Copper is extracted from copper pyrites by

Function of potassium ethyl xanthate in froth floatation process is to make the ore

Sulphide ore on roasting gives a gas $$X$$. $$X$$ reacts with $$\mathrm{Cl}_2$$ in the presence of activated charcoal to give $$Y$$. $$Y$$ is

Aqueous solution of a salt $$(A)$$ forms a dense white precipitate with $$\mathrm{BaCl}_2$$ solution. The precipitate dissolves in dilute $$\mathrm{HCl}$$ to produce a gas $$(B)$$ which decolourises acidified $$\mathrm{KMnO}_4$$ solution. $$A$$ and $$B$$ respectively are

Bond angle is $$\mathrm{PH}_4^{+}$$ is more than that of $$\mathrm{PH}_3$$. This is because

Incorrectly matched pair is

Phosphorus pentachloride

Identify the set of paramagnetic ions among the following.

How many moles of acidified $$\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$$ is required to liberate 6 moles of $$\mathrm{I}_2$$ from an aqueous solution of $$\mathrm{I}^{-}$$?

For $$\mathrm{Cu}_2 \mathrm{Cl}_2$$ and $$\mathrm{CuCl}_2$$ in aqueous medium, which of the following statement is correct?

The coordination number of $$\mathrm{Fe}$$ and $$\mathrm{Co}$$ in the complex ions, $$\left.\mathrm{Fe}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-}$$ and $$\left[\mathrm{Co}(\mathrm{SCN})_4\right]^{2-}$$ are respectively

Number of stereoisomers exhibited by $$\left[\mathrm{Co}(\mathrm{en})_2 \mathrm{Cl}_2\right]^{+}$$ is

Give the IUPAC name of $$\left[\mathrm{Pt}\left(\mathrm{NH}_3\right)_4\right]\left[\mathrm{Pt} \mathrm{Cl}_4\right]$$ is

Prolonged exposure of chloroform in humans may cause damage to liver. It is due to the formation of the following compound.

Which of the following halide shows highest reactivity towards $$\mathrm{S}_{\mathrm{N}} 1$$ reaction?

In the reaction,

The number of possible isomers for the organic compound X is

Which of the following on heating gives an ether as major products?

(P) $$\mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}_2 \mathrm{Br}+\mathrm{CH}_3 \mathrm{ONa}$$

(Q) $$\mathrm{C}_6 \mathrm{H}_5 \mathrm{ONa}+\mathrm{CH}_3 \mathrm{Br}$$

(R) $$\left(\mathrm{CH}_3\right)_3 \mathrm{C}-\mathrm{Cl}+\mathrm{CH}_3 \mathrm{ONa}$$

(S) $$\mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}=\mathrm{CHCl}+\mathrm{CH}_3 \mathrm{ONa}$$

The steps involved in the conversion of propan -2-ol to propan -1-ol are in the order

Which of the following is the strongest base?

The product 'P' is

Which of the following has the lowest boiling point?

The carbonyl compound that does not undergo aldol condensation is

The final product for the reaction is

Hinsberg's reagent is

Which one of the following vitamins is not stored in adipose tissue?

Hypothyroidism is caused by the deficiency of

$$\mathrm{C}_1-\mathrm{C}_4$$ glycosidic bond is not found in

Which of the following polymer has strongest intermolecular forces of attraction?

Which of the following monomers can undergo condensation polymerisation?

A food additive that acts as an antioxidant is

Which of the following is not related to drug-enzyme interaction?

$$0.4 \mathrm{~g}$$ of dihydrogen is made to react with $$7.4 \mathrm{~g}$$ of dichlorine to form hydrogen chloride. The volume of hydrogen chloride formed at $$273 \mathrm{~K}$$ and $$1 \mathrm{~bar}$$ pressure is

With regard to photoelectric effect, identify the correct statement among the following.

The last element of the $$p$$-block in 6 th period is represented by the outer most electronic configuration.

The conjugate base of $$\mathrm{NH}_3$$ is

A gas mixture contains $$25 \% \mathrm{~He}$$ and $$75 \% \mathrm{~CH}_4$$ by volume at a given temperature and pressure. The percentage by mass of methane in the mixture is approximately _________.

The percentage of $$s$$-character in the hybrid orbitals of nitrogen in $$\mathrm{NO}_2^{+}, \mathrm{NO}_3^{-}$$ respectively are

The formal charge on central oxygen atom in ozone is

When the same quantity of heat is absorbed by a system at two different temperatures $$T_1$$ and $$T_2$$, such that $$T_1>T_2$$, change in entropies are $$\Delta S_1$$ and $$\Delta S_2$$ respectively. Then

The oxidation number of nitrogen atoms in $$\mathrm{NH}_4 \mathrm{NO}_3$$ are

A Lewis acid '$$X$$' reacts with $$\mathrm{LiAlH}_4$$ in ether medium to give a highly toxic gas. This gas when heated with $$\mathrm{NH}_3$$ gives a compound commonly known as inorganic benzene. The gas is

The oxide of potassium that does not exist is

The metal that produce $$\mathrm{H}_2$$ with both dil. $$\mathrm{HCl}$$ and $$\mathrm{NaOH}(a q)$$ is

Which of the following is not a pair of functional isomers?

Identify 'X' in the following reaction.

Which of the following is not a green house gas?

A metal exists as an oxide with formula $$M_{0.96}$$ O. Metal, $$M$$ can exist as $$M^{2+}$$ and $$M^{3+}$$ in its oxide $$M_{0.96} \mathrm{O}$$. The percentage of $$\mathrm{M}^{3+}$$ in the oxide is nearly

A metal crystallises in face centred cubic structure with metallic radius $$\sqrt{2} \mathop A\limits^o$$. The volume of the unit cell (in $$\mathrm{m}^3$$ ) is

Silicon doped with gallium forms

The pair of electrolytes that posses same value for the constant $$(A)$$ in the Debye-Huckel-Onsager equation, $$\Lambda_m=\Lambda_m^{\circ}-A \sqrt{C}$$ is

Which of the following pair of solutions is isotonic?

Solute '$$X$$' dimerises in water to the extent of $$80\%$$. 2.5g of '$$X$$' in $$100 \mathrm{~g}$$ of water increases the boiling point by $$0.3^{\circ} \mathrm{C}$$. The molar mass of 'X' is $$[K_b=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}]$$

Given $$E_{F{e^{3 + }}/F{e^{2 + }}}^o = + 0.76\,V$$ and $$E_{\mathrm{I}_2 / \mathrm{I}^{-}}^0=+0.55 \mathrm{~V}$$. The equilibrium constant for the reaction taking place in galvanic cell consisting of above two electrodes is $$\left[\frac{2303 R T}{F}=0.06\right]$$

If an aqueous solution of $$\mathrm{NaF}$$ is electrolysed between inert electrodes, the product obtained at anode is

In which of the following cases a chemical reaction is possible?

The time required for $$60 \%$$ completion of a first order reaction is $$50 \mathrm{~min}$$. The time required for $$93.6 \%$$ completion of the same reaction will be

For an elementary reaction $$2 A+3 B \rightarrow 4 C+D$$ the rate of appearance of $C$ at time '$$T$$' is $$2.8 \times 10^{-3} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~S}^{-1}$$. Rate of disappearance of $$B$$ at '$$t$$' $t$ will be

The rate constant of a reaction is given by $$k=P Z e^{-E_a / R T}$$ under standard notation. In order to speed up the reaction, which of the following factors has to be decreased?

A sol of $$\mathrm{AgI}$$ is prepared by mixing equal volumes of $$0.1 \mathrm{~M} \mathrm{~AgNO}_3$$ and $$0.2 \mathrm{~M} \mathrm{~KI}$$, which of the following statement is correct?

During adsorption of a gas on a solid at low temperature

If $$2^x+2^y=2^{x+y}$$, then $$\frac{d y}{d x}$$ is

If $$f(x)=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)$$, then $$f^{\prime}(\sqrt{3})$$ is

The right hand and left hand limit of the function are respectively.

$$f(x)=\left\{\begin{array}{cc} \frac{e^{1 / x}-1}{e^{1 / x}+1}, & \text { if } x \neq 0 \\ 0, & \text { if } x=0 \end{array}\right.$$

If $$y=2 x^{n+1}+\frac{3}{x^n}$$, then $$x^2 \frac{d^{2 y}}{d x^2}$$ is

If the curves $$2 x=y^2$$ and $$2 x y=K$$ intersect perpendicularly, then the value of $$K^2$$ is

If $$(x e)^y=e^y$$, then $$\frac{d y}{d x}$$ is

If the side of a cube is increased by $$5 \%$$, then the surface area of a cube is increased by

The value of $$\int \frac{1+x^4}{1+x^6} d x$$ is

The maximum value of $$\frac{\log _e x}{x}$$, if $$x>0$$ is

The value of $$\int e^{\sin x} \sin 2 x d x$$ is

The value of $$\int_{-1 / 2}^{1 / 2} \cos ^{-1} x d x$$ is

If $$\int \frac{3 x+1}{(x-1)(x-2)(x-3)} d x A \log |x-1| B \log |x-2|+C \log |x-3|+C$$, then the values of $$A, B$$ and $$C$$ are respectively

Find the value of $$\int_0^1 \frac{\log (1+x)}{1+x^2} d x$$ is

The area of the region bounded by the curve $$y^2=8 x$$ and the line $$y=2 x$$ is

The value of $$\int_{-\pi / 2}^{\pi / 2} \frac{\cos x}{1+e^x} d x$$ is

The order of the differential equation obtained by eliminating arbitrary constants in the family of curves $$c_1 y=\left(c_2+c_3\right) e^{x+c_4}$$ is

The general solution of the differential equation $$x^2 d y-2 x y d x=x^4 \cos x d x$$ is

The area of the region bounded by the line $$y=2 x+1, X$$-axis and the ordinates $$x=-1$$ and $$x=1$$ is

The two vector $$\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$$ represent the two sides $$\overline{A B}$$ and $$\overline{A C}$$ respectively of a $$\triangle A B C$$. The length of the median through $$A$$ is

If $$\mathbf{a}$$ and $$\mathbf{b}$$ are unit vectors and $$\theta$$ is the angle between $$\mathbf{a}$$ and $$\mathbf{b}$$, then $$\sin \frac{\theta}{2}$$ is equal to

The curve passing through the point $$(1,2)$$ given that the slope of the tangent at any point $$(x, y)$$ is $$\frac{3 x}{y}$$ represents

If $$|\mathbf{a}+\mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=144|\mathbf{a}|=6$$, then $$|\mathbf{b}|$$ is equal to

The point $$(1,-3,4)$$ lies in the octant

If the vectors $$2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$$ and $$\lambda \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$$ are coplanar, then the value of $$\lambda$$ is

The distance of the point $$(1,2,-4)$$ from the line $$\frac{x-3}{2}=\frac{y-3}{3}=\frac{z+5}{6}$$ is

The sine of the angle between the straight line $$\frac{x-2}{3}=\frac{3-y}{-4}=\frac{z-4}{5}$$ and the plane $$2 x-2 y+z=5$$ is

If a line makes an angle of with each of $$X$$ and $$Y$$-axis, then the acute angle made by Z-axis is

Corner points of the feasible region determined by the system of linear constraints are $$(0,3),(1,1)$$ and $$(3,0)$$. Let $$z=p x=q y$$, where, $$p, q>0$$. Condition on $$p$$ and $$q$$, so that the minimum of $$z$$ occurs at $$(3,0)$$ and $$(1,1)$$ is

The feasible region of an LPP is shown in the figure. If $$z=11 x+7 y$$, then the maximum value of $$Z$$ occurs at

A die is thrown 10 times, the probability that an odd number will come up at least one time is

If $$A$$ and $$B$$ are two events such that $$P(A)=\frac{1}{3}, P(B)=\frac{1}{2}$$ and $$P(A \cap B)=\frac{1}{6}$$, then $$P\left(A^{\prime} / B\right)$$ is

Events $$E_1$$ and $$E_2$$ from a partition of the sample space $$S$$. $$A$$ is any event such that $$P\left(E_1\right)=P\left(\dot{E}_2\right)=\frac{1}{2}, P\left(E_2 / A\right)=\frac{1}{2}$$ and $$P\left(A / E_2\right)=\frac{2}{3}$$, then $$P\left(E_1 / A\right)$$ is

The probability of solving a problem by three persons $$A, B$$ and $$C$$ independently is $$\frac{1}{2}, \frac{1}{4}$$ and $$\frac{1}{3}$$ respectively. Then the probability of the problem is solved by any two of them is

If $$n(A)=2$$ and total number of possible relations from Set A to set B is 1024, then $$n(B)$$ is

The value of $$\sin ^2 51^{\circ}+\sin ^2 39^{\circ}$$ is

If $$\tan A+\cot A=2$$, then the value of $$\tan ^4 A+\cot ^4 A=$$

If $$A=\{1,2,3,4,5,6\}$$, then the number of subsets of A which contain at least two elements is

If $$z=x+i y$$, then the equation $$|z+1|=|z-1|$$ represents

The value of $${ }^{16} C_9+{ }^{16} C_{10}-{ }^{16} C_6-{ }^{16} C_7$$ is

The number of terms in the expansion of $$(x+y+z)^{10}$$ is

If $$P(n): 2^n< n !$$ Then the smallest positive integer for which $$P(n)$$ is true if

The two lines $$l x+m y=n$$ and $$l^{\prime} x+m^{\prime} y=n^{\prime}$$ are perpendicular if

If the parabola $$x^2=4$$ ay passes through the point $$(2,1)$$, then the length of the latus rectum is

If the sum of $$n$$ terms of an AP is given by $$S_n=n^2+n$$, then the common difference of the $$\mathrm{AP}$$ is

The negation of the statement "For all real numbers $$x$$ and $$y, x+y=y+x^{\prime \prime}$$ is

The standard deviation of the data 6, 7, 8, 9, 10 is

$$\lim _\limits{x \rightarrow 0}\left(\frac{\tan x}{\sqrt{2 x+4}-2}\right) \text { is equal to }$$

If a relation $$R$$ on the set $$\{1,2,3\}$$ be defined by $$R=\{(1,1)\}$$, then $$R$$ is

Let $$f:[2, \infty) \rightarrow R$$ be the function defined $$f(x)=x^2-4 x+5$$, then the ranges of $$f$$ is

If $$A, B, C$$ are three mutually exclusive and exhaustive events of an experiment such that $$P(A)=2 P(B)=3 P(C)$$, then $$P(B)$$ is equal to

The domain of the function defined by $$f(x)=\cos ^{-1} \sqrt{x-1}$$ is

The value of $$\cos \left(\sin ^{-1} \frac{\pi}{3}+\cos ^{-1} \frac{\pi}{3}\right)$$ is Does not exist

If $$A=\left(\begin{array}{lll}0 & 0 & 1 \\ 0 & 1 & 0 \\ 1 & 0 & 0\end{array}\right)$$ then $$A^4$$ is equal to

If $$A=\{a, b, c\}$$, then the number of binary operations on $$A$$ is

If $$\left(\begin{array}{ll}2 & 1 \\ 3 & 2\end{array}\right) A=\left(\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right)$$ then the matrix $$a$$ is

If $$f(x)=\left|\begin{array}{ccc}x^3-x & a+x & b+x \\ x-a & x^2-x & c+x \\ x-b & x-c & 0\end{array}\right|$$, then

If $$A$$ and $$B$$ are square matrices of same order and $$B$$ is a skew symmetric matrix, then $$A^{\prime} B A$$ is

If $$A$$ is a square matrix of order 3 and $$|A|=5$$, then $$\mid A$$ adj. $$A \mid$$ is

If $$f(x)=\left\{\begin{array}{cc}\frac{1-\cos K x}{x \sin x}, & \text { if } x \neq 0 \\ \frac{1}{2}, & \text { if } x=0\end{array}\right.$$ is continuous at $$x=0$$, then the value of $$K$$ is

If $$a_1 a_2 a_3 \ldots a_9$$ are in AP, then the value of $$\left|\begin{array}{lll}a_1 & a_2 & a_3 \\ a_4 & a_5 & a_6 \\ a_7 & a_8 & a_9\end{array}\right|$$ is

The value of acceleration due to gravity at a height of $$10 \mathrm{~km}$$ from the surface of earth is $$x$$. At what depth inside the earth is the value of the acceleration due to gravity has the same value $$x$$ ?

Young's modulus of a perfect rigid body is

A wheel starting from rest gains an angular velocity of $$10 \mathrm{~rad} / \mathrm{s}$$ after uniformly accelerated for $$5 \mathrm{~s}$$. The total angle through which it has turned is

Iceberg floats in water with part of it submerged. What is the fraction of the volume of iceberg submerged, if the density of ice is $$\rho_i=0.917 \mathrm{~g} \mathrm{~cm}^{-3}$$ ?

A sphere, a cube and a thin circular plate all of same material and same mass initially heated to same high temperature are allowed to cool down under similar conditions. Then, the

In an adiabatic expansion of an ideal gas the product of pressure and volume

A certain amount of heat energy is supplied to a monoatomic ideal gas which expands at constant pressure. What fraction of the heat energy is converted into work?

A tray of mass $$12 \mathrm{~kg}$$ is supported by two identical springs as shown in figure. When the tray is pressed down slightly and then released, it executes SHM with a time period of $$1.5 \mathrm{~s}$$. The spring constant of each spring is

A train whistling at constant frequency $$n$$ is moving towards a station at a constant speed $$v$$. The train goes past a stationary observer on the station. The frequency $$n$$ of the sound as heard by the observer is plotted as a function of time $$t$$. Identify the correct curve.

A point charge $$q$$ is placed at the corner of a cube of side $$a$$ as shown in the figure. What is the electric flux through the face $$A B C D$$ ?

The electric field lines on the left have twice the separation on those on the right as shown in figure. If the magnitude of the field at $$A$$ is $$40 \mathrm{~Vm}^{-1}$$, what is the force on $$20 \mu \mathrm{C}$$ charge kept at $$B$$ ?

An infinitely long thin straight wire has uniform charge density of $$\frac{1}{4} \times 10^{-2} \mathrm{~cm}^{-1}$$. What is the magnitude of electric field at a distance $$20 \mathrm{~cm}$$ from the axis of the wire?

A dipole moment $$p$$ and moment of inertia $$I$$ is placed in a uniform electric field $$\mathbf{E}$$. If it is displaced slightly from its stable equilibrium position, the period of oscillation of dipole is

The difference between equivalent capacitances of two identical capacitors connected in parallel to that in series is $$6 \mu \mathrm{F}$$. The value of capacitance of each capacitor is

Figure shows three points $$A, B$$ and $$C$$ in a region of uniform electric field $$\mathbf{E}$$. The line $$A B$$ is perpendicular and $$B C$$ is parallel to the field lines. Then, which of the following holds good ? ($$V_A, V_B$$ and $$V_C$$ represent the electric potential at points $$A, B$$ and $$C$$, respectively)

When a soap bubble is charged?

A hot filament liberates an electron with zero initial velocity. The anode potential is $$1200 \mathrm{~V}$$. The speed of the electron when it strikes the anode is

A metal rod of length $$10 \mathrm{~cm}$$ and a rectangular cross-section of $$1 \mathrm{~cm} \times \frac{1}{2} \mathrm{~cm}$$ is connected to a battery across opposite faces. The resistance will be

A car has a fresh storage battery of emf $$12 \mathrm{~V}$$ and internal resistance $$2 \times 10^{-2} \Omega$$. If the starter motor draws a current of $$80 \mathrm{~A}$$. Then, the terminal voltage when the starter is On is

A potentiometer has a uniform wire of length $$5 \mathrm{~m}$$. A battery of emf $$10 \mathrm{~V}$$ and negligible internal resistance is connected between its ends. A secondary cell connected to the circuit gives balancing length at $$200 \mathrm{~cm}$$. The emf of the secondary cell is

The colour code for a carbon resistor of resistance $$0.2 \mathrm{k} \Omega \pm 10 \%$$ is

Each resistance in the given cubical network has resistance of $$1 \Omega$$ and equivalent resistance between $$A$$ and $$B$$ is

$$I-V$$ characteristic of a copper wire of length $$L$$ and area of cross-section $$A$$ is shown in figure. The slope of the curve becomes

In the given figure, the magnetic field at $$O$$.

The magnetic field at the origin due to a current element $$i d \mathbf{l}$$ placed at a point with vector position $$\mathrm{r}$$ is

A long cylindrical wire of radius $$R$$ carries a uniform current $$I$$ flowing through it. The variation of magnetic field with distance $$r$$ from the axis of the wire is shown by

A cyclotron is used to accelerate protons $$\left({ }_1^l \mathrm{H}\right)$$ deuterons $$\left({ }_1^2 \mathrm{H}\right)$$ and $$\alpha$$-particles $$\left({ }_2^4 \mathrm{He}\right)$$. While exiting under similar conditions, the minimum $$\mathrm{KE}$$ is gained by

A paramagnetic sample shows a net magnetisation of $$8 \mathrm{Am}^{-1}$$ when placed in an external magnetic field of $$0.6 \mathrm{~T}$$ at a temperature of $$4 \mathrm{~K}$$. When the same sample is placed in an external magnetic field of $$0.2 \mathrm{~T}$$ at a temperature of $$16 \mathrm{~K}$$, the magnetisation will be

The ratio of magnetic field at the centre of a current carrying circular coil to its magnetic moment is $$x$$, if the current and the radius both are doubled. The new ratio will become

In a permanent magnet at room temperature

A rod of length $$2 \mathrm{~m}$$ slides with a speed of $$5 \mathrm{~ms}^{-1}$$ on a rectangular conducting frame as shown in figure. There exists a uniform magnetic filed of $$0.04 \mathrm{~T}$$ perpendicular to the plane of the figure. If the resistance of the rod is $$3 \Omega$$. The current through the rod is

The current in a coil of inductance $$0.2 \mathrm{H}$$ changes from $$5 \mathrm{~A}$$ to $$2 \mathrm{~A}$$ in $$0.5 \mathrm{~s}$$. The magnitude of the average induced emf in the coil is

In the given circuit the peak voltage across $$C, L$$ and $$R$$ are $$30 \mathrm{~V}, 110 \mathrm{~V}$$ and $$60 \mathrm{~V}$$, respectively. The rms value of the applied voltage is

The power factor of $$R-L$$ circuit is $$\frac{1}{\sqrt{3}}$$. If the inductive reactance is $$2 \Omega$$. The value of resistance is

In the given circuit, the resonant frequency is

A light beam of intensity $$20 \mathrm{~W} / \mathrm{cm}^2$$ is incident normally on a perfectly reflecting surface of sides $$25 \mathrm{~cm} \times 15 \mathrm{~cm}$$. The momentum imparted to the surface by the light per second is

An object approaches a convergent lens from the left of the lens with a uniform speed $$5 \mathrm{~m} / \mathrm{s}$$ and stops at the focus, the image

The refracting angle of prism is $$A$$ and refractive index of material of prism is $$\cot \frac{A}{2}$$. The angle of minimum deviation is $$A$$

The following figure shows a beam of light converging at point $$P$$. When a concave lens of focal length $$16 \mathrm{~cm}$$ is introduced in the path of the beam at a place shown by dotted line such that $$O P$$ becomes the axis of the lens, the beam converges at a distance $$x$$ from the lens. The value of $$x$$ will be equal to

Three polaroid sheets $$P_1, P_2$$ and $$P_3$$ are kept parallel to each other such that the angle between pass axes of $$P_1$$ and $$P_2$$ is $$45^{\circ}$$ and that between $$P_2$$ and $$P_3$$ is $$45^{\circ}$$. If unpolarised beam of light of intensity $$128 \mathrm{~Wm}^{-2}$$ is incident on $$P_1$$. What is the intensity of light oming out of $$P_3$$ ?

Two poles are separated by a distance of $$3.14 \mathrm{~m}$$. The resolving power of human eye is $$1 \mathrm{~min}$$ of an arc. The maximum distance from which he can identify the two poles distinctly is

In Young's double slit experiment, the distance between the slits and the screen is $$1.2 \mathrm{~m}$$ and the distance between the two slits is $$2.4 \mathrm{~mm}$$. If a thin transparent mica sheet of thickness $$1 \mu \mathrm{m}$$ and RI 1.5 is introduced between one of the interfering beams, the shift in the position of central bright fringe is

The de-Broglie wavelength associated with electron of hydrogen atom in this ground state is

The following graph represents the variation of photocurrent with anode potential for a metal surface. Here $$I_1, I_2$$ and $$I_3$$ represents intensities and $$\gamma_1, \gamma_2, \gamma_3$$ represent frequency for curves $$1,2$$ and $$3$$ respectively, then

The period of revolution of an electron revolving in nth orbit of $$\mathrm{H}$$-atom is proportional to

Angular momentum of an electron in hydrogen atom is $$\frac{3 h}{2 \pi}$$ ($$h$$ is the Planck's constant). The KE of the electron is

A beam of fast moving alpha particles were directed towards a thin film of gold. The parts $$A, B$$ and $$C$$ of the transmitted and reflected beams corresponding to the incident parts $$A, B$$ and $$C$$ of the beam are shown in the adjoining diagram. The number of alpha particles in

Two protons are kept at a separation of $$10 \mathrm{~nm}$$. Let $$F_n$$ and $$F_e$$ the nuclear force and the electromagnetic force between them

During a $$\beta^{-}$$-decay

A radio-active elements has half-life of 15 years. What is the fraction that will decay in 30 years?

A $$220 \mathrm{~V}$$ AC supply is connected between points $$A$$ and $$B$$ as shown in figure, what will be the potential difference $$V$$ across the capacitor?

In the following circuit what are P and Q

A positive hole in a semiconductor is

Two long straight parallel wires are a distance $$d$$ part. They carry steady equal currents flowing out of the plane of the paper. The variation of magnetic field $B$ along the line $$x x^{\prime}$$ is given by

A cylindrical wire has a mass $$(0.3 \pm 0.003) \mathrm{g}$$, radius $$(0.5 \pm 0.005) \mathrm{mm}$$ and length $$(6 \pm 0.06) \mathrm{cm}$$. The maximum percentage error in the measurement of its density is

At a metro station, a girl walks up a stationary escalator in $$20 \mathrm{~s}$$. If she remains stationary on the escalator, then the escalator take her up in $$30 \mathrm{~s}$$. The time taken by her to walk up on the moving escalator will be

Rain is falling vertically with a speed of $$12 \mathrm{~ms}^{-1}$$. A woman rides a bicycles with a speed of $$12 \mathrm{~ms}^{-1}$$ in east to west direction. What is the direction in which she should hold her umbrella?

One end of a string of length $$l$$ is connected to a particle of mass $$m$$ and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $$v$$, the net force on the particle (directed towards the centre) is ($$T$$ is the tension in the string)

A body is initially at rest. It undergoes one-dimensional motion with constant acceleration. The power delivered to it at time $$t$$ is proportional to

A thin uniform rectangular plate of mass $$2 \mathrm{~kg}$$ is placed in $$x y$$-plane as shown in figure. The moment of inertial about $$x$$-axis is $$I_x=0.2 \mathrm{~kgm}^2$$ and the moment of inertia about $$Y$$-axis is $$I_y=0.3 \mathrm{~kgm}^2$$. The radius of gyration of the plate about the axis passing through $$O$$ and perpendicular to the plane of the plate is