$\mathrm{Nd^{2+}}$ = __________

Consider the above reaction and identify the product B.

Which one of the following statements is correct for electrolysis of brine solution?

The oxidation state of phosphorus in hypophosphoric acid is + _____________.

A $\to$ B

The rate constants of the above reaction at 200 K and 300 K are 0.03 min$^{-1}$ and 0.05 min$^{-1}$ respectively. The activation energy for the reaction is ___________ J (Nearest integer)

(Given : $\mathrm{ln10=2.3}$

$\mathrm{R=8.3~J~K^{-1}~mol^{-1}}$

$\mathrm{\log5=0.70}$

$\mathrm{\log3=0.48}$

$\mathrm{\log2=0.30}$)

For the system of linear equations

$x+y+z=6$

$\alpha x+\beta y+7 z=3$

$x+2 y+3 z=14$

which of the following is NOT true ?

When $\mathrm{Cu}^{2+}$ ion is treated with $\mathrm{KI}$, a white precipitate, $\mathrm{X}$ appears in solution. The solution is titrated with sodium thiosulphate, the compound $\mathrm{Y}$ is formed. $\mathrm{X}$ and $\mathrm{Y}$ respectively are :

A protein '$\mathrm{X}$' with molecular weight of $70,000 \mathrm{~u}$, on hydrolysis gives amino acids. One of these amino acid is

Match List I with List II

Choose the correct answer from the options given below :

The logarithm of equilibrium constant for the reaction $\mathrm{Pd}^{2+}+4 \mathrm{Cl}^{-} \rightleftharpoons \mathrm{PdCl}_{4}^{2-}$ is ___________ (Nearest integer)

Given : $\frac{2.303 R \mathrm{~T}}{\mathrm{~F}}=0.06 \mathrm{~V}$

$$\mathrm{Pd}_{(\mathrm{aq})}^{2+}+2 \mathrm{e}^{-} \rightleftharpoons \mathrm{Pd}(\mathrm{s}) \quad \mathrm{E}^{\ominus}=0.83 \mathrm{~V}$$

$$\begin{aligned} & \mathrm{PdCl}_{4}^{2-}(\mathrm{aq})+2 \mathrm{e}^{-} \rightleftharpoons \mathrm{Pd}(\mathrm{s})+4 \mathrm{Cl}^{-}(\mathrm{aq}) \mathrm{E}^{\ominus}=0.65 \mathrm{~V} \end{aligned}$$

The enthalpy change for the conversion of $\frac{1}{2} \mathrm{Cl}_{2}(\mathrm{~g})$ to $\mathrm{Cl}^{-}$(aq) is ($-$) ___________ $\mathrm{kJ} \mathrm{mol}^{-1}$ (Nearest integer)

Given : $\Delta_{\mathrm{dis}} \mathrm{H}_{\mathrm{Cl}_{2(\mathrm{~g})}^{\theta}}^{\ominus}=240 \mathrm{~kJ} \mathrm{~mol}^{-1}, \Delta_{\mathrm{eg}} \mathrm{H}_{\mathrm{Cl_{(g)}}}^{\ominus}=-350 \mathrm{~kJ} \mathrm{~mol}^{-1}$,

${\mathrm{\Delta _{hyd}}H_{Cl_{(g)}^ - }^\Theta = - 380}$ $\mathrm{kJ~mol^{-1}}$

How many of the transformations given below would result in aromatic amines?

For reaction : $\mathrm{SO}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{SO}_{3}(\mathrm{~g})$

$\mathrm{K}_{\mathrm{p}}=2 \times 10^{12}$ at $27^{\circ} \mathrm{C}$ and $1 \mathrm{~atm}$ pressure. The $\mathrm{K}_{\mathrm{c}}$ for the same reaction is ____________ $\times 10^{13}$. (Nearest integer)

(Given $\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$)

The correct increasing order of the ionic radii is

The correct order of melting points of dichlorobenzenes is

Cobalt chloride when dissolved in water forms pink colored complex $\underline{\mathrm{X}}$ which has octahedral geometry. This solution on treating with conc $\mathrm{HCl}$ forms deep blue complex, $\underline{\mathrm{Y}}$ which has a $\underline{\mathrm{Z}}$ geometry. $\mathrm{X}, \mathrm{Y}$ and $\mathrm{Z}$, respectively, are

An organic compound 'A' with emperical formula $\mathrm{C}_{6} \mathrm{H}_{6} \mathrm{O}$ gives sooty flame on burning. Its reaction with bromine solution in low polarity solvent results in high yield of B. B is

Zinc reacts with hydrochloric acid to give hydrogen and zinc chloride. The volume of hydrogen gas produced at STP from the reaction of $11.5 \mathrm{~g}$ of zinc with excess $\mathrm{HCl}$ is __________ L (Nearest integer)

(Given : Molar mass of $\mathrm{Zn}$ is $65.4 \mathrm{~g} \mathrm{~mol}^{-1}$ and Molar volume of $\mathrm{H}_{2}$ at $\mathrm{STP}=22.7 \mathrm{~L}$ )

The number of real roots of the equation $\sqrt{x^{2}-4 x+3}+\sqrt{x^{2}-9}=\sqrt{4 x^{2}-14 x+6}$, is :

Match items of column I and II

	Column I (Mixture of compounds)		Column II (Separation Technique)
A.	$\mathrm{H_2O/CH_2Cl_2}$	i.	Crystalization
B.		ii.	Differential solvent extraction
C.	Kerosene / Naphthalene	iii.	Column chromatography
D.	$\mathrm{C_6H_{12}O_6/NaCl}$	iv.	Fractional Distillation

Correct match is

Consider the following reaction

The correct statement for product B is. It is

The correct order of basicity of oxides of vanadium is :

Choose the correct set of reagents for the following conversion.

trans $\left(\mathrm{Ph}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{3}\right) \rightarrow \operatorname{cis}\left(\mathrm{Ph}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{3}\right)$

Which transition in the hydrogen spectrum would have the same wavelength as the Balmer type transition from $\mathrm{n=4}$ to $\mathrm{n}=2$ of $\mathrm{He}^{+}$ spectrum

On complete combustion, $0.492 \mathrm{~g}$ of an organic compound gave $0.792 \mathrm{~g}$ of $\mathrm{CO}_{2}$. The % of carbon in the organic compound is ___________ (Nearest integer)

At $27^{\circ} \mathrm{C}$, a solution containing $2.5 \mathrm{~g}$ of solute in $250.0 \mathrm{~mL}$ of solution exerts an osmotic pressure of $400 \mathrm{~Pa}$. The molar mass of the solute is ___________ $\mathrm{g} \mathrm{~mol}^{-1}$ (Nearest integer)

(Given : $\mathrm{R}=0.083 \mathrm{~L} \mathrm{~bar} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$)

A bag contains 6 balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least 5 black balls is :

If ${\sin ^{ - 1}}{\alpha \over {17}} + {\cos ^{ - 1}}{4 \over 5} - {\tan ^{ - 1}}{{77} \over {36}} = 0,0 < \alpha < 13$, then ${\sin ^{ - 1}}(\sin \alpha ) + {\cos ^{ - 1}}(\cos \alpha )$ is equal to :

If the sum and product of four positive consecutive terms of a G.P., are 126 and 1296 , respectively, then the sum of common ratios of all such GPs is

Let $\mathrm{R}$ be a relation on $\mathrm{N} \times \mathbb{N}$ defined by $(a, b) ~\mathrm{R}~(c, d)$ if and only if $a d(b-c)=b c(a-d)$. Then $\mathrm{R}$ is

A wire of length $20 \mathrm{~m}$ is to be cut into two pieces. A piece of length $l_{1}$ is bent to make a square of area $A_{1}$ and the other piece of length $l_{2}$ is made into a circle of area $A_{2}$. If $2 A_{1}+3 A_{2}$ is minimum then $\left(\pi l_{1}\right): l_{2}$ is equal to :

Let A = \left( {\matrix{ 1 & 0 & 0 \cr 0 & 4 & { - 1} \cr 0 & {12} & { - 3} \cr } } \right)\(. Then the sum of the diagonal elements of the matrix \){(A + I)^{11}} is equal to :

The value of \int_\limits{\frac{\pi}{3}}^{\frac{\pi}{2}} \frac{(2+3 \sin x)}{\sin x(1+\cos x)} d x is equal to :

Let $y=f(x)=\sin ^{3}\left(\frac{\pi}{3}\left(\cos \left(\frac{\pi}{3 \sqrt{2}}\left(-4 x^{3}+5 x^{2}+1\right)^{\frac{3}{2}}\right)\right)\right)$. Then, at x = 1,

The effect of increase in temperature on the number of electrons in conduction band ($\mathrm{n_e}$) and resistance of a semiconductor will be as:

The drift velocity of electrons for a conductor connected in an electrical circuit is $\mathrm{V}_{\mathrm{d}}$. The conductor in now replaced by another conductor with same material and same length but double the area of cross section. The applied voltage remains same. The new drift velocity of electrons will be

The pressure of a gas changes linearly with volume from $\mathrm{A}$ to $\mathrm{B}$ as shown in figure. If no heat is supplied to or extracted from the gas then change in the internal energy of the gas will be

In the figure given below, a block of mass $M=490 \mathrm{~g}$ placed on a frictionless table is connected with two springs having same spring constant $\left(\mathrm{K}=2 \mathrm{~N} \mathrm{~m}^{-1}\right)$. If the block is horizontally displaced through '$\mathrm{X}$' $\mathrm{m}$ then the number of complete oscillations it will make in $14 \pi$ seconds will be _____________.

An inductor of $0.5 ~\mathrm{mH}$, a capacitor of $20 ~\mu \mathrm{F}$ and resistance of $20 ~\Omega$ are connected in series with a $220 \mathrm{~V}$ ac source. If the current is in phase with the emf, the amplitude of current of the circuit is $\sqrt{x}$ A. The value of $x$ is ___________

For all $z \in C$ on the curve $C_{1}:|z|=4$, let the locus of the point $z+\frac{1}{z}$ be the curve $\mathrm{C}_{2}$. Then :

Let 5 digit numbers be constructed using the digits $0,2,3,4,7,9$ with repetition allowed, and are arranged in ascending order with serial numbers. Then the serial number of the number 42923 is __________.

Let $\alpha>0$, be the smallest number such that the expansion of $\left(x^{\frac{2}{3}}+\frac{2}{x^{3}}\right)^{30}$ has a term $\beta x^{-\alpha}, \beta \in \mathbb{N}$. Then $\alpha$ is equal to ___________.

Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a}|=\sqrt{14},|\vec{b}|=\sqrt{6}$ and $|\vec{a} \times \vec{b}|=\sqrt{48}$. Then $(\vec{a} \cdot \vec{b})^{2}$ is equal to ___________.

If the variance of the frequency distribution

is 3, then $\alpha$ is equal to _____________.

A bar magnet with a magnetic moment $5.0 \mathrm{Am}^{2}$ is placed in parallel position relative to a magnetic field of $0.4 \mathrm{~T}$. The amount of required work done in turning the magnet from parallel to antiparallel position relative to the field direction is _____________.

Which of the following correctly represents the variation of electric potential $(\mathrm{V})$ of a charged spherical conductor of radius $(\mathrm{R})$ with radial distance $(\mathrm{r})$ from the center?

A rod with circular cross-section area $2 \mathrm{~cm}^{2}$ and length $40 \mathrm{~cm}$ is wound uniformly with 400 turns of an insulated wire. If a current of $0.4 \mathrm{~A}$ flows in the wire windings, the total magnetic flux produced inside windings is $4 \pi \times 10^{-6} \mathrm{~Wb}$. The relative permeability of the rod is

(Given : Permeability of vacuum $\mu_{0}=4 \pi \times 10^{-7} \mathrm{NA}^{-2}$)

At a certain depth "d " below surface of earth, value of acceleration due to gravity becomes four times that of its value at a height $\mathrm{3 R}$ above earth surface. Where $\mathrm{R}$ is Radius of earth (Take $\mathrm{R}=6400 \mathrm{~km}$ ). The depth $\mathrm{d}$ is equal to

100 balls each of mass $\mathrm{m}$ moving with speed $v$ simultaneously strike a wall normally and reflected back with same speed, in time $\mathrm{t ~s}$. The total force exerted by the balls on the wall is

If $\mathrm{R}, \mathrm{X}_{\mathrm{L}}$, and $\mathrm{X}_{\mathrm{C}}$ represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless :

The maximum potential energy of a block executing simple harmonic motion is $25 \mathrm{~J}$. A is amplitude of oscillation. At $\mathrm{A / 2}$, the kinetic energy of the block is

As shown in figure, a $70 \mathrm{~kg}$ garden roller is pushed with a force of $\vec{F}=200 \mathrm{~N}$ at an angle of $30^{\circ}$ with horizontal. The normal reaction on the roller is

(Given $\mathrm{g=10~m~s^{-2}}$)

For hydrogen atom, $\lambda_{1}$ and $\lambda_{2}$ are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of $\lambda_{1}$ and $\lambda_{2}$ is $\frac{x}{32}$. The value of $x$ is __________.

Two identical cells, when connected either in parallel or in series gives same current in an external resistance $5 ~\Omega$. The internal resistance of each cell will be ___________ $\Omega$.

The remainder on dividing $5^{99}$ by 11 is ____________.

Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to ____________.

Let $a_{1}, a_{2}, \ldots, a_{n}$ be in A.P. If $a_{5}=2 a_{7}$ and $a_{11}=18$, then

$12\left(\frac{1}{\sqrt{a_{10}}+\sqrt{a_{11}}}+\frac{1}{\sqrt{a_{11}}+\sqrt{a_{12}}}+\ldots+\frac{1}{\sqrt{a_{17}}+\sqrt{a_{18}}}\right)$ is equal to ____________.

If 1000 droplets of water of surface tension $0.07 \mathrm{~N} / \mathrm{m}$, having same radius $1 \mathrm{~mm}$ each, combine to from a single drop. In the process the released surface energy is :-

$\left( {\mathrm{Take}\,\pi = {{22} \over 7}} \right)$

The correct relation between $\gamma = {{{c_p}} \over {{c_v}}}$ and temperature T is :

If a source of electromagnetic radiation having power $15 \mathrm{~kW}$ produces $10^{16}$ photons per second, the radiation belongs to a part of spectrum is.

(Take Planck constant $h=6 \times 10^{-34} \mathrm{Js}$ )

Let $\alpha \in (0,1)$ and $\beta = {\log _e}(1 - \alpha )$. Let ${P_n}(x) = x + {{{x^2}} \over 2} + {{{x^3}} \over 3}\, + \,...\, + \,{{{x^n}} \over n},x \in (0,1)$. Then the integral $\int\limits_0^\alpha {{{{t^{50}}} \over {1 - t}}dt}$ is equal to

Let the shortest distance between the lines

$L: \frac{x-5}{-2}=\frac{y-\lambda}{0}=\frac{z+\lambda}{1}, \lambda \geq 0$ and

$L_{1}: x+1=y-1=4-z$ be $2 \sqrt{6}$. If $(\alpha, \beta, \gamma)$ lies on $L$,

then which of the following is NOT possible?

Let $\vec{a}=2 \hat{i}+\hat{j}+\hat{k}$, and $\vec{b}$ and $\vec{c}$ be two nonzero vectors such that $|\vec{a}+\vec{b}+\vec{c}|=|\vec{a}+\vec{b}-\vec{c}|$ and $\vec{b} \cdot \vec{c}=0$. Consider the following two statements:

(A) $|\vec{a}+\lambda \vec{c}| \geq|\vec{a}|$ for all $\lambda \in \mathbb{R}$.

(B) $\vec{a}$ and $\vec{c}$ are always parallel.

Then,

Let for $x \in \mathbb{R}$,

$$f(x)=\frac{x+|x|}{2} \text { and } g(x)=\left\{\begin{array}{cc} x, & x<0 \\ x^{2}, & x \geq 0 \end{array}\right. \text {. }$$

Then area bounded by the curve $y=(f \circ g)(x)$ and the lines $y=0,2 y-x=15$ is equal to __________.

The initial speed of a projectile fired from ground is $\mathrm{u}$. At the highest point during its motion, the speed of projectile is $\frac{\sqrt{3}}{2} u$. The time of flight of the projectile is :

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following

{Assume negligible air friction}

Two polaroide $\mathrm{A}$ and $\mathrm{B}$ are placed in such a way that the pass-axis of polaroids are perpendicular to each other. Now, another polaroid $\mathrm{C}$ is placed between $\mathrm{A}$ and $\mathrm{B}$ bisecting angle between them. If intensity of unpolarized light is $\mathrm{I}_{0}$ then intensity of transmitted light after passing through polaroid $\mathrm{B}$ will be:

A lift of mass $\mathrm{M}=500 \mathrm{~kg}$ is descending with speed of $2 \mathrm{~ms}^{-1}$. Its supporting cable begins to slip thus allowing it to fall with a constant acceleration of $2 \mathrm{~ms}^{-2}$. The kinetic energy of the lift at the end of fall through to a distance of $6 \mathrm{~m}$ will be _____________ $\mathrm{kJ}$.

The speed of a swimmer is $4 \mathrm{~km} \mathrm{~h}^{-1}$ in still water. If the swimmer makes his strokes normal to the flow of river of width $1 \mathrm{~km}$, he reaches a point $750 \mathrm{~m}$ down the stream on the opposite bank.

The speed of the river water is ___________ $\mathrm{km} ~\mathrm{h}^{-1}$

A solid sphere of mass $1 \mathrm{~kg}$ rolls without slipping on a plane surface. Its kinetic energy is $7 \times 10^{-3} \mathrm{~J}$. The speed of the centre of mass of the sphere is __________ $\operatorname{cm~s}^{-1}$

Expression for an electric field is given by $\overrightarrow{\mathrm{E}}=4000 x^{2} \hat{i} \frac{\mathrm{V}}{\mathrm{m}}$. The electric flux through the cube of side $20 \mathrm{~cm}$ when placed in electric field (as shown in the figure) is __________ $\mathrm{V} \mathrm{~cm}$.

A thin rod having a length of $1 \mathrm{~m}$ and area of cross-section $3 \times 10^{-6} \mathrm{~m}^{2}$ is suspended vertically from one end. The rod is cooled from $210^{\circ} \mathrm{C}$ to $160^{\circ} \mathrm{C}$. After cooling, a mass $\mathrm{M}$ is attached at the lower end of the rod such that the length of rod again becomes $1 \mathrm{~m}$. Young's modulus and coefficient of linear expansion of the rod are $2 \times 10^{11} \mathrm{~N} \mathrm{~m}^{-2}$ and $2 \times 10^{-5} \mathrm{~K}^{-1}$, respectively. The value of $\mathrm{M}$ is __________ $\mathrm{kg}$.

(Take $\mathrm{g=10~m~s^{-2}}$)

In a medium the speed of light wave decreases to $0.2$ times to its speed in free space The ratio of relative permittivity to the refractive index of the medium is $x: 1$. The value of $x$ is _________.

(Given speed of light in free space $=3 \times 10^{8} \mathrm{~m} \mathrm{~s}^{-1}$ and for the given medium $\mu_{\mathrm{r}}=1$)