q ; 0.05 \text { molar }) \| M^{+}(a q ; 1 \text { molar })\) \(\mid M(s)
\)
For the above electrolytic cell the magnitude of the cell potential \(\left|E_{\text {cell }}\right|=70 \mathrm{mV}\).
Question:
If the \(0.05\) molar solution of \(M^{+}\)is replaced by a \(0.0025\) molar \(M^{+}\) solution, then the magnitude of the cell potential would be

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)
	${\mathrm{I}}_1$	${\mathrm{I}}_2$	${\mathrm{I}}_3$
$\mathrm{n}$	$1681$	$3374$	$6050$
$\mathrm{n}+1$	$2081$	$3952$	$6122$
$\mathrm{n}+2$	$496$	$4562$	$6910$
$\mathrm{n}+3$	$738$	$1451$	$7733$

Under ambient conditions, the total number of gases released as products in the final step of the reaction scheme shown below is

Among the following, the correct statement(s) about polymers is(are)

The pair(s) of coordination complexes/ions exhibiting the same kind of isomerism is (are)

The species having pyramidal shape is

The crystalline form of borax has

Statement 1 The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil.
and Statement 2 Soft iron has a high magnetic permeability and cannot be easily magnetized or demagnetized.

Two identical concave mirrors each of focal length \(f\) are facing each other as shown in the schematic diagram. The focal length \(f\) is much larger than the size of the mirrors. A glass slab of thickness \(t\) and refractive index \(n_0\) is kept equidistant from the mirrors and perpendicular to their common principal axis. A monochromatic point light source \(S\) is embedded at the center of the slab on the principal axis, as shown in the schematic diagram. For the image to be formed on \(S\) itself, which of the following distances between the two mirrors is/are correct:

The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be $E_b^p$ and the binding energy of a neutron be $E_b^n$ in the nucleus.
Which of the following statement(s) is(are) correct?

The total number of \(\alpha\) and \(\beta\)-particles emitted in the nuclear reaction \({ }_{92} \mathrm{U}^{238} \longrightarrow{ }_{82} \mathrm{~Pb}^{214}\) is

Let $a_1, a_2, a_3, .........$ be a sequence of positive integers in arithmetic progression with common difference $2$. Also, let $b_1, b_2, b_3, ........$ be a sequence of positive integers in geometric progression with common ratio $2$. If $a_1=b_1=c$, then the number of all possible values of $c$, for which the equality $2 \left(a_1+a_2+........+a_n\right)=b_1+b_2+.....+b_n$ holds for some positive integer $n$, is _______