The element \(X\) on reaction with conc. \(\mathrm{HNO}_3\) forms two acidic oxides \(A\) and \(B\) of different shapes. Element \(Z\) on reaction with conc. \(\mathrm{H}_2 \mathrm{SO}_4\) forms two acidic oxides \(A\) and \(D\) of different shapes. What are \(X\) and \(Z\) ?

At \(25^{\circ} \mathrm{C}, \mathrm{K}_{\mathrm{a}}\) of formic acid is \(1.8 \times 10^{-4}\). What is the \(\mathrm{K}_{\mathrm{b}}\) of \(\mathrm{HCOO}^{-}\)?

Match the following.

The following are some statements related to VA group hydrides,
I. Reducing property increases from \(\mathrm{NH}_3\) to \(\mathrm{BiH}_3\).
II. Tendency to donate lone pair decreases from \(\mathrm{NH}_3\) to \(\mathrm{BiH}_3\).
III. Thermal stability of hydrides decreases from \(\mathrm{NH}_3\) to \(\mathrm{BiH}_3\).
IV. Bond angle of hydrides decreases from \(\mathrm{NH}_3\) to \(\mathrm{BiH}_3\).
The correct statements are

The solubility ' \(\mathrm{S}\) ' of \(\mathrm{Zr}_3\left(\mathrm{PO}_4\right)_4\) in terms of its solubility product, \(\mathrm{K}_{\mathrm{sp}}\) is

\(\begin{aligned}
& \mathrm{P}_2 \mathrm{O}_3+\mathrm{H}_2 \mathrm{O} \rightarrow \mathrm{X} \\
& \quad \text { Red } \mathrm{P}_4+\text { alkali } \rightarrow \mathrm{Y}
\end{aligned}\)
\(\mathrm{X}, \mathrm{Y}\) are oxoacids of phosphorous. The number of \(\mathrm{P}-\mathrm{OH}\) bonds in X . Y respectively is \(\mathrm{P}_2 \mathrm{O}_3+\mathrm{H}_2 \mathrm{O} \rightarrow \mathrm{X}\)

Which of the following is not correct about Grignard reagent?

Assertion (A) Fluorine has smaller negative electron gain enthalpy than chlorine.
Reason (R) The electron-electron repulsion is higher in chlorine than in fluorine.

Match the items of List - I with those of the entires of List - II
\(List - I\)
\(\begin{aligned} & \text { (I) } \sin ^2 5^{\circ}+\sin ^2 10^{\circ}+ \\ & \sin ^2 15^{\circ}+\ldots+\sin ^2 90^{\circ}=\end{aligned}\)
\(\begin{aligned} & \text { (II) } \tan ^2 5^{\circ} \cdot \tan ^2 10^{\circ} \text {. } \\ & \tan ^2 15^{\circ} \ldots \tan ^2 85^{\circ}= \\ & \end{aligned}\)
\(\begin{aligned} & \text { (III) } \cos ^2 5^{\circ}+\cos ^2 10^{\circ} \\ & +\cos ^2 15^{\circ}+\ldots+\cos ^2 180^{\circ}=\end{aligned}\)
\(\begin{gathered}\text { (IV) } \cot 5^{\circ}+\cot 10^{\circ}+\cot 15^{\circ} \\ +\ldots .+\cot 175^{\circ}=\end{gathered}\)
\(List - II\)
(A) \(0\)
(B) \(\frac{19}{2}\)
(C) \(18\)
(D) \(1\)
(E) \(-1\)

The elastic energy stored per unit volume in terms of longitudinal strain ' \(\epsilon\) ' and Young's modulus ' \(Y\) ' is

A ball projected vertically upwards with a velocity 'v' passes through a point \(P\) in its upward journey in a time of ' \(x\) ' seconds. From there, the time in which the ball again passes through the same point \(P\) is

The equation of the locus of the foot of the perpendicular drawn from the centre of the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\) to any tangent of the ellipse is

If $A$ and $B$ throw two dice $100$ times each simultaneously, then the probability that both of them will get even number as the total score at the same time in all the throws is