For the reaction $$\mathrm{N}_{2(\mathrm{~g})}+3 \mathrm{H}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{NH}_{3(\mathrm{~g})}$$, rate of disappearance of $$\mathrm{N}_{2(\mathrm{~g})}$$ is $$2.22 \times 10^{-3} \mathrm{~mol} \mathrm{~dm}^{-3}$$. What is the rate of appearance of $$\mathrm{NH}_{3(\mathrm{~g})}$$ ?

Identify the products obtained when chlorine reacts with hot and conc. $$\mathrm{NaOH}$$.

Which from following elements does NOT react with water?

Identify the type of hybridization involved in hexaaminecobalt (III) complex ion.

Calculate the solubility of a gas in water at $$0.8 \mathrm{~atm}$$ and $$25^{\circ} \mathrm{C}$$.

[Henry's law constant is $$6.85 \times 10^{-4} \mathrm{~mol} \mathrm{~dm}^{-3} \mathrm{~atm}^{-1}$$ ]

What is the value of temperature in degree Celsius at absolute zero ?

Which among the following reactions does NOT correctly match with its reagent?

Which among the following compounds is NOT prepared by Sandmeyer's reaction ?

Which among the following compounds undergoes SN$$^2$$ reaction fastly ?

Which of the following molecules possesses highest dipole-dipole interactions ?

What is the total volume occupied by atoms in bcc unit cell ?

Which among the following metals is involved in preparation of Grignard reagent ?

Which among the following properties of lanthanoids is NOT true?

Which of the following is a Lewis acid but NOT a Bronsted acid?

Which of the following aqueous solutions of salts will have highest $$\mathrm{pH}$$ value?

Which among the following compounds represents a soap molecule?

How long will it take to produce $$5.4 \mathrm{~g}$$ of $$\mathrm{Ag}$$ from molten $$\mathrm{AgCl}$$ by passing $$5 \mathrm{~amp}$$ current?

(Molar mass Ag = $$108 \mathrm{~g} \mathrm{~mol}^{-1}$$ )

Which of the following is NOT an example of secondary voltaic cell?

What is the number of unpaired electrons in $$\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}$$ complex?

Which among the following methods is used to prepare Grignard reagent?

Calculate the density of metal having volume of unit cell $$64 \times 10^{-24} \mathrm{~cm}^3$$ and molar mass of metal $$192 \mathrm{~g} \mathrm{~mol}^{-1}$$ containing 4 particles in unit cell.

Calculate the work done when 2 moles of an ideal gas expand from a volume of $$5 \mathrm{~dm}^3$$ to $$7 \times 10^{-3} \mathrm{~m}^3$$ against a constant external pressure of $$2.02 \times 10^5 \mathrm{~Nm}^{-2}$$ ?

Which among the following pair of monomers does not generate polyamide polymer?

What type of following phenomena is NOT exhibited by adsorption?

Find the rate constant of first order reaction in second having half life of 2.5 hours.

Which nitrogen atom of pyrimidine base numbered from 1 to 6 is bonded with furanose sugar ?

Identify the element with smallest ionic radius in +3 oxidation state from following.

Identify the product in the following reaction.

Which among following compounds possesses highest number of N atoms in it ?

What is the bond order of CO molecule?

Which of the following is NOT hydrogen like species?

What is the intermediate compound formed when chlorobenzene is treated with fused $$\mathrm{NaOH}$$ under pressure?

If rate of reaction is given as

$$\frac{1}{3} \frac{\mathrm{d}[\mathrm{x}]}{\mathrm{dt}}=-\frac{1}{2} \frac{\mathrm{d}[\mathrm{y}]}{\mathrm{dt}}=-\frac{\mathrm{d}[\mathrm{Z}]}{\mathrm{dt}}$$,

the reaction can be represented as

Which among the following compounds contains highest number of chlorine atoms in their single molecule ?

What is the heat of formation of $$\mathrm{HCl}_{(\mathrm{g})}$$ from following equation?

$$\mathrm{H}_{2(\mathrm{~g})}+\mathrm{Cl}_{2(\mathrm{g})} \rightarrow 2 \mathrm{HCl}_{(\mathrm{g})} \Delta_{\mathrm{f}} \mathrm{H}=-194 \mathrm{~kJ}$$

Identify the concentration of the solution from following so that values of ,$$\Delta \mathrm{T}_{\mathrm{f}}$$ and $$\mathrm{K}_{\mathrm{f}}$$ are same.

What is the product formed when cumene is air oxidised in presence of Co-naphthenate and further treated with dilute acid?

Identify the use of polystyrene for household purposes.

Identify compound $$\mathrm{A}$$ in following reaction

Benzene + Ozone (excess) $$\rightarrow$$ Benzenetriozonide $$\xrightarrow{\mathrm{A}}$$ Glyoxal

Which from following pairs of compounds is an example of metamerism?

If $$\mathrm{Q}$$ is the heat liberated from the system and $$\mathrm{W}$$ is the work done on the system then first law of thermodynamics can be written as,

Calculate the number of atoms in 5 gram metal that crystallises to form simple cubic unit cell structure having edge length $$336 \mathrm{~pm}$$. (Density of metal $$=9.4 \mathrm{~g} \mathrm{~cm}^{-3}$$ )

Identify the molecule in which central atom undergoes $$\mathrm{sp}^3$$ hybridisation?

Which one of the following conversions does NOT involve either oxidation or reduction?

Calculate $$\wedge_0$$ of $$\mathrm{CH}_2 \mathrm{ClCOOH}$$ if $$\wedge_0$$ for $$\mathrm{HCl}, \mathrm{KCl}$$ and $$\mathrm{CH}_2 \mathrm{ClCOOK}$$ are $$4.2,1.5$$ and $$1.1 \Omega^{-1} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$$ respectively?

Identify the product A in the following reaction.

Calculate the amount of solute dissolved in 160 gram solvent that boils at $$85^{\circ} \mathrm{C}$$, the molar mass of solute is $$120 \mathrm{~g} \mathrm{~mol}^{-1}$$. $$\left(\mathrm{K}_{\mathrm{b}}\right.$$ for solvent $$=2.7^{\circ} \mathrm{C} \mathrm{~kg} \mathrm{~mol}^{-1}$$ and boiling point of solvent $$=76^{\circ} \mathrm{C}$$)

Identify ether from the following compounds.

Which from following polymers is used to obtain bristles for brushes?

What is the $$\mathrm{pH}$$ of $$2 \times 10^{-3} \mathrm{M}$$ solution of monoacidic weak base if it ionises to the extent of $$5\%$$ ?

$$\int_\limits{\frac{\pi}{4}}^{\frac{3 \pi}{4}} \frac{\mathrm{d} x}{1+\cos x}$$ is equal to

If $$\tan ^{-1}\left(\frac{1-x}{1+x}\right)=\frac{1}{2} \tan ^{-1} x$$, then $$x$$ has the value

If $$p: \forall n \in I N, n^2+n$$ is an even number $$q: \forall n \in I N, n^2-n$$ is an odd numer, then the truth values of $$p \wedge q, p \vee q$$ and $$p \rightarrow q$$ are respectively

If the function $$f(x)=x^3-3(a-2) x^2+3 a x+7$$, for some $$a \in I R$$ is increasing in $$(0,1]$$ and decreasing in $$[1,5)$$, then a root of the equation $$\frac{f(x)-14}{(x-1)^2}=0(x \neq 1)$$ is

If $$\bar{a}=\hat{\boldsymbol{i}}-\hat{\boldsymbol{k}}, \bar{b}=x \hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+(1-x) \hat{\boldsymbol{k}}$$ and $$\bar{c}=y \hat{\boldsymbol{i}}+x \hat{\boldsymbol{j}}+(1+x-y) \hat{\boldsymbol{k}}$$, then $$[\bar{a} \bar{b} \bar{c}]$$ depends on

If $$\cot (A+B)=0$$, then $$\sin (A+2 B)$$ is equal to

The joint equation of pair of lines through the origin and making an equilateral triangle with the line $$y = 5$$ is

If $$f(x)=\sqrt{\tan x}$$ and $$g(x)=\sin x \cdot \cos x$$ then $$\int \frac{f(x)}{g(x)} \mathrm{d} x$$ is equal to (where $$C$$ is a constant of integration)

The general solution of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{3 x+y}{x-y}$$ is (where $$C$$ is a constant of integration.)

If $$A=\left[\begin{array}{lll}1 & 2 & 1 \\ 3 & 1 & 3\end{array}\right]$$ and $$B=\left[\begin{array}{ll}2 & 3 \\ 1 & 2 \\ 1 & 2\end{array}\right]$$, then $$(A B)^{-1}=$$

The distance between parallel lines

$$\frac{x-1}{2}=\frac{y-2}{-2}=\frac{z-3}{1}$$ and

$$\frac{x}{2}=\frac{y}{-2}=\frac{z}{1}$$ is :

Maximum value of $$Z=5 x+2 y$$, subject to $$2 x-y \geq 2, x+2 y \leq 8$$ and $$x, y \geq 0$$ is

The value of $$\sin \left(2 \sin ^{-1} 0.8\right)$$ is equal to

A line makes the same angle '$$\alpha$$' with each of the $$x$$ and $$y$$ axes. If the angle '$$\theta$$', which it makes with the $$z$$-axis, is such that $$\sin ^2 \theta=2 \sin ^2 \alpha$$, then the angle $$\alpha$$ is

The negation of the statement pattern $$p \vee(q \rightarrow \sim r)$$ is

Let $$\bar{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$\bar{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ be two vectors. If $$\bar{c}$$ is a vector such that $$\bar{b} \times \bar{c}=\bar{b} \times \bar{a}$$ and $$\bar{c} \cdot \bar{a}=0$$, then $$\bar{c} \cdot \bar{b}$$ is equal to

The incidence of occupational disease in an industry is such that the workmen have a $$10 \%$$ chance of suffering from it. The probability that out of 5 workmen, 3 or more will contract the disease is

If $$y=\log \sqrt{\frac{1+\sin x}{1-\sin x}}$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ at $$x=\frac{\pi}{3}$$ is

The variance and mean of 15 observations are respectively 6 and 10 . If each observation is increased by 8 then the new variance and new mean of resulting observations are respectively

If $$y=\sin \left(2 \tan ^{-1} \sqrt{\frac{1+x}{1-x}}\right)$$ then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ is equal to

The magnitude of the projection of the vector $$2 \hat{\mathbf{i}}+ 3\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ on the vector perpendicular to the plane containing the vectors $$\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$$ is

$$\matrix{ {f(x) = a{x^2} + bx + 1,} & {if} & {\left| {2x - 3} \right| \ge 2} \cr { = 3x + 2,} & {if} & {{1 \over 2} < x < {5 \over 2}} \cr } $$

is continuous on its domain, then $$a+b$$ has the value

If $$\bar{a}=\hat{\boldsymbol{i}}+\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}, \bar{b}=\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}+\hat{\boldsymbol{k}}$$ and $$\bar{c}=\hat{\boldsymbol{i}}-\hat{\boldsymbol{j}}-\hat{\boldsymbol{k}}$$ are three vectors then vector $$\bar{r}$$ in the plane of $$\bar{a}$$ and $$\bar{b}$$, whose projection on $$\bar{c}$$ is $$\frac{1}{\sqrt{3}}$$, is given by

A tetrahedron has verticles $$P(1,2,1), Q(2,1,3), R(-1,1,2)$$ and $$O(0,0,0)$$. Then the angle between the faces $$O P Q$$ and $$P Q R$$ is

The principal value of $$\sin ^{-1}\left(\sin \left(\frac{2 \pi}{3}\right)\right)$$ is

The differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{\sqrt{1-y^2}}{y}$$ determines a family of circles with

The value of the integral $$\int_\limits0^1 \sqrt{\frac{1-x}{1+x}} \mathrm{~d} x$$ is

If a question paper consists of 11 questions divided into two sections I and II. Section I consists of 6 questions and section II consists of 5 questions, then the number of different ways can student select 6 questions, taking at least 2 questions from each section, is

The area (in sq. units) of the region described by $$A=\left\{(x, y) / x^2+y^2 \leq 1\right.$$ and $$\left.y^2 \leq 1-x\right\}$$ is

A firm is manufacturing 2000 items. It is estimated that the rate of change of production $$P$$ with respect to additional number of workers $$x$$ is given by $$\frac{\mathrm{d} P}{\mathrm{~d} x}=100-12 \sqrt{x}$$. If the firm employs 25 more workers, then the new level of production of items is

$$\int \frac{3 x-2}{(x+1)(x-2)^2} \mathrm{~d} x=$$

(where $$C$$ is a constant of integration)

If the normal to the curve $$y=f(x)$$ at the point $$(3,4)$$ makes an angle $$\left(\frac{3 \pi}{4}\right)^c$$ with positive $$X$$-axis, then $$f^{\prime}(3)$$ is equal to

If $$P(A \cup B)=0.7, P(A \cap B)=0.2$$, then $$P\left(A^{\prime}\right)+P\left(B^{\prime}\right)$$ is

If $$\lim _\limits{x \rightarrow 1} \frac{x^2-a x+b}{(x-1)}=5$$, then $$(a+b)$$ is equal to

If $$y=\cos \left(\sin x^2\right)$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ at $$x=\sqrt{\frac{\pi}{2}}$$ is

Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Then mean of number of kings is

The polar co-ordinates of the point, whose Cartesian coordinates are $$(-2 \sqrt{3}, 2)$$, are

Let $$z$$ be a complex number such that $$|z|+z=3+i, i=\sqrt{-1}$$, then $$|z|$$ is equal to

Given $$A=\left[\begin{array}{ccc}x & 3 & 2 \\ 1 & y & 4 \\ 2 & 2 & z\end{array}\right]$$, if $$x y z=60$$ and $$8 x+4 y+3 z=20$$, then $$A$$.(adjA)

If $$y^{\frac{1}{m}}+y^{\frac{-1}{m}}=2 x, x \neq 1$$, then $$\left(x^2-1\right)\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)^2$$ is equal to

$$\int_\limits0^2[x] \mathrm{d} x+\int_\limits0^2|x-1| \mathrm{d} x=$$

(where $$[x]$$ denotes the greatest integer function.)

The equations of the lines passing through the point $$(3,2)$$ and making an acute angle of $$45^{\circ}$$ with the line $$x-2 y-3=0$$ are

If $$[x]$$ is greatest integer function and $$2[2 x-5]-1=7$$, then $$x$$ lies in

The Cartesian equation of a line passing through $$(1,2,3)$$ and parallel to $$x-y+2 z=5$$ and $$3 x+y+z=6$$ is

If the lines $$3 x-4 y-7=0$$ and $$2 x-3 y-5=0$$ pass through diameters of a circle of area $$49 \pi$$ square units, then the equation of the circle is

A spherical iron ball of $$10 \mathrm{~cm}$$ radius is coated with a layer of ice of uniform thickness that melts at the rate of $$50 \mathrm{~cm}^3 / \mathrm{min}$$. If the thickness of ice is $$5 \mathrm{~cm}$$, then the rate at which the thickness of ice decreases is

$$\int \frac{\sin \frac{5 x}{2}}{\sin \frac{x}{2}} d x=$$

(where $$C$$ is a constant of integration.)

The equation of the plane passing through the points $$(2,3,1),(4,-5,3)$$ and parallel to $$X$$-axis is

$$\text { If } \int e^{x^2} \cdot x^3 \mathrm{~d} x=e^{x^2} \cdot[f(x)+C]$$ (where $$C$$ is a constant of integration.) and $$f(1)=0$$, then value of $$f(2)$$ will be

The negation of the statement, "The payment will be made if and only if the work is finished in time" is

The magnetic susceptibility of the material of a rod is 349 and permeability of vacuum $$\mu_0$$ is $$4 \pi \times 10^{-7}$$ SI units. Absolute permeability of the material of the rod in SI units is

The magnetic flux through a coil of resistance '$$R$$' changes by an amount '$$\Delta \phi$$' in time '$$\Delta \mathrm{t}$$'. The total quantity of induced electric charge '$$\mathrm{Q}$$' is

A body weighs $$500 \mathrm{~N}$$ on the surface of the earth. At what distance below the surface of the earth it weighs $$250 \mathrm{~N}$$ ? (Radius of earth, $$\mathrm{R}=6400 \mathrm{~km}$$ )

Three discs $$\mathrm{x}, \mathrm{y}$$ and $$\mathrm{z}$$ having radii $$2 \mathrm{~m}, 3 \mathrm{~m}$$ and $$6 \mathrm{~m}$$ respectively are coated on outer surfaces. The wavelength corresponding to maximum intensity are $$300 \mathrm{~nm}, 400 \mathrm{~nm}$$ and $$500 \mathrm{~nm}$$ respectively. If $$\mathrm{P}_{\mathrm{x}}, \mathrm{P}_{\mathrm{y}}$$ and $$\mathrm{P}_{\mathrm{z}}$$ are power radiated by them respectively then

A stationary wave is represented by $$\mathrm{y}=10 \sin \left(\frac{\pi \mathrm{x}}{4}\right) \cos (20 \pi \mathrm{t})$$ where $$\mathrm{x}$$ and $$\mathrm{y}$$ are in $$\mathrm{cm}$$ and $$\mathrm{t}$$ in second. The distance between two consecutive nodes is

When the rms velocity of a gas is denoted by '$$v$$', which one of the following relations is true?

($$\mathrm{T}=$$ Absolute temperature of the gas.)

A parallel plate air capacitor has a uniform electric field 'E' in the space between the plates. Area of each plate is A and the distance between the plates is '$$\mathrm{d}$$'. The energy stored in the capacitor is $$\left[\varepsilon_0=\right.$$ permittivity of free space)

Two massless springs of spring constant $$\mathrm{K}_1$$ and $$\mathrm{K}_2$$ are connected one after the other forming a single chain, suspended vertically and certain mass is attached to the free end. If '$$e_1$$' and '$$e_2$$' are their respective extensions and '$$\mathrm{f}$$' is their stretching force, the total extension produced is

The time taken by a particle executing simple harmonic motion of period '$$\mathrm{T}$$', to move from the mean position to half the maximum displacement is

Using Bohr's model, the orbital period of electron in hydrogen atom in the $$\mathrm{n}^{\text {th }}$$ orbit is $$\left(\varepsilon_0=\right.$$ permittivity of vacuum, $$\mathrm{h}=$$ Planck's constant, $$\mathrm{m}=$$ mass of electron, $$\mathrm{e}=$$ electronic charge)

A parallel plate capacitor is charged and then disconnected from the charging battery. If the plates are now moved further apart by pulling them by means of insulating handles, then

If the kinetic energy of a free electron doubles, it's de Broglie wavelength ($$\lambda$$) changes by a factor

In the following network, the current through galvanometer will

In a medium, the phase difference between two particles separated by a distance '$$x$$' is $$\left(\frac{\pi}{5}\right)^{\text {c }}$$. If the frequency of the oscillation of particles is $$25 \mathrm{~Hz}$$ and the velocity of propagation of the waves is $$75 \mathrm{~m} / \mathrm{s}$$, then the value of $$x$$ is

The work done in blowing a soap bubble of radius $$\mathrm{R}$$ is '$$\mathrm{W}_1$$' at room temperature. Now the soap solution is heated. From the heated solution another soap bubble of radius $$2 \mathrm{R}$$ is blown and the work done is '$$\mathrm{W}_2$$'. Then

A capacitor of capacitance $$50 \mu \mathrm{F}$$ is connected to a.c. source $$\mathrm{e}=220 \sin 50 \mathrm{t}$$ ($$\mathrm{e}$$ in volt, $$\mathrm{t}$$ in second). The value of peak current is

Two waves are superimposed whose ratio of intensities is $$9: 1$$. The ratio of maximum and minimum intensity is

The masses and radii of the moon and the earth are $$\mathrm{M_1, R_1}$$ and $$\mathrm{M_2, R_2}$$ respectively. Their centres are at a distance $$\mathrm{d}$$ apart. What should be the minimum speed with which a body of mass '$$m$$' should be projected from a point midway between their centres, so as to escape to infinity?

A monoatomic gas $$\left(\gamma=\frac{5}{3}\right)$$ initially at $$27^{\circ} \mathrm{C}$$ having volume '$$\mathrm{V}$$' is suddenly compressed to one-eighth of its original volume $$\left(\frac{\mathrm{V}}{8}\right)$$. After the compression its temperature becomes

Two parallel conducting wires of equal length are placed distance 'd' apart, carry currents '$$\mathrm{I}_1$$' and '$$\mathrm{I}_2$$' respectively in opposite directions. The resultant magnetic field at the midpoint of the distance between both the wires is

Self inductance of a solenoid cannot be increased by

For a NAND gate, the inputs and outputs are given below.

The values taken by C, D, E, F are respectively

An electron and a proton having the same momenta enter perpendicularly into a magnetic field. What are their trajectories in the field?

The resistance offered by an inductor $$\left(X_L\right)$$ in an a.c. circuit is

The force between the plates of a parallel plate capacitor of capacitance '$$\mathrm{C}$$' and distance of separation of the plates '$$\mathrm{d}$$' with a potential difference '$$\mathrm{V}$$' between the plates is

Consider the following statements about stationary waves.

A. The distance between two adjacent nodes or antinodes is equal to $$\frac{\lambda}{2}(\lambda=$$ wavelength of the wave)

B. A node is always formed at the open end of the open organ pipe.

Choose the correct option from the following.

If the radius of the spherical gaussian surface is increased then the electric flux due to a point charge enclosed by the surface

The wave number of the last line of the Balmer series in hydrogen spectrum will be

(Rydberg's constant $$=10^7 \mathrm{~m}^{-1}$$ )

A bucket containing water is revolved in a vertical circle of radius $$r$$. To prevent the water from falling down, the minimum frequency of revolution required is

($$\mathrm{g}=$$ acceleration due to gravity)

Two monatomic ideal gases A and B of molecular masses '$$m_1$$' and '$$m_2$$' respectively are enclosed in separate containers kept at the same temperature. The ratio of the speed of sound in gas A to that in gas B is given by

A particle starts oscillating simple harmonically from its mean position with time period '$$T$$'. At time $$t=\frac{T}{12}$$, the ratio of the potential energy to kinetic energy of the particle is $$\left(\sin 30^{\circ}=\cos 60^{\circ}=0.5, \cos 30^{\circ}=\sin 60^{\circ}=\sqrt{3} / 2\right)$$

A hollow pipe of length $$0.8 \mathrm{~m}$$ is closed at one end. At its open end, a $$0.5 \mathrm{~m}$$ long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of pipe. If the tension in the string is $$50 \mathrm{~N}$$ and speed of sound in air is $$320 \mathrm{~m} / \mathrm{s}$$, the mass of the string is

A graph of magnetic flux $$(\phi)$$ versus current (I) is drawn for four inductors A, B, C, D. Larger value of self inductance is for inductor.

A parallel beam of monochromatic light falls normally on a single narrow slit. The angular width of the central maximum in the resulting diffraction pattern

A body moving in a circular path with a constant speed has constant

A steel coin of thickness '$$\mathrm{d}$$' and density '$$\rho$$' is floating on water of surface tension '$$T$$'. The radius of the coin $$(R)$$ is [$$\mathrm{g}=$$ acceleration due to gravity]

A door $$1.2 \mathrm{~m}$$ wide requires a force of $$1 \mathrm{~N}$$ to be applied perpendicular at the free end to open or close it. The perpendicular force required at a point $$0.2 \mathrm{~m}$$ distant from the hinges for opening or closing the door is

The thermodynamic process in which no work is done on or by the gas is

The given circuit has two ideal diodes $$D_1$$ and $$D_2$$ connected as shown in the figure. The current flowing through the resistance $$R_1$$ will be

In a Fraunhofer diffraction at a single slit of width 'd' and incident light of wavelength $$5500 \mathop A\limits^o$$, the first minimum is observed at an angle $$30^{\circ}$$. The first secondary maxima is observed at an angle $$\theta$$, equal to

A galvanometer of resistance $$200 \Omega$$ is to be converted into an ammeter. The value of shunt resistance which allows $$3 \%$$ of the mains current through the galvanometer is equal to (nearly)

The speed of light in two media $$M_1$$ and $$M_2$$ are $$1.5 \times 10^8$$ $$\mathrm{m} / \mathrm{s}$$ and $$2 \times 10^8 \mathrm{~m} / \mathrm{s}$$ respectively. If the light undergoes total internal reflection, the critical angle between the two media is

The minimum distance between an object and its real image formed by a convex lens of focal length 'f' is

Heat given to a body, which raises its temperature by 1ºC is known as

A shell is fired at an angle of $$30^{\circ}$$ to the horizontal with velocity $$196 \mathrm{~m} / \mathrm{s}$$. The time of flight is

$$\left[\sin 30^{\circ}=\frac{1}{2}=\cos 60^{\circ}\right]$$

Three equal charges '$$\mathrm{q}_1$$', '$$^{\prime} \mathrm{q}_2$$' and '$$\mathrm{q}_3$$' are placed on the three corners of a square of side 'a'. If the force between $$\mathrm{q}_1$$ and $$\mathrm{q}_2$$ is '$$\mathrm{F}_{12}$$' and that between $$\mathrm{q}_1$$ and $$\mathrm{q}_3$$ is '$$\mathrm{F}_{13}$$', then the ratio of magnitudes $$\left(\frac{F_{12}}{F_{13}}\right)$$ is

A coil having an inductance of $$\frac{1}{\pi} \mathrm{H}$$ is connected in series with a resistance of $$300 \Omega$$. If A.C. Source $$(20 \mathrm{~V}-200 \mathrm{~Hz})$$ is connected across the combination, the phase angle between voltage and current is

In a full wave rectifier circuit without filter, the output current is

The excess pressure inside a soap bubble of radius $$2 \mathrm{~cm}$$ is 50 dyne/cm$$^2$$. The surface tension is

Two bodies of masses '$$\mathrm{m}$$' and '$$3 \mathrm{~m}$$' are rotating in horizontal speed of the body of mass '$$m$$' is $$n$$ times that of the value of heavier body; while the centripetal force is same for both. The value of $$n$$ is