Octahedral complexes of copper(II) undergo structural distortion (Jahn-Teller). Which one of the given copper (II) complexes will show the maximum structural distortion? (en - ethylenediamine; $\mathrm{H}_{2} \mathrm{~N}_{-} \mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{NH}_{2}$)

The Hinsberg reagent is

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Amylose is insoluble in water.

Reason R: Amylose is a long linear molecule with more than 200 glucose units.

In the light of the above statements, choose the correct answer from the options given below.

$1.80 \mathrm{~g}$ of solute A was dissolved in $62.5 \mathrm{~cm}^{3}$ of ethanol and freezing point of the solution was found to be $155.1 \mathrm{~K}$. The molar mass of solute A is ________ g $\mathrm{mol}^{-1}$.

[Given : Freezing point of ethanol is 156.0 K.

Density of ethanol is 0.80 g cm^$-$3.

Freezing point depression constant of ethanol is 2.00 K kg mol^$-$1]

The number of stereoisomers formed in a reaction of $(±)\mathrm{Ph}(\mathrm{C}=\mathrm{O}) \mathrm{C}(\mathrm{OH})(\mathrm{CN}) \mathrm{Ph}$ with $\mathrm{HCN}$ is ___________.

$\left[\right.$where $\mathrm{Ph}$ is $-\mathrm{C}_{6} \mathrm{H}_{5}$]

If the system of equations

$$\begin{aligned} &x+y+z=6 \\ &2 x+5 y+\alpha z=\beta \\ &x+2 y+3 z=14 \end{aligned}$$

has infinitely many solutions, then $\alpha+\beta$ is equal to

$$\text { Let the function } f(x)=\left\{\begin{array}{cl} \frac{\log _{e}(1+5 x)-\log _{e}(1+\alpha x)}{x} & ;\text { if } x \neq 0 \\ 10 & ; \text { if } x=0 \end{array} \text { be continuous at } x=0 .\right.$$

Then $\alpha$ is equal to

If $[t]$ denotes the greatest integer $\leq t$, then the value of $\int_{0}^{1}\left[2 x-\left|3 x^{2}-5 x+2\right|+1\right] \mathrm{d} x$ is :

Given below are the quantum numbers for 4 electrons.

A. $\mathrm{n}=3,l=2, \mathrm{~m}_{1}=1, \mathrm{~m}_{\mathrm{s}}=+1 / 2$

B. $\mathrm{n}=4,l=1, \mathrm{~m}_{1}=0, \mathrm{~m}_{\mathrm{s}}=+1 / 2$

C. $\mathrm{n}=4,l=2, \mathrm{~m}_{1}=-2, \mathrm{~m}_{\mathrm{s}}=-1 / 2$

D. $\mathrm{n}=3,l=1, \mathrm{~m}_{1}=-1, \mathrm{~m}_{\mathrm{s}}=+1 / 2$

The correct order of increasing energy is

$$\begin{aligned} &\mathrm{C}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g})+400 \mathrm{~kJ} \\ &\mathrm{C}(\mathrm{s})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{CO}(\mathrm{g})+100 \mathrm{~kJ} \end{aligned}$$

When coal of purity 60% is allowed to burn in presence of insufficient oxygen, 60% of carbon is converted into 'CO' and the remaining is converted into '$\mathrm{CO}_{2}$'. The heat generated when $0.6 \mathrm{~kg}$ of coal is burnt is _________.

Which of the following $3\mathrm{d}$-metal ion will give the lowest enthalpy of hydration $\left(\Delta_{\text {hyd }} \mathrm{H}\right)$ when dissolved in water ?

Correct structure of $\gamma$-methylcyclohexane carbaldehyde is

Compound 'A' undergoes following sequence of reactions to give compound 'B'.

The correct structure and chirality of compound 'B' is

[where Et is $\left.-\mathrm{C}_{2} \mathrm{H}_{5}\right]$

When ethanol is heated with conc. $\mathrm{H}_{2} \mathrm{SO}_{4}$, a gas is produced. The compound formed, when this gas is treated with cold dilute aqueous solution of Baeyer's reagent, is

Consider, $\mathrm{PF}_{5}, \mathrm{BrF}_{5}, \mathrm{PCl}_{3}, \mathrm{SF}_{6},\left[\mathrm{ICl}_{4}\right]^{-}, \mathrm{ClF}_{3}$ and $\mathrm{IF}_{5}$.

Amongst the above molecule(s)/ion(s), the number of molecule(s)/ion(s) having $\mathrm{sp}^{3}\mathrm{~d}^{2}$ hybridisation is __________.

A 1.84 mg sample of polyhydric alcoholic compound 'X' of molar mass 92.0 g/mol gave 1.344 mL of $\mathrm{H}_{2}$ gas at STP. The number of alcoholic hydrogens present in compound 'X' is ________.

Consider the reaction

$4 \mathrm{HNO}_{3}(1)+3 \mathrm{KCl}(\mathrm{s}) \rightarrow \mathrm{Cl}_{2}(\mathrm{~g})+\mathrm{NOCl}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})+3 \mathrm{KNO}_{3}(\mathrm{~s})$

The amount of $\mathrm{HNO}_{3}$ required to produce $110.0 \mathrm{~g}$ of $\mathrm{KNO}_{3}$ is

(Given: Atomic masses of $\mathrm{H}, \mathrm{O}, \mathrm{N}$ and $\mathrm{K}$ are $1,16,14$ and 39, respectively.)

$200 \mathrm{~mL}$ of $0.01 \,\mathrm{M} \,\mathrm{HCl}$ is mixed with $400 \mathrm{~mL}$ of $0.01 \,\mathrm{M} \,\mathrm{H}_{2} \mathrm{SO}_{4}$. The $\mathrm{pH}$ of the mixture is _________.

Given: $\log {2}=0.30, \log 3=0.48, \log 5=0.70, \log 7=0.84, \log 11=1.04$

In liquation process used for tin (Sn), the metal :

Given below are two statements.

Statement I : The compound is optically active.

Statement II : is mirror image of above compound A.

In the light of the above statement, choose the most appropriate answer from the options given below.

For a cell, $\mathrm{Cu}(\mathrm{s})\left|\mathrm{Cu}^{2+}(0.001 \,\mathrm{M}) \| \mathrm{Ag}^{+}(0.01 \,\mathrm{M})\right| \mathrm{Ag}(\mathrm{s})$

the cell potential is found to be $0.43 \mathrm{~V}$ at $298 \mathrm{~K}$. The magnitude of standard electrode potential for $\mathrm{Cu}^{2+} / \mathrm{Cu}$ is _________ $\times 10^{-2} \mathrm{~V}$.

[Given : $E_{A{g^ + }/Ag}^\Theta$ = 0.80 V and ${{2.303RT} \over F}$ = 0.06 V]

Assuming $1 \,\mu \mathrm{g}$ of trace radioactive element X with a half life of 30 years is absorbed by a growing tree. The amount of X remaining in the tree after 100 years is ______ $\times\, 10^{-1} \mu \mathrm{g}$.

[Given : ln 10 = 2.303; log 2 = 0.30]

If $z \neq 0$ be a complex number such that $\left|z-\frac{1}{z}\right|=2$, then the maximum value of $|z|$ is :

Which of the following matrices can NOT be obtained from the matrix $\left[\begin{array}{cc}-1 & 2 \\ 1 & -1\end{array}\right]$ by a single elementary row operation ?

Given below are two statements.

Statement I : Stannane is an example of a molecular hydride.

Statement II : Stannane is a planar molecule.

In the light of the above statement, choose the most appropriate answer from the options given below.

A compound 'X' is a weak acid and it exhibits colour change at pH close to the equivalence point during neutralization of NaOH with $\mathrm{CH}_{3} \mathrm{COOH}$. Compound 'X' exists in ionized form in basic medium. The compound 'X' is

Sum of oxidation state (magnitude) and coordination number of cobalt in $\mathrm{Na}\left[\mathrm{Co}(\mathrm{bpy}) \mathrm{Cl}_{4}\right]$ is _________.

For $I(x)=\int \frac{\sec ^{2} x-2022}{\sin ^{2022} x} d x$, if $I\left(\frac{\pi}{4}\right)=2^{1011}$, then

If the solution curve of the differential equation $\frac{d y}{d x}=\frac{x+y-2}{x-y}$ passes through the points $(2,1)$ and $(\mathrm{k}+1,2), \mathrm{k}>0$, then

Let $y=y(x)$ be the solution curve of the differential equation $\frac{d y}{d x}+\left(\frac{2 x^{2}+11 x+13}{x^{3}+6 x^{2}+11 x+6}\right) y=\frac{(x+3)}{x+1}, x>-1$, which passes through the point $(0,1)$. Then $y(1)$ is equal to :

Let $\vec{a}, \vec{b}, \vec{c}$ be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is 14 and $(\vec{a} \times \vec{b}) \cdot(\vec{b} \times \vec{c})+(\vec{b} \times \vec{c}) \cdot(\vec{c} \times \vec{a})+(\vec{c} \times \vec{a}) \cdot(\vec{a} \times \vec{b})=168$, then $|\vec{a}|+|\vec{b}|+|\vec{c}|$ is equal to :

The number of natural numbers lying between 1012 and 23421 that can be formed using the digits $2,3,4,5,6$ (repetition of digits is not allowed) and divisible by 55 is _________.

If $[t]$ denotes the greatest integer $\leq t$, then the number of points, at which the function $f(x)=4|2 x+3|+9\left[x+\frac{1}{2}\right]-12[x+20]$ is not differentiable in the open interval $(-20,20)$, is __________.

Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a}+\vec{b}|^{2}=|\vec{a}|^{2}+2|\vec{b}|^{2}, \vec{a} \cdot \vec{b}=3$ and $|\vec{a} \times \vec{b}|^{2}=75$. Then $|\vec{a}|^{2}$ is equal to __________.

$\text { Let } S=\left\{(x, y) \in \mathbb{N} \times \mathbb{N}: 9(x-3)^{2}+16(y-4)^{2} \leq 144\right\}$ and $T=\left\{(x, y) \in \mathbb{R} \times \mathbb{R}:(x-7)^{2}+(y-4)^{2} \leq 36\right\}$. Then $n(S \cap T)$ is equal to __________.

Match List I with List II.

Choose the correct answer from the options given below :

An object of mass $1 \mathrm{~kg}$ is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be [If, $\mathrm{g}=10 \mathrm{~ms}^{-2}$ and radius of earth $=6400 \mathrm{~km}$ ]

Two bodies of masses $m_{1}=5 \mathrm{~kg}$ and $m_{2}=3 \mathrm{~kg}$ are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the body of mass $\mathrm{m}_{1}$ will be : [Take $\left.\mathrm{g}=10 \mathrm{~ms}^{-2}\right]$

If momentum of a body is increased by 20%, then its kinetic energy increases by

The root mean square speed of smoke particles of mass $5 \times 10^{-17} \mathrm{~kg}$ in their Brownian motion in air at NTP is approximately. [Given $\mathrm{k}=1.38 \times 10^{-23} \mathrm{JK}^{-1}$]

Light enters from air into a given medium at an angle of $45^{\circ}$ with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of $15^{\circ}$ from its original direction. The refractive index of the medium is:

A tube of length $50 \mathrm{~cm}$ is filled completely with an incompressible liquid of mass $250 \mathrm{~g}$ and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity $x \sqrt{F} \,\mathrm{rad} \,\mathrm{s}^{-1}$. If $\mathrm{F}$ be the force exerted by the liquid at the other end then the value of $x$ will be __________.

Let $m_{1}, m_{2}$ be the slopes of two adjacent sides of a square of side a such that $a^{2}+11 a+3\left(m_{1}^{2}+m_{2}^{2}\right)=220$. If one vertex of the square is $(10(\cos \alpha-\sin \alpha), 10(\sin \alpha+\cos \alpha))$, where $\alpha \in\left(0, \frac{\pi}{2}\right)$ and the equation of one diagonal is $(\cos \alpha-\sin \alpha) x+(\sin \alpha+\cos \alpha) y=10$, then $72\left(\sin ^{4} \alpha+\cos ^{4} \alpha\right)+a^{2}-3 a+13$ is equal to :

Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is :

Let $\alpha, \beta(\alpha>\beta)$ be the roots of the quadratic equation $x^{2}-x-4=0 .$ If $P_{n}=\alpha^{n}-\beta^{n}$, $n \in \mathrm{N}$, then $\frac{P_{15} P_{16}-P_{14} P_{16}-P_{15}^{2}+P_{14} P_{15}}{P_{13} P_{14}}$ is equal to __________.

Let $X=\left[\begin{array}{l}1 \\ 1 \\ 1\end{array}\right]$ and $A=\left[\begin{array}{ccc}-1 & 2 & 3 \\ 0 & 1 & 6 \\ 0 & 0 & -1\end{array}\right]$. For $\mathrm{k} \in N$, if $X^{\prime} A^{k} X=33$, then $\mathrm{k}$ is equal to _______.

Let $A B$ be a chord of length 12 of the circle $(x-2)^{2}+(y+1)^{2}=\frac{169}{4}$. If tangents drawn to the circle at points $A$ and $B$ intersect at the point $P$, then five times the distance of point $P$ from chord $A B$ is equal to __________.

Two identical thin metal plates has charge $q_{1}$ and $q_{2}$ respectively such that $q_{1}>q_{2}$. The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between them is :

A $1 \mathrm{~m}$ long wire is broken into two unequal parts $\mathrm{X}$ and $\mathrm{Y}$. The $\mathrm{X}$ part of the wire is streched into another wire W. Length of $W$ is twice the length of $X$ and the resistance of $\mathrm{W}$ is twice that of $\mathrm{Y}$. Find the ratio of length of $\mathrm{X}$ and $\mathrm{Y}$.

A wire X of length $50 \mathrm{~cm}$ carrying a current of $2 \mathrm{~A}$ is placed parallel to a long wire $\mathrm{Y}$ of length $5 \mathrm{~m}$. The wire $\mathrm{Y}$ carries a current of $3 \mathrm{~A}$. The distance between two wires is $5 \mathrm{~cm}$ and currents flow in the same direction. The force acting on the wire $\mathrm{Y}$ is

A circuit element $\mathrm{X}$ when connected to an a.c. supply of peak voltage $100 \mathrm{~V}$ gives a peak current of $5 \mathrm{~A}$ which is in phase with the voltage. A second element $\mathrm{Y}$ when connected to the same a.c. supply also gives the same value of peak current which lags behind the voltage by $\frac{\pi}{2}$. If $\mathrm{X}$ and $\mathrm{Y}$ are connected in series to the same supply, what will be the rms value of the current in ampere?

An unpolarised light beam of intensity $2 I_{0}$ is passed through a polaroid P and then through another polaroid Q which is oriented in such a way that its passing axis makes an angle of $30^{\circ}$ relative to that of P. The intensity of the emergent light is

A ball is released from a height h. If $t_{1}$ and $t_{2}$ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between $t_{1}$ and $t_{2}$.

A metal wire of length $0.5 \mathrm{~m}$ and cross-sectional area $10^{-4} \mathrm{~m}^{2}$ has breaking stress $5 \times 10^{8} \,\mathrm{Nm}^{-2}$. A block of $10 \mathrm{~kg}$ is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be _________ $\mathrm{ms}^{-1}$.

The velocity of a small ball of mass $0.3 \mathrm{~g}$ and density $8 \mathrm{~g} / \mathrm{cc}$ when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $1.3 \mathrm{~g} / \mathrm{cc}$, then the value of viscous force acting on the ball will be $x \times 10^{-4} \mathrm{~N}$, The value of $x$ is _________. [use $\left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right]$

The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is $10 \mathrm{~s}$. If the metallic bob is immersed in water, then the new time period becomes $5 \sqrt{x}$ s. The value of $x$ will be ________.

A $8 \mathrm{~V}$ Zener diode along with a series resistance $\mathrm{R}$ is connected across a $20 \mathrm{~V}$ supply (as shown in the figure). If the maximum Zener current is $25 \mathrm{~mA}$, then the minimum value of R will be _______ $\Omega$.

A capacitor of capacitance 500 $\mu$F is charged completely using a dc supply of 100 V. It is now connected to an inductor of inductance 50 mH to form an LC circuit. The maximum current in LC circuit will be _______ A.

Let $\mathrm{A}(\alpha,-2), \mathrm{B}(\alpha, 6)$ and $\mathrm{C}\left(\frac{\alpha}{4},-2\right)$ be vertices of a $\triangle \mathrm{ABC}$. If $\left(5, \frac{\alpha}{4}\right)$ is the circumcentre of $\triangle \mathrm{ABC}$, then which of the following is NOT correct about $\triangle \mathrm{ABC}$?

Let $\mathrm{S}=\{z=x+i y:|z-1+i| \geq|z|,|z|<2,|z+i|=|z-1|\}$. Then the set of all values of $x$, for which $w=2 x+i y \in \mathrm{S}$ for some $y \in \mathbb{R}$, is :

A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the gas from D to E to F will be

The domain of the function $f(x)=\sin ^{-1}\left(\frac{x^{2}-3 x+2}{x^{2}+2 x+7}\right)$ is :

Two identical metallic spheres $\mathrm{A}$ and $\mathrm{B}$ when placed at certain distance in air repel each other with a force of $\mathrm{F}$. Another identical uncharged sphere $\mathrm{C}$ is first placed in contact with $\mathrm{A}$ and then in contact with $\mathrm{B}$ and finally placed at midpoint between spheres A and B. The force experienced by sphere C will be:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Alloys such as constantan and manganin are used in making standard resistance coils.

Reason R: Constantan and manganin have very small value of temperature coefficient of resistance.

In the light of the above statements, choose the correct answer from the options given below.

A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws n balls per second, the maximum height the balls can reach is

An $\alpha$ particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particles will be:

The torque of a force $5 \hat{i}+3 \hat{j}-7 \hat{k}$ about the origin is $\tau$. If the force acts on a particle whose position vector is $2 i+2 j+k$, then the value of $\tau$ will be

Nearly 10% of the power of a $110 \mathrm{~W}$ light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of $1 \mathrm{~m}$ from the bulb to a distance of $5 \mathrm{~m}$ is $a \times 10^{-2} \mathrm{~W} / \mathrm{m}^{2}$. The value of 'a' will be _________.

The speed of a transverse wave passing through a string of length $50 \mathrm{~cm}$ and mass $10 \mathrm{~g}$ is $60 \mathrm{~ms}^{-1}$. The area of cross-section of the wire is $2.0 \mathrm{~mm}^{2}$ and its Young's modulus is $1.2 \times 10^{11} \mathrm{Nm}^{-2}$. The extension of the wire over its natural length due to its tension will be $x \times 10^{-5} \mathrm{~m}$. The value of $x$ is __________.