The correct order of spin only magnetic moments for the following complex ions is

The major product formed in the following reaction is:

Choose the halogen which is most reactive towards $\mathrm{S}_{\mathrm{N}} 1$ reaction in the given compounds (A, B, C & D)

The number of given statement/s which is/are correct is __________.

(A) The stronger the temperature dependence of the rate constant, the higher is the activation energy.

(B) If a reaction has zero activation energy, its rate is independent of temperature.

(C) The stronger the temperature dependence of the rate constant, the smaller is the activation energy.

(D) If there is no correlation between the temperature and the rate constant then it means that the reaction has negative activation energy.

The number of following factors which affect the percent covalent character of the ionic bond is _________

(A) Polarising power of cation

(B) Extent of distortion of anion

(C) Polarisability of the anion

(D) Polarising power of anion

Let $A=\left[\begin{array}{ccc}2 & 1 & 0 \\ 1 & 2 & -1 \\ 0 & -1 & 2\end{array}\right]$. If $|\operatorname{adj}(\operatorname{adj}(\operatorname{adj} 2 A))|=(16)^{n}$, then $n$ is equal to :

\lim_\limits{x \rightarrow 0}\left(\left(\frac{\left(1-\cos ^{2}(3 x)\right.}{\cos ^{3}(4 x)}\right)\left(\frac{\sin ^{3}(4 x)}{\left(\log _{e}(2 x+1)\right)^{5}}\right)\right) is equal to _____________.

The number of ways, in which 5 girls and 7 boys can be seated at a round table so that no two girls sit together, is :

Let $I(x)=\int \frac{(x+1)}{x\left(1+x e^{x}\right)^{2}} d x, x > 0$. If \lim_\limits{x \rightarrow \infty} I(x)=0, then $I(1)$ is equal to :

Let $\alpha, \beta, \gamma$ be the three roots of the equation $x^{3}+b x+c=0$. If $\beta \gamma=1=-\alpha$, then $b^{3}+2 c^{3}-3 \alpha^{3}-6 \beta^{3}-8 \gamma^{3}$ is equal to :

If the solution curve of the differential equation $\left(y-2 \log _{e} x\right) d x+\left(x \log _{e} x^{2}\right) d y=0, x > 1$ passes through the points $\left(e, \frac{4}{3}\right)$ and $\left(e^{4}, \alpha\right)$, then $\alpha$ is equal to ____________.

Which of the following complex is octahedral, diamagnetic and the most stable?

$2 \mathrm{IO}_{3}^{-}+x \mathrm{I}^{-}+12 \mathrm{H}^{+} \rightarrow 6 \mathrm{I}_{2}+6 \mathrm{H}_{2} \mathrm{O}$

What is the value of $x$ ?

Molar mass of the hydrocarbon (X) which on ozonolysis consumes one mole of $\mathrm{O}_{3}$ per mole of $(\mathrm{X})$ and gives one mole each of ethanal and propanone is _________ $\mathrm{g}~ \mathrm{mol}^{-1}$

(Molar mass of $\mathrm{C}: 12 \mathrm{~g} \mathrm{~mol}^{-1}, \mathrm{H}: 1 \mathrm{~g} \mathrm{~mol}^{-1}$ )

The vapour pressure vs. temperature curve for a solution solvent system is shown below.

The boiling point of the solvent is __________ ${ }^{\circ} \mathrm{C}$.

The number of arrangements of the letters of the word "INDEPENDENCE" in which all the vowels always occur together is :

Let $R$ be the focus of the parabola $y^{2}=20 x$ and the line $y=m x+c$ intersect the parabola at two points $P$ and $Q$.

Let the point $G(10,10)$ be the centroid of the triangle $P Q R$. If $c-m=6$, then $(P Q)^{2}$ is :

Let the number of elements in sets $A$ and $B$ be five and two respectively. Then the number of subsets of $A \times B$ each having at least 3 and at most 6 elements is :

Let $S_{K}=\frac{1+2+\ldots+K}{K}$ and \sum_\limits{j=1}^{n} S_{j}^{2}=\frac{n}{A}\left(B n^{2}+C n+D\right), where $A, B, C, D \in \mathbb{N}$ and $A$ has least value. Then

Match List I with List II:

	LIST I (Reagent)		LIST II (Product)
A.		I.
B.	$\mathrm{HBF_4,\Delta}$	II.
C.	$\mathrm{Cu,HCl}$	III.
D.	$\mathrm{CuCN/KCN}$	IV.

Choose the correct answer from the options given below:

Which halogen is known to cause the reaction given below :

$2 \mathrm{Cu}^{2+}+4 \mathrm{X}^{-} \rightarrow \mathrm{Cu}_{2} \mathrm{X}_{2}(\mathrm{s})+\mathrm{X}_{2}$

The water gas on reacting with cobalt as a catalyst forms

$0.5 \mathrm{~g}$ of an organic compound $(\mathrm{X})$ with $60 \%$ carbon will produce __________ $\times 10^{-1} \mathrm{~g}$ of $\mathrm{CO}_{2}$ on complete combustion.

The titration curve of weak acid vs. strong base with phenolphthalein as indictor) is shown below. The $\mathrm{K}_{\text {phenolphthalein }}=4 \times 10^{-10}$.

Given: $\log 2=0.3$

The number of following statement/s which is/are correct about phenolphthalein is ___________

A. It can be used as an indicator for the titration of weak acid with weak base.

B. It begins to change colour at $\mathrm{pH}=8.4$

C. It is a weak organic base

D. It is colourless in acidic medium

When a $60 \mathrm{~W}$ electric heater is immersed in a gas for 100 s in a constant volume container with adiabatic walls, the temperature of the gas rises by $5^{\circ} \mathrm{C}$. The heat capacity of the given gas is ___________ $\mathrm{J} \mathrm{K}^{-1}$ (Nearest integer)

Let $f(x)=\frac{\sin x+\cos x-\sqrt{2}}{\sin x-\cos x}, x \in[0, \pi]-\left\{\frac{\pi}{4}\right\}$. Then $f\left(\frac{7 \pi}{12}\right) f^{\prime \prime}\left(\frac{7 \pi}{12}\right)$ is equal to

The area of the region $\left\{(x, y): x^{2} \leq y \leq 8-x^{2}, y \leq 7\right\}$ is :

If for $z=\alpha+i \beta,|z+2|=z+4(1+i)$, then $\alpha+\beta$ and $\alpha \beta$ are the roots of the equation :

If the points with position vectors $\alpha \hat{i}+10 \hat{j}+13 \hat{k}, 6 \hat{i}+11 \hat{j}+11 \hat{k}, \frac{9}{2} \hat{i}+\beta \hat{j}-8 \hat{k}$ are collinear, then $(19 \alpha-6 \beta)^{2}$ is equal to :

Let $[t]$ denote the greatest integer $\leq t$. Then \frac{2}{\pi} \int_\limits{\pi / 6}^{5 \pi / 6}(8[\operatorname{cosec} x]-5[\cot x]) d x is equal to __________.

Let $A=\{0,3,4,6,7,8,9,10\}$ and $R$ be the relation defined on $A$ such that $R=\{(x, y) \in A \times A: x-y$ is odd positive integer or $x-y=2\}$. The minimum number of elements that must be added to the relation $R$, so that it is a symmetric relation, is equal to ____________.

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

Assertion A: Butan -1- ol has higher boiling point than ethoxyethane.

Reason R: Extensive hydrogen bonding leads to stronger association of molecules.

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

The correct order of electronegativity for given elements is:

In chromyl chloride, the number of d-electrons present on chromium is same as in

(Given at no. of $\mathrm{Ti}: 22, \mathrm{~V}: 23, \mathrm{Cr}: 24, \mathrm{Mn}: 25, \mathrm{Fe}: 26$ )

The reaction

$\frac{1}{2} \mathrm{H}_{2}(\mathrm{~g})+\mathrm{AgCl}(\mathrm{s}) \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{Cl}^{-}(\mathrm{aq})+\mathrm{Ag}(\mathrm{s})$

occurs in which of the given galvanic cell.

Sulphur (S) containing amino acids from the following are:

(a) isoleucine (b) cysteine (c) lysine (d) methionine (e) glutamic acid

Match List I with List II:

	LIST I (Reagents used)		LIST II (Compound with Functional group detected)
A.	Alkaline solution of copper sulphate and sodium citrate	I.
B.	Neutral $\mathrm{FeCl_3}$	II.
C.	Alkaline chloroform solution	III.
D.	Potassium iodide and sodium hypochlorite	IV.

Choose the correct answer from the options given below:

In a bolt factory, machines $A, B$ and $C$ manufacture respectively $20 \%, 30 \%$ and $50 \%$ of the total bolts. Of their output 3, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product. If the bolt drawn is found the defective, then the probability that it is manufactured by the machine $C$ is :

The shortest distance between the lines $\frac{x-4}{4}=\frac{y+2}{5}=\frac{z+3}{3}$ and $\frac{x-1}{3}=\frac{y-3}{4}=\frac{z-4}{2}$ is :

Let $C(\alpha, \beta)$ be the circumcenter of the triangle formed by the lines

$4 x+3 y=69$

$4 y-3 x=17$, and

$x+7 y=61$.

Then $(\alpha-\beta)^{2}+\alpha+\beta$ is equal to :

Let $P=\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac{1}{2} \\ -\frac{1}{2} & \frac{\sqrt{3}}{2}\end{array}\right], A=\left[\begin{array}{ll}1 & 1 \\ 0 & 1\end{array}\right]$ and $Q=P A P^{T}$. If $P^{T} Q^{2007} P=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$, then $2 a+b-3 c-4 d$ equal to :

Certain galvanometers have a fixed core made of non magnetic metallic material. The function of this metallic material is

If $a_{\alpha}$ is the greatest term in the sequence $\alpha_{n}=\frac{n^{3}}{n^{4}+147}, n=1,2,3, \ldots$, then $\alpha$ is equal to _____________.

Let $[t]$ denote the greatest integer $\leq t$. If the constant term in the expansion of $\left(3 x^{2}-\frac{1}{2 x^{5}}\right)^{7}$ is $\alpha$, then $[\alpha]$ is equal to ___________.

Consider a circle $C_{1}: x^{2}+y^{2}-4 x-2 y=\alpha-5$. Let its mirror image in the line $y=2 x+1$ be another circle $C_{2}: 5 x^{2}+5 y^{2}-10 f x-10 g y+36=0$. Let $r$ be the radius of $C_{2}$. Then $\alpha+r$ is equal to _________.

Dimension of $\frac{1}{\mu_{0} \in_{0}}$ should be equal to

Given below are two statements:

Statement I: If heat is added to a system, its temperature must increase.

Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase.

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

Two forces having magnitude $A$ and $\frac{A}{2}$ are perpendicular to each other. The magnitude of their resultant is:

At any instant the velocity of a particle of mass $500 \mathrm{~g}$ is $\left(2 t \hat{i}+3 t^{2} \hat{j}\right) \mathrm{ms}^{-1}$. If the force acting on the particle at $t=1 \mathrm{~s}$ is $(\hat{i}+x \hat{j}) \mathrm{N}$. Then the value of $x$ will be:

A cylindrical wire of mass $(0.4 \pm 0.01) \mathrm{g}$ has length $(8 \pm 0.04) \mathrm{cm}$ and radius $(6 \pm 0.03) \mathrm{mm}$. The maximum error in its density will be:

Two projectiles A and B are thrown with initial velocities of $40 \mathrm{~m} / \mathrm{s}$ and $60 \mathrm{~m} / \mathrm{s}$ at angles $30^{\circ}$ and $60^{\circ}$ with the horizontal respectively. The ratio of their ranges respectively is $\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$

An aluminium rod with Young's modulus $Y=7.0 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$ undergoes elastic strain of $0.04 \%$. The energy per unit volume stored in the rod in SI unit is:

A current of $2 \mathrm{~A}$ flows through a wire of cross-sectional area $25.0 \mathrm{~mm}^{2}$. The number of free electrons in a cubic meter are $2.0 \times 10^{28}$. The drift velocity of the electrons is __________ $\times 10^{-6} \mathrm{~ms}^{-1}$ (given, charge on electron $=1.6 \times 10^{-19} \mathrm{C}$ ).

A nucleus with mass number 242 and binding energy per nucleon as $7.6~ \mathrm{MeV}$ breaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as $8.1 ~\mathrm{MeV}$, the total gain in binding energy is _________ $\mathrm{MeV}$.

An oscillating LC circuit consists of a $75 ~\mathrm{mH}$ inductor and a $1.2 ~\mu \mathrm{F}$ capacitor. If the maximum charge to the capacitor is $2.7 ~\mu \mathrm{C}$. The maximum current in the circuit will be ___________ $\mathrm{mA}$

Given below are two statements:

Statement I: If $\mathrm{E}$ be the total energy of a satellite moving around the earth, then its potential energy will be $\frac{E}{2}$.

Statement II: The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy $\mathrm{E}$.

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

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius $\mathrm{R}$, with distance $r$ from the centre O is represented by:

A charge particle moving in magnetic field B, has the components of velocity along B as well as perpendicular to B. The path of the charge particle will be

Proton $(\mathrm{P})$ and electron (e) will have same de-Broglie wavelength when the ratio of their momentum is (assume, $\mathrm{m}_{\mathrm{p}}=1849 \mathrm{~m}_{\mathrm{e}}$ ):

An organ pipe $40 \mathrm{~cm}$ long is open at both ends. The speed of sound in air is $360 \mathrm{~ms}^{-1}$. The frequency of the second harmonic is ___________ $\mathrm{Hz}$.

The momentum of a body is increased by $50 \%$. The percentage increase in the kinetic energy of the body is ___________ $\%$.

Two vertical parallel mirrors A and B are separated by $10 \mathrm{~cm}$. A point object $\mathrm{O}$ is placed at a distance of $2 \mathrm{~cm}$ from mirror $\mathrm{A}$. The distance of the second nearest image behind mirror A from the mirror $\mathrm{A}$ is _________ $\mathrm{cm}$.

An air bubble of diameter $6 \mathrm{~mm}$ rises steadily through a solution of density $1750 \mathrm{~kg} / \mathrm{m}^{3}$ at the rate of $0.35 \mathrm{~cm} / \mathrm{s}$. The co-efficient of viscosity of the solution (neglect density of air) is ___________ Pas (given, $\mathrm{g}=10 \mathrm{~ms}^{-2}$ ).

The moment of inertia of a semicircular ring about an axis, passing through the center and perpendicular to the plane of ring, is $\frac{1}{x} \mathrm{MR}^{2}$, where $\mathrm{R}$ is the radius and $M$ is the mass of the semicircular ring. The value of $x$ will be __________.

The largest natural number $n$ such that $3^{n}$ divides $66 !$ is ___________.

Let the mean and variance of 8 numbers $x, y, 10,12,6,12,4,8$ be $9$ and $9.25$ respectively. If $x > y$, then $3 x-2 y$ is equal to _____________.

An air bubble of volume $1 \mathrm{~cm}^{3}$ rises from the bottom of a lake $40 \mathrm{~m}$ deep to the surface at a temperature of $12^{\circ} \mathrm{C}$. The atmospheric pressure is $1 \times 10^{5} \mathrm{~Pa}$ the density of water is $1000 \mathrm{~kg} / \mathrm{m}^{3}$ and $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$. There is no difference of the temperature of water at the depth of $40 \mathrm{~m}$ and on the surface. The volume of air bubble when it reaches the surface will be:

In a reflecting telescope, a secondary mirror is used to:

For a nucleus ${ }_{\mathrm{A}}^{\mathrm{A}} \mathrm{X}$ having mass number $\mathrm{A}$ and atomic number $\mathrm{Z}$

A. The surface energy per nucleon $\left(b_{\mathrm{s}}\right)=-a_{1} A^{2 / 3}$.

B. The Coulomb contribution to the binding energy $\mathrm{b}_{\mathrm{c}}=-a_{2} \frac{Z(Z-1)}{A^{4 / 3}}$

C. The volume energy $\mathrm{b}_{\mathrm{v}}=a_{3} A$

D. Decrease in the binding energy is proportional to surface area.

E. While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons. ( $a_{1}, a_{2}$ and $a_{3}$ are constants)

Choose the most appropriate answer from the options given below:

In this figure the resistance of the coil of galvanometer G is $2 ~\Omega$. The emf of the cell is $4 \mathrm{~V}$. The ratio of potential difference across $\mathrm{C}_{1}$ and $\mathrm{C}_{2}$ is:

The magnetic intensity at the center of a long current carrying solenoid is found to be $1.6 \times 10^{3} \mathrm{Am}^{-1}$. If the number of turns is 8 per cm, then the current flowing through the solenoid is __________ A.

An electric dipole of dipole moment is $6.0 \times 10^{-6} ~\mathrm{C m}$ placed in a uniform electric field of $1.5 \times 10^{3} ~\mathrm{NC}^{-1}$ in such a way that dipole moment is along electric field. The work done in rotating dipole by $180^{\circ}$ in this field will be ___________ $\mathrm{m J}$.

Let $\vec{a}=6 \hat{i}+9 \hat{j}+12 \hat{k}, \vec{b}=\alpha \hat{i}+11 \hat{j}-2 \hat{k}$ and $\vec{c}$ be vectors such that $\vec{a} \times \vec{c}=\vec{a} \times \vec{b}$. If

$\vec{a} \cdot \vec{c}=-12, \vec{c} \cdot(\hat{i}-2 \hat{j}+\hat{k})=5$, then $\vec{c} \cdot(\hat{i}+\hat{j}+\hat{k})$ is equal to _______________.

For the logic circuit shown, the output waveform at $\mathrm{Y}$ is:

The weight of a body on the earth is $400 \mathrm{~N}$. Then weight of the body when taken to a depth half of the radius of the earth will be: