The ratio of the shortest wavelength of two spectral series of hydrogen spectrum is found to be about \(9\). The spectral series are

Given below are two statements :
Statement (I): Experimentally determined oxygen-oxygen bond lengths in the \(\mathrm{O}_3\) are found to be same and the bond length is greater than that of a \(\mathrm{O}=\mathrm{O}\) (double bond) but less than that of a single \((O-O)\) bond.
Statement (II) : The strong lone pair-lone pair repulsion between oxygen atoms is solely responsible for the fact that the bond length in ozone is smaller than that of a double bond \((\mathrm{O}=\mathrm{O})\) but more than that of a single bond \((\mathrm{O}-\mathrm{O})\).
In the light of the above statements, choose the correct answer from the options given below :

Consider the above reaction where \(6.1 \,g\) of benzoic acid is used to get \(7.8\, g\) of \(m\) -bromo benzoic acid. The percentage yield of the product is ....... . (Round off to the Nearest integer) [Given : Atomic masses : \(C =12.0 \,u , H : 1.0\, u,O : 16.0 \,u , Br =80.0 \,u ]\)

Consider the two different first order reactions given below \(\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}\) (Reaction 1\()\) \(\mathrm{P} \rightarrow \mathrm{Q}\) (Reaction \(2\)) The ratio of the half life of Reaction \(1\) : Reaction \(2\) is \(5: 2\). If \(t_1\) and \(t_2\) represent the time taken to complete \(2 / 3^{\text {dd }}\) and \(4 / 5^{\text {dd }}\) of Reaction \(1\) and Reaction \(2\), respectively, then the value of the ratio \(\mathrm{t}_1: \mathrm{t}_2\) is _______ \(\times 10^{-1}\) (nearest integer). [Given: \(\log _{10}(3)=0.477\) and \(\log _{10}(5)=0.699\) ]

Match List \(I\) with List \(II\).

List \(-I\)(Element)	List \(-II\) (Electronic Configuration)
\(A.\) \(N\)	\(I.\) \([\mathrm{Ar}] 3 \mathrm{~d}^{10} 4 \mathrm{~s}^2 4 \mathrm{p}^5\)
\(B.\) \(S\)	\(II.\) \([\mathrm{Ne}] 3 \mathrm{~s}^2 3 \mathrm{p}^4\)
\(C.\) \(Br\)	\(III.\) \([\mathrm{He}] 2 \mathrm{~s}^2 2 \mathrm{p}^3\)
\(D.\) \(Kr\)	\(IV.\) \([\mathrm{Ar}] 3 \mathrm{~d}^{10} 4 \mathrm{~s}^2 4 \mathrm{p}^6\)

Choose the correct answer from the options given below:

Given below are two statements: one is labelled as Assertion \((A)\) and the other is labelled as Reason \((R)\). Assertion \((A)\): The total number of geometrical isomers shown by \(\left[\mathrm{Co}(\mathrm{en})_2 \mathrm{Cl}_2\right]^{+}\)complex ion is three Reason \((R)\): \(\left[\mathrm{Co}(\mathrm{en})_2 \mathrm{Cl}_2\right]^{+}\)complex ion has an octahedral geometry. In the light of the above statements, choose the most appropriate answer from the options given below :

The \(IUPAC\) symbols for the element with atomic number \(119\) would be:

Let the normals at all the points on a given curve pass through a fixed point \((a, b) .\) If the curve passes through \((3,-3)\) and \((4,-2 \sqrt{2}),\) and given that \(a-2 \sqrt{2} b=3,\) then \(\left(a^{2}+b^{2}+a b\right)\) is equal to ..... .

A vector \(\vec A \) is rotated by a small angle \(\Delta \theta\) radian \(( \Delta \theta << 1)\) to get a new vector \(\vec B\) In that case \(\left| {\vec B - \vec A} \right|\) is

Let \(\mathrm{a}=\max _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}\) and \(\beta=\min _{x \in R}\left\{8^{2 \sin 3 x} \cdot 4^{4 \cos 3 x}\right\}\) If \(8 x^{2}+b x+c=0\) is a quadratic equation whose roots are \(\alpha^{1 / 5}\) and \(\beta^{1 / 5}\), then the value of \(c-b\) is equal to:

When 1 g each of compounds AB and \(\mathrm{AB}_2\) are dissolved in 15 g of water separately, they increased the boiling point of water by 2.7 K and 1.5 K respectively. The atomic mass of A (in amu) is ____ \(\times 10^{-1}\) (Nearest integer)
(Given : Molal boiling point elevation constant is \(\left.0.5 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)\)

Let A and B be the two points of intersection of the line \(y+5=0\) and the mirror image of the parabola \(y^2=4 x\) with respect to the line \(x+y+4=0\). If d denotes the distance between A and B , and a denotes the area of \(\triangle S A B\), where \(S\) is the focus of the parabola \(y^2=4 x\), then the value of \((a+d)\) is \(\qquad\) -

Let a focus of the ellipse \(E: \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1\) be \(S(4, 0)\) and its eccentricity be \(\dfrac{4}{5}\). If the point \(P(3, \alpha)\) lies on \(E\) and \(O\) is the origin, then the area of \(\triangle POS\) is equal to: