Combustion of glucose $$(\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6)$$ produces $$\mathrm{CO}_2$$ and water. The amount of oxygen (in $$\mathrm{g}$$) required for the complete combustion of $$900 \mathrm{~g}$$ of glucose is :

[Molar mass of glucose in $$\mathrm{g} \mathrm{~mol}^{-1}=180$$]

Thiosulphate reacts differently with iodine and bromine in the reactions given below:

$$\begin{aligned} & 2 \mathrm{~S}_2 \mathrm{O}_3^{2-}+\mathrm{I}_2 \rightarrow \mathrm{S}_4 \mathrm{O}_6^{2-}+2 \mathrm{I}^{-} \\ & \mathrm{S}_2 \mathrm{O}_3^{2-}+5 \mathrm{Br}_2+5 \mathrm{H}_2 \mathrm{O} \rightarrow 2 \mathrm{SO}_4^{2-}+4 \mathrm{Br}^{-}+10 \mathrm{H}^{+} \end{aligned}$$

Which of the following statement justifies the above dual behaviour of thiosulphate?

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

Assertion A: The stability order of +1 oxidation state of $$\mathrm{Ga}$$, In and $$\mathrm{Tl}$$ is Ga < In < Tl.

Reason R: The inert pair effect stabilizes the lower oxidation state down the group.

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

Iron (III) catalyses the reaction between iodide and persulphate ions, in which

A. $$\mathrm{Fe}^{3+}$$ oxidises the iodide ion

B. $$\mathrm{Fe}^{3+}$$ oxidises the persulphate ion

C. $$\mathrm{Fe}^{2+}$$ reduces the iodide ion

D. $$\mathrm{Fe}^{2+}$$ reduces the persulphate ion

Choose the most appropriate answer from the options given below:

Which of the following are aromatic?

Among the following halogens

$$\mathrm{F}_2, \mathrm{Cl}_2, \mathrm{Br}_2 \text { and } \mathrm{I}_2$$

Which can undergo disproportionation reactions?

Which among the following compounds will undergo fastest S_N2 reaction.

Match List I with List II

Choose the correct answer from the options given below:

Choose the correct answer from the options given below:

Match List I with List II

Choose the correct answer from the options given below:

Number of Complexes with even number of electrons in $$\mathrm{t_{2 g}}$$ orbitals is -

$$\left[\mathrm{Fe}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+},\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+},\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{3+},\left[\mathrm{Cu}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+},\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$$

For the given hypothetical reactions, the equilibrium constants are as follows :

$$\begin{aligned} & \mathrm{X} \rightleftharpoons \mathrm{Y} ; \mathrm{K}_1=1.0 \\ & \mathrm{Y} \rightleftharpoons \mathrm{Z} ; \mathrm{K}_2=2.0 \\ & \mathrm{Z} \rightleftharpoons \mathrm{W} ; \mathrm{K}_3=4.0 \end{aligned}$$

The equilibrium constant for the reaction $$\mathrm{X} \rightleftharpoons \mathrm{W}$$ is

An octahedral complex with the formula $$\mathrm{CoCl}_3 \cdot \mathrm{nNH}_3$$ upon reaction with excess of $$\mathrm{AgNO}_3$$ solution gives 2 moles of $$\mathrm{AgCl}$$. Consider the oxidation state of $$\mathrm{Co}$$ in the complex is '$$x$$'. The value of "$$x+n$$" is __________.

In the given compound, the number of 2$$^\circ$$ carbon atom/s is ________.

Identify the major products A and B respectively in the following set of reactions.

Identify the product (P) in the following reaction:

Given below are two statements :

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

Given below are two statements:

Statement I: $$\mathrm{N}\left(\mathrm{CH}_3\right)_3$$ and $$\mathrm{P}\left(\mathrm{CH}_3\right)_3$$ can act as ligands to form transition metal complexes.

Statement II: As N and P are from same group, the nature of bonding of $$\mathrm{N}\left(\mathrm{CH}_3\right)_3$$ and $$\mathrm{P}\left(\mathrm{CH}_3\right)_3$$ is always same with transition metals.

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

The incorrect statement regarding the given structure is

Match List I with List II

Choose the correct answer from the options given below:

If $$279 \mathrm{~g}$$ of aniline is reacted with one equivalent of benzenediazonium chloride, the maximum amount of aniline yellow formed will be ________ g. (nearest integer)

(consider complete conversion).

Consider the following reaction

$$\mathrm{A}+\mathrm{B} \rightarrow \mathrm{C}$$

The time taken for A to become $$1 / 4^{\text {th }}$$ of its initial concentration is twice the time taken to become $$1 / 2$$ of the same. Also, when the change of concentration of B is plotted against time, the resulting graph gives a straight line with a negative slope and a positive intercept on the concentration axis.

The overall order of the reaction is ________.

Major product B of the following reaction has ________ $$\pi$$-bond.

A hypothetical electromagnetic wave is show below.

The frequency of the wave is $$\mathrm{x} \times 10^{19} \mathrm{~Hz}$$.

$$\mathrm{x}=$$ _________ (nearest integer)

Consider the figure provided.

$$1 \mathrm{~mol}$$ of an ideal gas is kept in a cylinder, fitted with a piston, at the position A, at $$18^{\circ} \mathrm{C}$$. If the piston is moved to position $$\mathrm{B}$$, keeping the temperature unchanged, then '$$\mathrm{x}$$' $$\mathrm{L}$$ atm work is done in this reversible process.

$$\mathrm{x}=$$ ________ $$\mathrm{L}$$ atm. (nearest integer)

[Given : Absolute temperature $$={ }^{\circ} \mathrm{C}+273.15, \mathrm{R}=0.08206 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}{ }^{-1} \mathrm{~K}^{-1}$$]

A solution containing $$10 \mathrm{~g}$$ of an electrolyte $$\mathrm{AB}_2$$ in $$100 \mathrm{~g}$$ of water boils at $$100.52^{\circ} \mathrm{C}$$. The degree of ionization of the electrolyte $$(\alpha)$$ is _________ $$\times 10^{-1}$$. (nearest integer)

[Given : Molar mass of $$\mathrm{AB}_2=200 \mathrm{~g} \mathrm{~mol}^{-1}, \mathrm{~K}_{\mathrm{b}}$$ (molal boiling point elevation const. of water) $$=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$$, boiling point of water $$=100^{\circ} \mathrm{C} ; \mathrm{AB}_2$$ ionises as $$\mathrm{AB}_2 \rightarrow \mathrm{A}^{2+}+2 \mathrm{~B}^{-}]$$

Number of molecules from the following which are exceptions to octet rule is _________.

$$\mathrm{CO}_2, \mathrm{NO}_2, \mathrm{H}_2 \mathrm{SO}_4, \mathrm{BF}_3, \mathrm{CH}_4, \mathrm{SiF}_4, \mathrm{ClO}_2, \mathrm{PCl}_5, \mathrm{BeF}_2, \mathrm{C}_2 \mathrm{H}_6, \mathrm{CHCl}_3, \mathrm{CBr}_4$$

The number of optical isomers in following compound is : __________.

The 'spin only' magnetic moment value of $$\mathrm{MO}_4{ }^{2-}$$ is ________ BM. (Where M is a metal having least metallic radii. among $$\mathrm{Sc}, \mathrm{Ti}, \mathrm{V}, \mathrm{Cr}, \mathrm{Mn}$$ and $$\mathrm{Zn}$$ ).

(Given atomic number: $$\mathrm{Sc}=21, \mathrm{Ti}=22, \mathrm{~V}=23, \mathrm{Cr}=24, \mathrm{Mn}=25$$ and $$\mathrm{Zn}=30$$)

Number of amine compounds from the following giving solids which are soluble in $$\mathrm{NaOH}$$ upon reaction with Hinsberg's reagent is _________.

Let $$A=\left[\begin{array}{lll}2 & a & 0 \\ 1 & 3 & 1 \\ 0 & 5 & b\end{array}\right]$$. If $$A^3=4 A^2-A-21 I$$, where $$I$$ is the identity matrix of order $$3 \times 3$$, then $$2 a+3 b$$ is equal to

The value of $$k \in \mathbb{N}$$ for which the integral $$I_n=\int_0^1\left(1-x^k\right)^n d x, n \in \mathbb{N}$$, satisfies $$147 I_{20}=148 I_{21}$$ is

Let $$f(x)=4 \cos ^3 x+3 \sqrt{3} \cos ^2 x-10$$. The number of points of local maxima of $$f$$ in interval $$(0,2 \pi)$$ is

The set of all $$\alpha$$, for which the vectors $$\vec{a}=\alpha t \hat{i}+6 \hat{j}-3 \hat{k}$$ and $$\vec{b}=t \hat{i}-2 \hat{j}-2 \alpha t \hat{k}$$ are inclined at an obtuse angle for all $$t \in \mathbb{R}$$, is

Let the circles $$C_1:(x-\alpha)^2+(y-\beta)^2=r_1^2$$ and $$C_2:(x-8)^2+\left(y-\frac{15}{2}\right)^2=r_2^2$$ touch each other externally at the point $$(6,6)$$. If the point $$(6,6)$$ divides the line segment joining the centres of the circles $$C_1$$ and $$C_2$$ internally in the ratio $$2: 1$$, then $$(\alpha+\beta)+4\left(r_1^2+r_2^2\right)$$ equals

Let $$f(x)$$ be a positive function such that the area bounded by $$y=f(x), y=0$$ from $$x=0$$ to $$x=a>0$$ is $$e^{-a}+4 a^2+a-1$$. Then the differential equation, whose general solution is $$y=c_1 f(x)+c_2$$, where $$c_1$$ and $$c_2$$ are arbitrary constants, is

Let $$H: \frac{-x^2}{a^2}+\frac{y^2}{b^2}=1$$ be the hyperbola, whose eccentricity is $$\sqrt{3}$$ and the length of the latus rectum is $$4 \sqrt{3}$$. Suppose the point $$(\alpha, 6), \alpha>0$$ lies on $$H$$. If $$\beta$$ is the product of the focal distances of the point $$(\alpha, 6)$$, then $$\alpha^2+\beta$$ is equal to

The number of critical points of the function $$f(x)=(x-2)^{2 / 3}(2 x+1)$$ is

Let $$y=y(x)$$ be the solution of the differential equation $$(1+y^2) e^{\tan x} d x+\cos ^2 x(1+e^{2 \tan x}) d y=0, y(0)=1$$. Then $$y\left(\frac{\pi}{4}\right)$$ is equal to

Let the sum of two positive integers be 24 . If the probability, that their product is not less than $$\frac{3}{4}$$ times their greatest possible product, is $$\frac{m}{n}$$, where $$\operatorname{gcd}(m, n)=1$$, then $$n$$-$$m$$ equals

For the function $$f(x)=(\cos x)-x+1, x \in \mathbb{R}$$, between the following two statements

(S1) $$f(x)=0$$ for only one value of $$x$$ in $$[0, \pi]$$.

(S2) $$f(x)$$ is decreasing in $$\left[0, \frac{\pi}{2}\right]$$ and increasing in $$\left[\frac{\pi}{2}, \pi\right]$$.

Let $$P(x, y, z)$$ be a point in the first octant, whose projection in the $$x y$$-plane is the point $$Q$$. Let $$O P=\gamma$$; the angle between $$O Q$$ and the positive $$x$$-axis be $$\theta$$; and the angle between $$O P$$ and the positive $$z$$-axis be $$\phi$$, where $$O$$ is the origin. Then the distance of $$P$$ from the $$x$$-axis is

Let $$z$$ be a complex number such that $$|z+2|=1$$ and $$\operatorname{lm}\left(\frac{z+1}{z+2}\right)=\frac{1}{5}$$. Then the value of $$|\operatorname{Re}(\overline{z+2})|$$ is

The sum of all the solutions of the equation $$(8)^{2 x}-16 \cdot(8)^x+48=0$$ is :

The equations of two sides $$\mathrm{AB}$$ and $$\mathrm{AC}$$ of a triangle $$\mathrm{ABC}$$ are $$4 x+y=14$$ and $$3 x-2 y=5$$, respectively. The point $$\left(2,-\frac{4}{3}\right)$$ divides the third side $$\mathrm{BC}$$ internally in the ratio $$2: 1$$, the equation of the side $$\mathrm{BC}$$ is

If $$\sin x=-\frac{3}{5}$$, where $$\pi< x <\frac{3 \pi}{2}$$, then $$80\left(\tan ^2 x-\cos x\right)$$ is equal to

Let $$[t]$$ be the greatest integer less than or equal to $$t$$. Let $$A$$ be the set of all prime factors of 2310 and $$f: A \rightarrow \mathbb{Z}$$ be the function $$f(x)=\left[\log _2\left(x^2+\left[\frac{x^3}{5}\right]\right)\right]$$. The number of one-to-one functions from $$A$$ to the range of $$f$$ is

If the set $$R=\{(a, b): a+5 b=42, a, b \in \mathbb{N}\}$$ has $$m$$ elements and $$\sum_\limits{n=1}^m\left(1-i^{n !}\right)=x+i y$$, where $$i=\sqrt{-1}$$, then the value of $$m+x+y$$ is

If the shortest distance between the lines

$$\begin{array}{ll} L_1: \vec{r}=(2+\lambda) \hat{i}+(1-3 \lambda) \hat{j}+(3+4 \lambda) \hat{k}, & \lambda \in \mathbb{R} \\ L_2: \vec{r}=2(1+\mu) \hat{i}+3(1+\mu) \hat{j}+(5+\mu) \hat{k}, & \mu \in \mathbb{R} \end{array}$$

is $$\frac{m}{\sqrt{n}}$$, where $$\operatorname{gcd}(m, n)=1$$, then the value of $$m+n$$ equals

Let $$I(x)=\int \frac{6}{\sin ^2 x(1-\cot x)^2} d x$$. If $$I(0)=3$$, then $$I\left(\frac{\pi}{12}\right)$$ is equal to

If the orthocentre of the triangle formed by the lines $$2 x+3 y-1=0, x+2 y-1=0$$ and $$a x+b y-1=0$$, is the centroid of another triangle, whose circumcentre and orthocentre respectively are $$(3,4)$$ and $$(-6,-8)$$, then the value of $$|a-b|$$ is _________.

If the range of $$f(\theta)=\frac{\sin ^4 \theta+3 \cos ^2 \theta}{\sin ^4 \theta+\cos ^2 \theta}, \theta \in \mathbb{R}$$ is $$[\alpha, \beta]$$, then the sum of the infinite G.P., whose first term is 64 and the common ratio is $$\frac{\alpha}{\beta}$$, is equal to __________.

Let $$\vec{a}=9 \hat{i}-13 \hat{j}+25 \hat{k}, \vec{b}=3 \hat{i}+7 \hat{j}-13 \hat{k}$$ and $$\vec{c}=17 \hat{i}-2 \hat{j}+\hat{k}$$ be three given vectors. If $$\vec{r}$$ is a vector such that $$\vec{r} \times \vec{a}=(\vec{b}+\vec{c}) \times \vec{a}$$ and $$\vec{r} \cdot(\vec{b}-\vec{c})=0$$, then $$\frac{|593 \vec{r}+67 \vec{a}|^2}{(593)^2}$$ is equal to __________.

Let the positive integers be written in the form :

If the $$k^{\text {th }}$$ row contains exactly $$k$$ numbers for every natural number $$k$$, then the row in which the number 5310 will be, is __________.

The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which are not divisible by 3 , is equal to ________.

Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables $$X$$ and $$Y$$ respectively denote the number of blue and yellow balls. If $$\bar{X}$$ and $$\bar{Y}$$ are the means of $$X$$ and $$Y$$ respectively, then $$7 \bar{X}+4 \bar{Y}$$ is equal to ___________.

Let $$\alpha=\sum_\limits{r=0}^n\left(4 r^2+2 r+1\right){ }^n C_r$$ and $$\beta=\left(\sum_\limits{r=0}^n \frac{{ }^n C_r}{r+1}\right)+\frac{1}{n+1}$$. If $$140<\frac{2 \alpha}{\beta}<281$$, then the value of $$n$$ is _________.

Let $$A=\left[\begin{array}{cc}2 & -1 \\ 1 & 1\end{array}\right]$$. If the sum of the diagonal elements of $$A^{13}$$ is $$3^n$$, then $$n$$ is equal to ________.

Let the area of the region enclosed by the curve $$y=\min \{\sin x, \cos x\}$$ and the $$x$$ axis between $$x=-\pi$$ to $$x=\pi$$ be $$A$$. Then $$A^2$$ is equal to __________.

The value of $$\lim _\limits{x \rightarrow 0} 2\left(\frac{1-\cos x \sqrt{\cos 2 x} \sqrt[3]{\cos 3 x} \ldots \ldots . \sqrt[10]{\cos 10 x}}{x^2}\right)$$ is __________.

A stationary particle breaks into two parts of masses $$m_A$$ and $$m_B$$ which move with velocities $$v_A$$ and $$v_B$$ respectively. The ratio of their kinetic energies $$\left(K_B: K_A\right)$$ is :

Two charged conducting spheres of radii $$a$$ and $$b$$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

Two planets $$A$$ and $$B$$ having masses $$m_1$$ and $$m_2$$ move around the sun in circular orbits of $$r_1$$ and $$r_2$$ radii respectively. If angular momentum of $$A$$ is $$L$$ and that of $$B$$ is $$3 \mathrm{~L}$$, the ratio of time period $$\left(\frac{T_A}{T_B}\right)$$ is:

Average force exerted on a non-reflecting surface at normal incidence is $$2.4 \times 10^{-4} \mathrm{~N}$$. If $$360 \mathrm{~W} / \mathrm{cm}^2$$ is the light energy flux during span of 1 hour 30 minutes, Then the area of the surface is:

In an expression $$a \times 10^b$$ :

A clock has $$75 \mathrm{~cm}, 60 \mathrm{~cm}$$ long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will travel $$x$$ distance more than the tip of minute hand. The value of $$x$$ in meter is nearly (Take $$\pi=3.14$$) :

The output $$\mathrm{Y}$$ of following circuit for given inputs is :

A player caught a cricket ball of mass $$150 \mathrm{~g}$$ moving at a speed of $$20 \mathrm{~m} / \mathrm{s}$$. If the catching process is completed in $$0.1 \mathrm{~s}$$, the magnitude of force exerted by the ball on the hand of the player is:

Three bodies A, B and C have equal kinetic energies and their masses are $$400 \mathrm{~g}, 1.2 \mathrm{~kg}$$ and $$1.6 \mathrm{~kg}$$ respectively. The ratio of their linear momenta is :

Young's modulus is determined by the equation given by $$\mathrm{Y}=49000 \frac{\mathrm{m}}{\mathrm{l}} \frac{\mathrm{dyne}}{\mathrm{cm}^2}$$ where $$M$$ is the mass and $$l$$ is the extension of wire used in the experiment. Now error in Young modules $$(Y)$$ is estimated by taking data from $$M-l$$ plot in graph paper. The smallest scale divisions are $$5 \mathrm{~g}$$ and $$0.02 \mathrm{~cm}$$ along load axis and extension axis respectively. If the value of $M$ and $l$ are $$500 \mathrm{~g}$$ and $$2 \mathrm{~cm}$$ respectively then percentage error of $$Y$$ is :

Paramagnetic substances:

A. align themselves along the directions of external magnetic field.

B. attract strongly towards external magnetic field.

C. has susceptibility little more than zero.

D. move from a region of strong magnetic field to weak magnetic field.

Choose the most appropriate answer from the options given below:

A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature $$(27^{\circ} \mathrm{C})$$. The ratio of specific heat of gases at constant volume respectively is:

A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:

The diameter of a sphere is measured using a vernier caliper whose 9 divisions of main scale are equal to 10 divisions of vernier scale. The shortest division on the main scale is equal to $$1 \mathrm{~mm}$$. The main scale reading is $$2 \mathrm{~cm}$$ and second division of vernier scale coincides with a division on main scale. If mass of the sphere is 8.635 $$\mathrm{g}$$, the density of the sphere is:

Critical angle of incidence for a pair of optical media is $$45^{\circ}$$. The refractive indices of first and second media are in the ratio:

A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is:

(Assume h = 6.63 $$\times 10^{-34} \mathrm{~J} \mathrm{~s}, \mathrm{~m}_{\mathrm{e}}=9.0 \times 10^{-31} \mathrm{~kg}$$ and $$\mathrm{m}_{\mathrm{p}}=1836$$ times $$\mathrm{m}_{\mathrm{e}}$$ )

Correct Bernoulli's equation is (symbols have their usual meaning) :

Binding energy of a certain nucleus is $$18 \times 10^8 \mathrm{~J}$$. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:

In the given circuit, the terminal potential difference of the cell is :

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio $$\frac{V_a}{V_d}$$ and the ratio $$\frac{V_b}{V_c}$$ is:

A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is $$\left(\frac{a-1}{a}\right)$$ then the value of $$a$$ is _________.

An electric field, $$\overrightarrow{\mathrm{E}}=\frac{2 \hat{i}+6 \hat{j}+8 \hat{k}}{\sqrt{6}}$$ passes through the surface of $$4 \mathrm{~m}^2$$ area having unit vector $$\hat{n}=\left(\frac{2 \hat{i}+\hat{j}+\hat{k}}{\sqrt{6}}\right)$$. The electric flux for that surface is _________ $$\mathrm{Vm}$$.

Three vectors $$\overrightarrow{\mathrm{OP}}, \overrightarrow{\mathrm{OQ}}$$ and $$\overrightarrow{\mathrm{OR}}$$ each of magnitude $$\mathrm{A}$$ are acting as shown in figure. The resultant of the three vectors is $$\mathrm{A} \sqrt{x}$$. The value of $$x$$ is _________.

A square loop PQRS having 10 turns, area $$3.6 \times 10^{-3} \mathrm{~m}^2$$ and resistance $$100 \Omega$$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude $$\mathrm{B}=0.5 \mathrm{~T}$$ as shown. Work done in pulling the loop out of the field in $$1.0 \mathrm{~s}$$ is _________ $$\times 10^{-6} \mathrm{~J}$$.

A liquid column of height $$0.04 \mathrm{~cm}$$ balances excess pressure of a soap bubble of certain radius. If density of liquid is $$8 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}$$ and surface tension of soap solution is $$0.28 \mathrm{~Nm}^{-1}$$, then diameter of the soap bubble is __________ $$\mathrm{cm}$$. (if $$\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}$$ )

A uniform thin metal plate of mass $$10 \mathrm{~kg}$$ with dimensions is shown. The ratio of $$\mathrm{x}$$ and y coordinates of center of mass of plate in $$\frac{n}{9}$$. The value of $$n$$ is ________.

Resistance of a wire at $$0^{\circ} \mathrm{C}, 100^{\circ} \mathrm{C}$$ and $$t^{\circ} \mathrm{C}$$ is found to be $$10 \Omega, 10.2 \Omega$$ and $$10.95 \Omega$$ respectively. The temperature $$t$$ in Kelvin scale is _________.

A parallel beam of monochromatic light of wavelength $$600 \mathrm{~nm}$$ passes through single slit of $$0.4 \mathrm{~mm}$$ width. Angular divergence corresponding to second order minima would be _________ $$\times 10^{-3} \mathrm{~rad}$$.

An electron with kinetic energy $$5 \mathrm{~eV}$$ enters a region of uniform magnetic field of 3 $$\mu \mathrm{T}$$ perpendicular to its direction. An electric field $$\mathrm{E}$$ is applied perpendicular to the direction of velocity and magnetic field. The value of E, so that electron moves along the same path, is __________ $$\mathrm{NC}^{-1}$$.

(Given, mass of electron $$=9 \times 10^{-31} \mathrm{~kg}$$, electric charge $$=1.6 \times 10^{-19} \mathrm{C}$$)

In an alpha particle scattering experiment distance of closest approach for the $$\alpha$$ particle is $$4.5 \times 10^{-14} \mathrm{~m}$$. If target nucleus has atomic number 80 , then maximum velocity of $$\alpha$$-particle is __________ $$\times 10^5 \mathrm{~m} / \mathrm{s}$$ approximately.

($$\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \mathrm{SI}$$ unit, mass of $$\alpha$$ particle $$=6.72 \times 10^{-27} \mathrm{~kg}$$)