Consider the following spectral lines for atomic hydrogen: $\\$A. First line of Paschen series $\\$B. Second line of Balmer series $\\$C. Third line of Paschen series $\\$D. Fourth line of Bracket sereis$\\$The correct arrangement of the above lines in ascending order of energy is:

Match List-I with List-II.

List-I	List-II
Pair of Compounds	Type of Isomers
A. 2-Methylpropene and but-1-ene	I. Stereoisomers
B. Cis-but-2-ene and trans-but-2-ene	II. Position isomers
C. 2-Butanol and diethyl ether	III. Chain isomers
D. But-1-ene and but-2-ene	IV. Functional group isomers

Let $\mathrm{y}^{2}=12 \mathrm{x}$ be the parabola with its vertex at O . Let P be a point on the parabola and A be a point on the x -axis such that $\angle \mathrm{OPA}=90^{\circ}$. Then the locus of the centroid of such triangles OPA is :

A random variable $X$ takes values $0,1,2,3$ with probabilities $\frac{2 \mathrm{a}+1}{30}, \frac{8 \mathrm{a}-1}{30}, \frac{4 \mathrm{a}+1}{30}$, b respectively, where $\mathrm{a}, \mathrm{b} \in \mathbf{R}$. Let $\mu$ and $\sigma$ respectively be the mean and standard deviation of $X$ such that $\sigma^{2}+\mu^{2}=2.\\$ Then $\frac{\mathrm{a}}{\mathrm{b}}$ is equal to :

Let $z$ be the complex number satisfying $|z-5| \leq 3$ and having maximum positive principal argument. Then $34\left|\frac{5 z-12}{5 i z+16}\right|^{2}$ is equal to:

Let the line $L_{1}$ be parallel to the vector $-3 \hat{i}+2 \hat{j}+4 \hat{k}$ and pass through the point $(2,6,7)$ and the line $L_{2}$ be parallel to the vector $2 \hat{i}+\hat{j}+3 \hat{k}$ and pass through the point $(4,3,5)$. If the line $\mathrm{L}_{3}$ is parallel to the vector $-3 \hat{i}+5 \hat{j}+16 \hat{k}$ and intersects the lines $\mathrm{L}_{1}$ and $\mathrm{L}_{2}$ at the points C and D , respectively, then $|\overrightarrow{\mathrm{CD}}|^{2}$ is equal to :

Let $\mathrm{A}=\{2,3,5,7,9\}$. Let R be the relation on A defined by x Ry if and only if $2 \mathrm{x} \leq 3 \mathrm{y}$. Let $\ell$ be the number of elements in R , and m be the minimum number of elements required to be added in R to make it a symmetric relation. Then $\ell+\mathrm{m}$ is equal to:

Let one end of a focal chord of the parabola $y^{2}=16 x$ be (16, 16). If $\mathrm{P}(\alpha, \beta)$ divides this focal chord internally in the ratio $5: 2$, then the minimum value of $\alpha+\beta$ is equal to :

The largest $\mathrm{n} \in \mathrm{N}$, for which $7^{\mathrm{n}}$ divides 101!, is :

A spherical body of radius $r$ and density $\sigma$ falls freely through a viscous liquid having density $\rho$ and viscosity $\eta$ and attains a terminal velocity $\mathrm{v}_{0}$. Estimated maximum error in the quantity $\eta$ is : (Ignore errors associated with $\sigma, \rho$ and g , gravitational acceleration)

As shown in the diagram, when the incident ray is parallel to base of the prism, the emergent ray grazes along the second surface.$\\$ $\\$If refractive index of the material of prism is $\sqrt{2}$, the angle $\theta$ of prism is.

The correct order of the rate of the reaction for the following reaction with respect to nucleophiles is: $\\ \mathrm{CH}_{3} \mathrm{Br}+\mathrm{Nu}^{\Theta} \longrightarrow \mathrm{CH}_{3} \mathrm{Nu}+\mathrm{Br}^{\Theta}$

An infinitely long straight wire carrying current I is bent in a planer shape as shown in the diagram. The radius of the circular part is r . The magnetic field at the centre O of the circular loop is :$\\$

Given below are two statements: Statement I: Crystal Field Stabilization Energy (CFSE) of $\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}$ is greater than that of $\left[\mathrm{Mn}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{2+}.\\$ Statement II: Potassium ferricyanide has a greater spin-only magnetic moment than sodium Ferrocyanide. In the light of the above statements, choose the correct answer from the options given below:

For the matrices $\mathrm{A}=\left[\begin{array}{ll}3 & -4 \\ 1 & -1\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{ll}-29 & 49 \\ -13 & 18\end{array}\right]$, if $\left(A^{15}+B\right)\left[\begin{array}{l}x \\ y\end{array}\right]=\left[\begin{array}{l}0 \\ 0\end{array}\right]$, then among the following which one is true?

Let $\alpha$ and $\beta$ be the roots of equation $x^{2}+2 a x+(3 a+10) =0$ such that $\alpha<1<\beta$. Then the set of all possible values of $a$ is :

For a triangle $A B C$, let $\vec{p}=\overrightarrow{B C}, \vec{q}=\overrightarrow{C A}$ and $\overrightarrow{\mathrm{r}}=\overrightarrow{\mathrm{BA}}$. If $|\overrightarrow{\mathrm{p}}|=2 \sqrt{3},|\overrightarrow{\mathrm{q}}|=2$ and $\cos \theta=\frac{1}{\sqrt{3}}$, where $\theta$ is the angle between $\vec{P}$ and $\vec{q}$, then $|\overrightarrow{\mathrm{p}} \times(\overrightarrow{\mathrm{q}}-3 \overrightarrow{\mathrm{r}})|^{2}+3|\overrightarrow{\mathrm{r}}|^{2}$ is equal to:

A large drum having radius R is spinning around its axis with angular velocity $\omega$, as shown in figure. The minimum value of $\omega$ so that a body of mass M remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass M is $\mu$, is :$\\$

Two known resistance of $\mathrm{R} \Omega$ and $2 \mathrm{R} \Omega$ and and one unknown resistance $\mathrm{X} \Omega$ are connected in a circuit as shown in the figure. If the equivalent resistance between points A and B in the circuit is $\mathrm{X} \Omega$, then the value of X is $\_\_\_\_$ $\Omega.\\$

Consider the following data: $\\ \Delta_{\mathrm{f}} \mathrm{H}^{\Theta}($ methane, g$)=-\mathrm{X} \mathrm{kJ} \mathrm{mol}^{-1}\\$ Enthalpy of sublimation of graphite $=\mathrm{Y} \mathrm{kJ} \mathrm{mol}^{-1}\\$ Dissociation enthalpy of $\mathrm{H}_{2}=\mathrm{Z} \mathrm{kJ} \mathrm{mol}^{-1}\\$ The bond enthalpy of $\mathrm{C}-\mathrm{H}$ bond is given by: