If \(P=(2,-3,4), Q=(-1,-4,0), R=(2,1,0)\) are three points and \(S\) is the foot of the perpendicular drawn from \(\mathrm{R}\) to \(\mathrm{PQ}\), then the \(\mathrm{X}\)-coordinate of \(\mathrm{S}\) is

The orthogonal projection of \(\mathbf{a}\) on \(\mathbf{b}\) is

Which among the following represents the combined equation of a pair of lines through point \((1,0)\) and parallel to the lines represented by \(2 x^2-x y-y^2=0\).

In \(P\) and \(Q\) are square matrices such that \(P^{2006}=0\) and \(P Q=P+Q\), then \(\operatorname{det}(Q)\) will be

If $x^3-2x^2{y}^2+5x+y-5=0$, then at $\left(1,1\right), y^{\text{'}\text{'}}\left(1\right)=$

If \(y=\sinh ^{-1}\left(\frac{1-x}{1+x}\right)\) then \(\frac{d y}{d x}\)

For any natural number \(n,\left(15 \times 5^{2 n}\right)+\left(2 \times 2^{3 n}\right)\) is divisible by

A compound \(A\) contains \(C\) and \(H\) only and has molecular mass 72. It's photochlorination gives a mixture containing only one monochloro and two dichloro hydrocarbons. The IUPAC name is

A line moves such that the portion of it intercepted between the coordinate axes is of constant length \(a\), then the locus of the mid point of that line segment is

$10 \mathrm{g}$ of a gas at $\mathrm{STP}$ occupies a volume of $2 \mathrm{L}$. At what temperature will the volume be doubled, if pressure and amount of the gas remains constant?

A dipole is placed in a uniform electric field, its potential energy will be minimum when the angle between its axis and field is

Match the following
\(\begin{array}{ll}
\text{List - I} & \text{List - II} \\
\text{A) } \mathrm{Al}_2 \mathrm{O}_3+2 \mathrm{NaOH}+3 \mathrm{H}_2 \mathrm{O} \rightarrow 2 \mathrm{Na}\left[\mathrm{Al}(\mathrm{OH})_4\right] & \text{I) Roasting} \\
\text{B) } \mathrm{Ni}(\mathrm{CO})_4 \xrightarrow{230^{\circ} \mathrm{C}} \mathrm{Ni}+4 \mathrm{CO} & \text{II) Calcination} \\
\text{C) } \mathrm{Fe}_2 \mathrm{O}_3 \cdot 3 \mathrm{H}_2 \mathrm{O} \xrightarrow{\Delta} \mathrm{Fe}_2 \mathrm{O}_3+3 \mathrm{H}_2 \mathrm{O} & \text{II) Vapour phase refining} \\
\text{D) } 2 \mathrm{PbS}+3 \mathrm{O}_2 \rightarrow 2 \mathrm{PbO}+2 \mathrm{SO}_2 & \text{IV) Electrolysis} \\
& \text{V) Leaching}
\end{array}\)
The correct answer is

Which gas among the following has the maximum global warming potential?