Which of the following reactions are disproportionation reactions?

(A) $\mathrm{Cu}^{+} \rightarrow \mathrm{Cu}^{2+}+\mathrm{Cu}$

(B) $3 \mathrm{MnO}_4^{2-}+4 \mathrm{H}^{+} \longrightarrow 2

\mathrm{MnO}_4^{-}+\mathrm{MnO}_2+2 \mathrm{H}_2 \mathrm{O}$

(C) $2 \mathrm{KMnO}_4 \longrightarrow \mathrm{K}_2 \mathrm{MnO}_4+\mathrm{MnO}_2+\mathrm{O}_2$

(D) $2 \mathrm{MnO}_4^{-}+3 \mathrm{Mn}^{2+}+2 \mathrm{H}_2 \mathrm{O} \longrightarrow 5 \mathrm{MnO}_2+4 \mathrm{H}^{+}$

Choose the correct answer from the options given below :

Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following :

Identify $A$ and $B$ in the following sequence of reaction

Which of the following complex is homoleptic?

In Kjeldahl's method for estimation of nitrogen, $\mathrm{CuSO}_4$ acts as :

Given below are two statements :

Statement (I) : Potassium hydrogen phthalate is a primary standard for standardisation of sodium hydroxide solution.

Statement (II) : In this titration phenolphthalein can be used as indicator.

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

In case of isoelectronic species the size of $\mathrm{F}^{-}, \mathrm{Ne}$ and $\mathrm{Na}^{+}$is affected by :

Ionic reactions with organic compounds proceed through :

(A) homolytic bond cleavage

(B) heterolytic bond cleavage

(C) free radical formation

(D) primary free radical

(E) secondary free radical

Choose the correct answer from the options given below :

Which of the following compound will most easily be attacked by an electrophile?

Given below are two statements :

Statement (I) : A solution of $\left[\mathrm{Ni}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$ is green in colour.

Statement (II) : A solution of $\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}$ is colourless.

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

We have three aqueous solutions of $\mathrm{NaCl}$ labelled as ' $\mathrm{A}$ ', ' $\mathrm{B}$ ' and ' $\mathrm{C}$ ' with concentration $0.1 \mathrm{M}$, $0.01 \mathrm{M}$ and $0.001 \mathrm{M}$, respectively. The value of van 't Hoff factor(i) for these solutions will be in the order :

Given below are two statements :

Statement (I) : The $\mathrm{NH}_2$ group in Aniline is ortho and para directing and a powerful activating group.

Statement (II) : Aniline does not undergo Friedel-Craft's reaction (alkylation and acylation).

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

According to the wave-particle duality of matter by de-Broglie, which of the following graph plot presents most appropriate relationship between wavelength of electron $(\lambda)$ and momentum of electron $(p)$?

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

Assertion (A): $\mathrm{PH}_3$ has lower boiling point than $\mathrm{NH}_3$.

Reason (R) : In liquid state $\mathrm{NH}_3$ molecules are associated through vander Waal's forces, but $\mathrm{PH}_3$ molecules are associated through hydrogen bonding.

In the light of the above statements, choose the most appropriate 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) : Haloalkanes react with KCN to form alkyl cyanides as a main product while with $\mathrm{AgCN}$ form isocyanide as the main product.

Reason (R) : $\mathrm{KCN}$ and $\mathrm{AgCN}$ both are highly ionic compounds.

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

If one strand of a DNA has the sequence ATGCTTCA, sequence of the bases in complementary strand is :

In acidic medium, $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ shows oxidising action as represented in the half reaction:

$$ \mathrm{Cr}_2 \mathrm{O}_7{ }^{2-}+\mathrm{XH}^{+}+\mathrm{Ye}^{\ominus} \rightarrow 2 \mathrm{~A}+\mathrm{ZH}_2 \mathrm{O} $$

$\mathrm{X}, \mathrm{Y}, \mathrm{Z}$ and $\mathrm{A}$ are respectively are :

Given below are two statements :

Statement (I) : Aminobenzene and aniline are same organic compounds.

Statement (II) : Aminobenzene and aniline are different organic compounds.

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

Match List - I with List - II.

List I (Reactions)	List II (Reagents)
(A)	(I) CH3MgBr, H2O
(B) C6H5COC6H5 ⟶ C6H5CH=C6H5	(II) Zn(Hg) and conc. HCl
(C) C6H5CHO ⟶ C6H5CH(OH)CH3	(III) NaBH4, H+
(D)	(IV) DIBAL-H, H2O

Choose the correct answer from the options given below :

Arrange the bonds in order of increasing ionic character in the molecules. $\mathrm{LiF}$, $\mathrm{K}_2 \mathrm{O}, \mathrm{N}_2, \mathrm{SO}_2$ and $\mathrm{ClF}_3$ :

The number of white coloured salts, among the following is

(a) $\mathrm{SrSO}_4$

(b) $\mathrm{Mg}\left(\mathrm{NH}_4\right) \mathrm{PO}_4$

(c) $\mathrm{BaCrO}_4$

(d) $\mathrm{Mn}(\mathrm{OH})_2$

(e) $\mathrm{PbSO}_4$

(f) $\mathrm{PbCrO}_4$

(g) $\mathrm{AgBr}$

(h) $\mathrm{PbI}_2$

(i) $\mathrm{CaC}_2 \mathrm{O}_4$

(j) $\left[\mathrm{Fe}(\mathrm{OH})_2\left(\mathrm{CH}_3 \mathrm{COO}\right)\right]$

Total number of deactivating groups in aromatic electrophilic substitution reaction among the following is _______ .

The potential for the given half cell at $298 \mathrm{~K}$ is (-) __________ $\times 10^{-2} \mathrm{~V}$

$$ \begin{aligned} & 2 \mathrm{H}_{(\mathrm{aq})}^{+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{H}_2(\mathrm{~g}) \\\\ & {\left[\mathrm{H}^{+}\right]=1 \mathrm{M}, \mathrm{P}_{\mathrm{H}_2}=2 \mathrm{~atm}} \end{aligned} $$

(Given : $2.303 \mathrm{RT} / \mathrm{F}=0.06 \mathrm{~V}, \log 2=0.3$ )

Among the following oxides of p-block elements, number of oxides having amphoteric nature is ________.

$\mathrm{Cl}_2 \mathrm{O}_7, \mathrm{CO}, \mathrm{PbO}_2, \mathrm{~N}_2 \mathrm{O}, \mathrm{NO}, \mathrm{Al}_2 \mathrm{O}_3, \mathrm{SiO}_2, \mathrm{~N}_2 \mathrm{O}_5, \mathrm{SnO}_2$

Consider the following reaction :

$$ 3 \mathrm{PbCl}_2+2\left(\mathrm{NH}_4\right)_3 \mathrm{PO}_4 \rightarrow \mathrm{Pb}_3\left(\mathrm{PO}_4\right)_2+6 \mathrm{NH}_4 \mathrm{Cl} $$

If $72 ~\mathrm{mmol}$ of $\mathrm{PbCl}_2$ is mixed with $50 ~\mathrm{mmol}$ of $\left(\mathrm{NH}_4\right)_3 \mathrm{PO}_4$, then the amount of $\mathrm{Pb}_3\left(\mathrm{PO}_4\right)_2$ formed is ________ mmol (nearest integer).

The number of molecules/ion/s having trigonal bipyramidal shape is _______.

$\mathrm{PF}_5, \mathrm{BrF}_5, \mathrm{PCl}_5,\left[\mathrm{Pt} \mathrm{Cl}_4\right]^{2-}, \mathrm{BF}_3, \mathrm{Fe}(\mathrm{CO})_5$

The lowest oxidation number of an atom in a compound $\mathrm{A}_2 \mathrm{B}$ is -2 . The number of electrons in its valence shell is _______.

$\mathrm{K}_{\mathrm{a}}$ for $\mathrm{CH}_3 \mathrm{COOH}$ is $1.8 \times 10^{-5}$ and $\mathrm{K}_{\mathrm{b}}$ for $\mathrm{NH}_4 \mathrm{OH}$ is $1.8 \times 10^{-5}$. The $\mathrm{pH}$ of ammonium acetate solution will be _________.

Number of optical isomers possible for 2-chlorobutane ________.

The ratio of $\frac{{ }^{14} \mathrm{C}}{{ }^{12} \mathrm{C}}$ in a piece of wood is $\frac{1}{8}$ part that of atmosphere. If half life of ${ }^{14} \mathrm{C}$ is 5730 years, the age of wood sample is ________ years.

A bag contains 8 balls, whose colours are either white or black. 4 balls are drawn at random without replacement and it was found that 2 balls are white and other 2 balls are black. The probability that the bag contains equal number of white and black balls is :

The value of the integral $\int\limits_0^{\pi / 4} \frac{x \mathrm{~d} x}{\sin ^4(2 x)+\cos ^4(2 x)}$ equals :

If $\mathrm{A}=\left[\begin{array}{cc}\sqrt{2} & 1 \\ -1 & \sqrt{2}\end{array}\right], \mathrm{B}=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right], \mathrm{C}=\mathrm{ABA}^{\mathrm{T}}$ and $\mathrm{X}=\mathrm{A}^{\mathrm{T}} \mathrm{C}^2 \mathrm{~A}$, then $\operatorname{det} \mathrm{X}$ is equal to :

If $\tan \mathrm{A}=\frac{1}{\sqrt{x\left(x^2+x+1\right)}}, \tan \mathrm{B}=\frac{\sqrt{x}}{\sqrt{x^2+x+1}}$ and

$\tan \mathrm{C}=\left(x^{-3}+x^{-2}+x^{-1}\right)^{1 / 2}, 0<\mathrm{A}, \mathrm{B}, \mathrm{C}<\frac{\pi}{2}$, then $\mathrm{A}+\mathrm{B}$ is equal to :

If $\mathrm{n}$ is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then $\mathrm{n}$ is equal to :

Let $\mathrm{S}=|\mathrm{z} \in \mathrm{C}:| z-1 \mid=1$ and $(\sqrt{2}-1)(z+\bar{z})-i(z-\bar{z})=2 \sqrt{2} \mid$. Let $z_1, z_2 \in \mathrm{S}$ be such that $\left|z_1\right|=\max\limits_{z \in s}|z|$ and $\left|z_2\right|=\min\limits _{z \in S}|z|$. Then $\left|\sqrt{2} z_1-z_2\right|^2$ equals :

Let the median and the mean deviation about the median of 7 observation $170,125,230,190,210$, a, b be 170 and $\frac{205}{7}$ respectively. Then the mean deviation about the mean of these 7 observations is :

Let $\overrightarrow{\mathrm{a}}=-5 \hat{i}+\hat{j}-3 \hat{k}, \overrightarrow{\mathrm{b}}=\hat{i}+2 \hat{j}-4 \hat{k}$ and

$\overrightarrow{\mathrm{c}}=(((\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}) \times \hat{i}) \times \hat{i}) \times \hat{i}$. Then $\vec{c} \cdot(-\hat{i}+\hat{j}+\hat{k})$ is equal to :

Let $\mathbf{S}=\left\{x \in \mathbf{R}:(\sqrt{3}+\sqrt{2})^x+(\sqrt{3}-\sqrt{2})^x=10\right\}$. Then the number of elements in $\mathrm{S}$ is :

The area enclosed by the curves $x y+4 y=16$ and $x+y=6$ is equal to :

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ and $g: \mathbf{R} \rightarrow \mathbf{R}$ be defined as

$f(x)=\left\{\begin{array}{ll}\log _{\mathrm{e}} x, & x>0 \\ \mathrm{e}^{-x}, & x \leq 0\end{array}\right.$ and

$g(x)=\left\{\begin{array}{ll}x, & x \geqslant 0 \\ \mathrm{e}^x, & x<0\end{array}\right.$. Then, gof : $\mathbf{R} \rightarrow \mathbf{R}$ is :

If the system of equations

$$ \begin{aligned} & 2 x+3 y-z=5 \\\\ & x+\alpha y+3 z=-4 \\\\ & 3 x-y+\beta z=7 \end{aligned} $$

has infinitely many solutions, then $13 \alpha \beta$ is equal to :

For $0<\theta<\pi / 2$, if the eccentricity of the hyperbola

$x^2-y^2 \operatorname{cosec}^2 \theta=5$ is $\sqrt{7}$ times eccentricity of the

ellipse $x^2 \operatorname{cosec}^2 \theta+y^2=5$, then the value of $\theta$ is :

Let $y=y(x)$ be the solution of the differential equation

$\frac{\mathrm{d} y}{\mathrm{~d} x}=2 x(x+y)^3-x(x+y)-1, y(0)=1$.

Then, $\left(\frac{1}{\sqrt{2}}+y\left(\frac{1}{\sqrt{2}}\right)\right)^2$ equals :

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be defined as :

$$ f(x)= \begin{cases}\frac{a-b \cos 2 x}{x^2} ; & x<0 \\\\ x^2+c x+2 ; & 0 \leq x \leq 1 \\\\ 2 x+1 ; & x>1\end{cases} $$

If $f$ is continuous everywhere in $\mathbf{R}$ and $m$ is the number of points where $f$ is NOT differential then $\mathrm{m}+\mathrm{a}+\mathrm{b}+\mathrm{c}$ equals :

Let $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, \mathrm{a}>\mathrm{b}$ be an ellipse, whose eccentricity is $\frac{1}{\sqrt{2}}$ and the length of the latusrectum is $\sqrt{14}$. Then the square of the eccentricity of $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is :

Let $3, a, b, c$ be in A.P. and $3, a-1, b+1, c+9$ be in G.P. Then, the arithmetic mean of $a, b$ and $c$ is :

Let $C: x^2+y^2=4$ and $C^{\prime}: x^2+y^2-4 \lambda x+9=0$ be two circles. If the set of all values of $\lambda$ so that the circles $\mathrm{C}$ and $\mathrm{C}$ intersect at two distinct points, is $\mathrm{R}-[\mathrm{a}, \mathrm{b}]$, then the point $(8 \mathrm{a}+12,16 \mathrm{~b}-20)$ lies on the curve :

If $5 f(x)+4 f\left(\frac{1}{x}\right)=x^2-2, \forall x \neq 0$ and $y=9 x^2 f(x)$, then $y$ is strictly increasing in :

If the shortest distance between the lines

$\frac{x-\lambda}{-2}=\frac{y-2}{1}=\frac{z-1}{1}$ and $\frac{x-\sqrt{3}}{1}=\frac{y-1}{-2}=\frac{z-2}{1}$ is 1 , then the sum of all possible values of $\lambda$ is :

If $x=x(t)$ is the solution of the differential equation $(t+1) \mathrm{d} x=\left(2 x+(t+1)^4\right) \mathrm{dt}, x(0)=2$, then, $x(1)$ equals _________.

The number of elements in the set $\mathrm{S}=\{(x, y, z): x, y, z \in \mathbf{Z}, x+2 y+3 z=42, x, y, z \geqslant 0\}$ equals __________.

If the Coefficient of $x^{30}$ in the expansion of $\left(1+\frac{1}{x}\right)^6\left(1+x^2\right)^7\left(1-x^3\right)^8 ; x \neq 0$ is $\alpha$, then $|\alpha|$ equals ___________.

Let $3,7,11,15, \ldots, 403$ and $2,5,8,11, \ldots, 404$ be two arithmetic progressions. Then the sum, of the common terms in them, is equal to ___________.

Let $\{x\}$ denote the fractional part of $x$ and $f(x)=\frac{\cos ^{-1}\left(1-\{x\}^2\right) \sin ^{-1}(1-\{x\})}{\{x\}-\{x\}^3}, x \neq 0$. If $\mathrm{L}$ and $\mathrm{R}$ respectively denotes the left hand limit and the right hand limit of $f(x)$ at $x=0$, then $\frac{32}{\pi^2}\left(\mathrm{~L}^2+\mathrm{R}^2\right)$ is equal to ___________.

Let the line $\mathrm{L}: \sqrt{2} x+y=\alpha$ pass through the point of the intersection $\mathrm{P}$ (in the first quadrant) of the circle $x^2+y^2=3$ and the parabola $x^2=2 y$. Let the line $\mathrm{L}$ touch two circles $\mathrm{C}_1$ and $\mathrm{C}_2$ of equal radius $2 \sqrt{3}$. If the centres $Q_1$ and $Q_2$ of the circles $C_1$ and $C_2$ lie on the $y$-axis, then the square of the area of the triangle $\mathrm{PQ}_1 \mathrm{Q}_2$ is equal to ___________.

Let $\mathrm{P}=\{\mathrm{z} \in \mathbb{C}:|z+2-3 i| \leq 1\}$ and $\mathrm{Q}=\{\mathrm{z} \in \mathbb{C}: z(1+i)+\bar{z}(1-i) \leq-8\}$. Let in $\mathrm{P} \cap \mathrm{Q}$, $|z-3+2 i|$ be maximum and minimum at $z_1$ and $z_2$ respectively. If $\left|z_1\right|^2+2\left|z_2\right|^2=\alpha+\beta \sqrt{2}$, where $\alpha, \beta$ are integers, then $\alpha+\beta$ equals _____________.

If $\int\limits_{-\pi / 2}^{\pi / 2} \frac{8 \sqrt{2} \cos x \mathrm{~d} x}{\left(1+\mathrm{e}^{\sin x}\right)\left(1+\sin ^4 x\right)}=\alpha \pi+\beta \log _{\mathrm{e}}(3+2 \sqrt{2})$, where $\alpha, \beta$ are integers, then $\alpha^2+\beta^2$ equals :

Let the line of the shortest distance between the lines

$$ \begin{aligned} & \mathrm{L}_1: \overrightarrow{\mathrm{r}}=(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(\hat{i}-\hat{j}+\hat{k}) \text { and } \\\\ & \mathrm{L}_2: \overrightarrow{\mathrm{r}}=(4 \hat{i}+5 \hat{j}+6 \hat{k})+\mu(\hat{i}+\hat{j}-\hat{k}) \end{aligned} $$

intersect $\mathrm{L}_1$ and $\mathrm{L}_2$ at $\mathrm{P}$ and $\mathrm{Q}$ respectively. If $(\alpha, \beta, \gamma)$ is the mid point of the line segment $\mathrm{PQ}$, then $2(\alpha+\beta+\gamma)$ is equal to ____________.

Let $A=\{1,2,3, \ldots, 20\}$. Let $R_1$ and $R_2$ two relation on $A$ such that

$R_1=\{(a, b): b$ is divisible by $a\}$

$R_2=\{(a, b): a$ is an integral multiple of $b\}$.

Then, number of elements in $R_1-R_2$ is equal to _____________.

Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is 0.04 , the acceleration of the system in $\mathrm{ms}^{-2}$ is :

(Consider that the string is massless and unstretchable and the pulley is also massless and frictionless) :

If $\mathrm{R}$ is the radius of the earth and the acceleration due to gravity on the surface of earth is $g=\pi^2 \mathrm{~m} / \mathrm{s}^2$, then the length of the second's pendulum at a height $\mathrm{h}=2 R$ from the surface of earth will be, :

10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is :

Two moles a monoatomic gas is mixed with six moles of a diatomic gas. The molar specific heat of the mixture at constant volume is :

The dimensional formula of angular impulse is :

A monochromatic light of wavelength $6000 ~\mathring{A}$ is incident on the single slit of width $0.01 \mathrm{~mm}$. If the diffraction pattern is formed at the focus of the convex lens of focal length $20 \mathrm{~cm}$, the linear width of the central maximum is :

A ball of mass $0.5 \mathrm{~kg}$ is attached to a string of length $50 \mathrm{~cm}$. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is $400 \mathrm{~N}$. The maximum possible value of angular velocity of the ball in $\mathrm{rad} / \mathrm{s}$ is, :

The reading in the ideal voltmeter $(\mathrm{V})$ shown in the given circuit diagram is :

A galvanometer has a resistance of $50 ~\Omega$ and it allows maximum current of $5 \mathrm{~mA}$. It can be converted into voltmeter to measure upto $100 \mathrm{~V}$ by connecting in series a resistor of resistance :

The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly :

A parallel plate capacitor has a capacitance $\mathrm{C}=200~ \mathrm{pF}$. It is connected to $230 \mathrm{~V}$ ac supply with an angular frequency $300~ \mathrm{rad} / \mathrm{s}$. The rms value of conduction current in the circuit and displacement current in the capacitor respectively are :

The de Broglie wavelengths of a proton and an $\alpha$ particle are $\lambda$ and $2 \lambda$ respectively. The ratio of the velocities of proton and $\alpha$ particle will be :

The radius $(\mathrm{r})$, length $(l)$ and resistance $(\mathrm{R})$ of a metal wire was measured in the laboratory as

$$ \begin{aligned} & \mathrm{r}=(0.35 \pm 0.05) ~\mathrm{cm} \\\\ & \mathrm{R}=(100 \pm 10) ~\mathrm{ohm} \\\\ & l=(15 \pm 0.2)~ \mathrm{cm} \end{aligned} $$

The percentage error in resistivity of the material of the wire is :

Two identical capacitors have same capacitance $C$. One of them is charged to the potential $V$ and other to the potential $2 \mathrm{~V}$. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is :

A simple pendulum of length $1 \mathrm{~m}$ has a wooden bob of mass $1 \mathrm{~kg}$. It is struck by a bullet of mass $10^{-2} \mathrm{~kg}$ moving with a speed of $2 \times 10^2 \mathrm{~ms}^{-1}$. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is. (use $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )

The pressure and volume of an ideal gas are related as $\mathrm{PV}^{\frac{3}{2}}=\mathrm{K}$ (Constant). The work done when the gas is taken from state $A\left(P_1, V_1, T_1\right)$ to state $B\left(P_2, V_2, T_2\right)$ is :

In series LCR circuit, the capacitance is changed from $C$ to $4 C$. To keep the resonance frequency unchanged, the new inductance should be:

A particle moving in a circle of radius $\mathrm{R}$ with uniform speed takes time $\mathrm{T}$ to complete one revolution.

If this particle is projected with the same speed at an angle $\theta$ to the horizontal, the maximum height attained by it is equal to $4 R$. The angle of projection $\theta$ is then given by :

With rise in temperature, the Young's modulus of elasticity :

In the given circuit if the power rating of Zener diode is $10 \mathrm{~mW}$, the value of series resistance $R_s$ to regulate the input unregulated supply is :

A rectangular loop of sides $12 \mathrm{~cm}$ and $5 \mathrm{~cm}$, with its sides parallel to the $x$-axis and $y$-axis respectively, moves with a velocity of $5 \mathrm{~cm} / \mathrm{s}$ in the positive $x$ axis direction, in a space containing a variable magnetic field in the positive $z$ direction. The field has a gradient of $10^{-3} \mathrm{~T} / \mathrm{cm}$ along the negative $x$ direction and it is decreasing with time at the rate of $10^{-3} \mathrm{~T} / \mathrm{s}$. If the resistance of the loop is $6 \mathrm{~m} \Omega$, the power dissipated by the loop as heat is __________ $\times 10^{-9} \mathrm{~W}$.

A plane is in level flight at constant speed and each of its two wings has an area of $40 \mathrm{~m}^2$. If the speed of the air is $180 \mathrm{~km} / \mathrm{h}$ over the lower wing surface and $252 \mathrm{~km} / \mathrm{h}$ over the upper wing surface, the mass of the plane is ___________ kg.

(Take air density to be $1 \mathrm{~kg} \mathrm{~m}^{-3}$ and $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle $\theta$ with each other. When suspended in water the angle remains the same. If density of the material of the sphere is $1.5 \mathrm{~g} / \mathrm{cc}$, the dielectric constant of water will be __________.

(Take density of water $=1 \mathrm{~g} / \mathrm{cc}$ )

A particle is moving in one dimension (along $x$ axis) under the action of a variable force. It's initial position was $16 \mathrm{~m}$ right of origin. The variation of its position $(x)$ with time $(t)$ is given as $x=-3 t^3+18 t^2+16 t$, where $x$ is in $\mathrm{m}$ and $\mathrm{t}$ is in $\mathrm{s}$.

The velocity of the particle when its acceleration becomes zero is _________ $\mathrm{m} / \mathrm{s}$.

The radius of a nucleus of mass number 64 is 4.8 fermi. Then the mass number of another nucleus having radius of 4 fermi is $\frac{1000}{x}$, where $x$ is _______.

A regular polygon of 6 sides is formed by bending a wire of length $4 \pi$ meter.

If an electric current of $4 \pi \sqrt{3}$ A is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be $x \times 10^{-7} \mathrm{~T}$.

The value of $x$ is _________.

The distance between object and its 3 times magnified virtual image as produced by a convex lens is $20 \mathrm{~cm}$. The focal length of the lens used is __________ $\mathrm{cm}$.

Three identical spheres each of mass $2 \mathrm{M}$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $4 \mathrm{~m}$ each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is $\frac{4 \sqrt{2}}{x}$, where the value of $x$ is ___________ .

A tuning fork resonates with a sonometer wire of length $1 \mathrm{~m}$ stretched with a tension of $6 \mathrm{~N}$. When the tension in the wire is changed to $54 \mathrm{~N}$, the same tuning fork produces 12 beats per second with it. The frequency of the tuning fork is ________________ $\mathrm{Hz}$.

The current in a conductor is expressed as $I=3 t^2+4 t^3$, where $I$ is in Ampere and $t$ is in second. The amount of electric charge that flows through a section of the conductor during $t=1 \mathrm{~s}$ to $t=2 \mathrm{~s}$ is __________ C.