A pair of compounds having the same boiling points are

Identify A, B and C in the sequence.

$$\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{Br} \underset{\text { Alc. }}{\stackrel{\mathrm{KCN}}{\longrightarrow}} A \stackrel{\mathrm{LiAlH}_4}{\longrightarrow} B \stackrel{\mathrm{HNO}_2}{\longrightarrow} C$$

$$\begin{aligned} & \mathrm{CH}_3-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_2 \mathrm{OH} \stackrel{\mathrm{PCC}}{\longrightarrow} \\\\ & \mathrm{CH}_3-\mathrm{CH}=\mathrm{CH}-\mathrm{CHO} \end{aligned}$$

Hybridisation change involved at $$\mathrm{C}$$-$$1$$ in the above reaction.

If a didentate ligand ethane-1, 2-diamine is progressively added in the molar ratio en : Ni :: 1: 1, 2 : 1, 3 : 1 to $$\left[\mathrm{Ni}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$$ aq solution, following co-ordination entities are formed.

I. $$\left[\mathrm{Ni}\left(\mathrm{H}_2 \mathrm{O}\right)_4 \mathrm{en}\right]^{2+}(a q)$$ - pale blue

II. $$\left[\mathrm{Ni}\left(\mathrm{H}_2 \mathrm{O}\right)_2(\mathrm{en})_2\right]^{2+}(\mathrm{aq})$$ - blue/purple

III. $$\left[\mathrm{Ni}(\mathrm{en})_3\right]^{2+}(\mathrm{aq})$$ - violet

The wavelength in $$\mathrm{nm}$$ of light absorbed in case of I and III are respectively

Which of the following is an organometallic compound

A better reagent to oxidise primary alcohols into aldehyde is

In the reaction,

$${C_6}{H_5}CN\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{(ii)\,{H_3}{O^ + }}^{(i)\,SnC{l_2} + HCl}} X\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{}^{conc.\,KOH}} Y + Z$$

Formation of $$X, Y$$ and $$Z$$ are known by

Compounds P and R in the following reaction are

$$\mathrm{C{H_3}CHO\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{(ii)\,{H_3}{O^ + }}^{(i)\,C{H_3}MgBr}} P\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{Heat}^{conc.\,{H_2}S{O_4}}} Q\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{\matrix{ {(i)\,{B_2}{H_6}} \cr {(ii)\,{H_2}{O_2}/O{H^ - }} \cr } }} R}$$

Aniline does not undergo

The heating of phenyl methyl ether with HI produces an aromatic compound $$A$$ which on treatment with conc. $$\mathrm{HNO}_3$$ gives $$B$$. $$A$$ and $$B$$ respectively are

Y in the above reaction is

Sucrose is dextrorotatory but after hydrolysis the mixture show laevorotation, this is because of

The correct order of match between column X and column Y is

In the reaction,

P, Q and R respectively are

Thyroxine produced in the thyroid gland is an iodinated derivative of

Which one of the following is a non-narcotic analgesic?

Receptors are proteins and crucial to body communication process. These receptors are embedded in

Which of the following monomers form biodegradable polymers ?

Match the List-I with List - I in the following.

	List-I		List-II
1.	Caprolactum	a.
2.	Vinyl chloride	b.
3.	Styrene	c.
4.	Propene	d.

The correct order of first ionisation enthalpy of given elements is

Which of the following statement is incorrect?

A gas at a pressure of $$2 \mathrm{~atm}$$ is heated from $$25^{\circ} \mathrm{C}$$ to $$323^{\circ} \mathrm{C}$$ and simultaneously compressed of $$\frac{2}{3}$$rd of its original value. Then the final pressure is

Lattice enthalpy for $$\mathrm{NaCl}$$ is $$+788 \mathrm{~kJ} \mathrm{~mol}^{-1}$$ and $$\Delta H_{\text {hyd }}^{\circ}=-784 \mathrm{~kJ} \mathrm{~mol}^{-1}$$. Enthalpy of solution of $$\mathrm{NaCl}$$ is

At $$500 \mathrm{~K}$$, for a reversible reaction $$A_2(g)+B_2(g) \rightleftharpoons 2 A B(g)$$ in a closed container, $$K_C=2 \times 10^{-5}$$. In the presence of catalyst, the equilibrium is attaining 10 times faster. The equilibrium constant $$K_C$$ in the presence of catalyst at the same temperature is

A weak acid with $$\mathrm{p} K_a ~5.9$$ and weak base with $$\mathrm{p} K_b ~5.8$$ are mixed in equal proportions. $$\mathrm{pH}$$ of the resulting solution is

Temperature of $$25^{\circ} \mathrm{C}$$ in Fahrenheit and Kelvin scale respectively are

The number of protons, neutrons and electrons in the ion $${ }_{16}^{32} \mathrm{~S}^{2-}$$ respectively are

A pair of amphoteric oxides is

The composition of water gas is

IUPAC name of the compound is

Among the following.

The set which represents aromatic species is

Which one of the following gases converts haemoglobin into carboxy haemoglobin?

What is the oxidation number of $$\mathrm{S}$$ in $$\mathrm{H}_2 \mathrm{S}_2 \mathrm{O}_8$$ ?

A $$30 \%$$ solution of hydrogen peroxide is

If '$$a$$' stands for the edge length of the cubic systems. The ratio of radii in simple cubic, body centred cubic and face centred cubic unit cells is

Dimerisation of solute molecules in low dielectric constant solvent is due to

The swelling in feet and ankles of an aged person due to sitting continuously for long hours during travel, is reduced by soaking the feet in warm salt water. This is because of

A sample of water is found to contain $$5.85 \%$$ $$\left(\frac{w}{w}\right)$$ of $$A B$$ (molecular mass 58.5 ) and $$9.50 \%$$ $$\left(\frac{w}{w}\right) X Y_2$$ (molecular mass 95). Assuming $$80 \%$$ ionisation of $$A B$$ and $$60 \%$$ ionisation of $$X Y_2$$, the freezing point of water sample is [Given, $$K_f$$ for water $$1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$$, Freezing point of pure water is $$273 \mathrm{~K}$$ and $$A, B$$ and $$Y$$ are monovalent ions.]

Match the column A (type of crystalline solid) with the column B (example for each type)

A metal crystallises in a body centred cubic lattice with the metallic radius $$\sqrt3\mathop A\limits^o $$. The volume of the unit cell in $$\mathrm{m}^3$$ is

The resistance of $$0.1 \mathrm{~M}$$ weak acid $$\mathrm{H} A$$ in a conductivity cell is $$2 \times 10^3 \mathrm{~Ohm}$$. The cell constant of the cell is $$0.78 ~\mathrm{C} \mathrm{~m}^{-1}$$ and $$\lambda_{\mathrm{m}}^{\circ}$$ of acid $$\mathrm{H} A$$ is $$390 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$$. The $$\mathrm{pH}$$ of the solution is

In which one of the following reactions, rate constant has the unit $$\mathrm{mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$$ ?

For a reaction, the value of rate constant at $$300 \mathrm{~K}$$ is $$6.0 \times 10^5 \mathrm{~s}^{-1}$$. The value of Arrhenius factor $$A$$ at infinitely high temperature is

The rate constant $$k_1$$ and $$k_2$$ for two different reactions are $$10^{16} \times e^{-2000 / T}$$ and $$10^{15} \times e^{-1000 / T}$$ respectively. The temperature at which $$k_1=k_2$$ is

During the electrolysis of brine, by using inert electrodes,

Consider the following 4 electrodes

$$\begin{aligned} & \mathrm{A}: \mathrm{Ag}^{+}(0.0001 \mathrm{M}) / \mathrm{Ag}(s) ; \\ & \mathrm{B}: \mathrm{Ag}^{+}(0.1 \mathrm{M}) / \mathrm{Ag}(s) ; \\ & \mathrm{C}: \mathrm{Ag}^{+}(0.01 \mathrm{M}) / \mathrm{Ag}(s) ; \\ & \mathrm{D}: \mathrm{Ag}^{+}(0.001 \mathrm{M}) / \mathrm{Ag}(s) ; E^{\circ}{ }_{\mathrm{Ag}^{+} / \mathrm{Ag}}=+0.80 \mathrm{~V} \end{aligned}$$

Then reduction potential in volts of the electrodes in the order.

When $$\mathrm{FeCl}_3$$ is added to excess of hot water gives a sol '$$X$$'. When $$\mathrm{FeCl}_3$$ is added to $$\mathrm{NaOH}(a q)$$ solution, gives sol '$$Y$$'

$$X$$ and $$Y$$ formed in the above processes respectively are

The reducing agent in the given equations

$$4 \mathrm{Ag}(s)+8 \mathrm{CN}^{-}(a q)+2 \mathrm{H}_2 \mathrm{O}(a q)+\mathrm{O}_2(g) \longrightarrow 4\left[\mathrm{Ag}(\mathrm{CN})_2\right]^{-}(a q)+4 \mathrm{OH}^{-}(a q)$$

$$2\left[\mathrm{Ag}(\mathrm{CN})_2\right]^{-}(a q)+\mathrm{Zn}(s) \longrightarrow {\left[\mathrm{Zn}(\mathrm{CN})_4\right]^{2-}(a q)+2 \mathrm{Ag}(s)}$$

For the formation of which compound in Ellingham diagram $$\Delta G^{\circ}$$ becomes more and more negative with increase in temperature?

Which of the following compound does not give dinitrogen on heating?

Aqueous solution of raw sugar when passed over beds of animal charcoal, it becomes colourless. Pick the correct set of terminologies that can be used for the above example.

For Freundlich adsorption isotherm, a graph of $$\log (x / m)$$ vs $$\log (p)$$ gives a straight line. The slope of line and its $$Y$$-axis intercept respectively are

In solid state, $$\mathrm{PCl}_5$$ is a/an

In which one of the following pairs, both the elements does not have $$(n-1) d^{10} n s^2$$ configuration in its elementary state?

Which of the following is correct with respect to melting point of a transition element?

$$a \mathrm{MnO}_4^{-}+b \mathrm{~S}_2 \mathrm{O}_3^{2-}+\mathrm{H}_2 \mathrm{O} \longrightarrow x \mathrm{MnO}_2 +y \mathrm{SO}_4^{2-}+z \mathrm{OH}^{-}$$

$$a$$ and $$y$$ respectively are

Which formula and name combination is incorrect?

Which of the following system in an octahedral complex has maximum unpaired electrons?

The correct decreasing order of basicity of hydrides of group- 15 elements is

Which one of the following oxoacids of phosphorus can reduce $$\mathrm{AgNO}_3$$ to metallic silver?

If a line makes an angle of $$\frac{\pi}{3}$$ with each $$X$$ and $$Y$$ axis, then the acute angle made by $$\mathrm{Z}$$-axis is

The length of perpendicular drawn from the point $$(3,-1,11)$$ to the line $$\frac{x}{2}=\frac{y-2}{3}=\frac{z-3}{4}$$ is

The equation of the plane through the points $$(2,1,0),(3,2,-2)$$ and $$(3,1,7)$$ is

The point of intersection of the line $$x+1=\frac{y+3}{3}=\frac{-z+2}{2}$$ with the plane $$3 x+4 y+5 z=10$$ is

If $$(2,3,-1)$$ is the foot of the perpendicular from $$(4,2,1)$$ to a plane, then the equation of the plane is

$$|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=144$$ and $$|\mathbf{a}|=4$$, then $$|\mathbf{b}|$$ is equal to

If $$\mathbf{a}+2 \mathbf{b}+3 \mathbf{c}=0$$ and $$(\mathbf{a} \times \mathbf{b})+(\mathbf{b} \times \mathbf{c})+(\mathbf{c} \times \mathbf{a})=\lambda(\mathbf{b} \times \mathbf{c})$$, then the value of $$\lambda$$ is equal to

A bag contains $$2 n+1$$ coins. It is known that $$n$$ of these coins have head on both sides whereas, the other $$n+1$$ coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is $$\frac{31}{42}$$, then the value of $$n$$ is

Let $$A=\{x, y, z, u\}$$ and $$B=\{a, b\}$$. A function $$f: A \rightarrow B$$ is selected randomly. The probability that the function is an onto function is

The shaded region in the figure given is the solution of which of the inequations?

If $$A$$ and $$B$$ are events, such that $$P(A)=\frac{1}{4}, P(A / B)=\frac{1}{2}$$ and $$P(B / A)=\frac{2}{3}$$, then $$P(B)$$ is

The value of $$e^{\log _{10} \tan 1^{\circ}+\log _{10} \tan 2^{\circ}+\log _{10} \tan 3^{\circ}+\ldots+\log _{10} \tan 89^{\circ}}$$ is

$$\text { The value of }\left|\begin{array}{ccc} \sin ^2 14^{\circ} & \sin ^2 66^{\circ} & \tan 135^{\circ} \\ \sin ^2 66^{\circ} & \tan 135^{\circ} & \sin ^2 14^{\circ} \\ \tan 135^{\circ} & \sin ^2 14^{\circ} & \sin ^2 66^{\circ} \end{array}\right|$$ is

The modulus of the complex number $$\frac{(1+i)^2(1+3 i)}{(2-6 i)(2-2 i)}$$ is

Given that $$a, b$$ and $$x$$ are real numbers and $$a < b, x < 0$$, then

Ten chairs are numbered as 1 to 10. Three women and two men wish to occupy one chair each. First the women choose the chairs marked 1 to 6 , then the men choose the chairs from the remaining. The number of possible ways is

Which of the following is an empty set?

If $$f(x)=a x+b$$, where $$a$$ and $$b$$ are integers, $$f(-1)=-5$$ and $$f(3)=3$$, then $$a$$ and $$b$$ are respectively

If $$p\left(\frac{1}{q}+\frac{1}{r}\right), q\left(\frac{1}{r}+\frac{1}{p}\right), r\left(\frac{1}{p}+\frac{1}{q}\right)$$ are in $$\mathrm{AP}$$, then $$p, q, r$$

A line passes through $$(2,2)$$ and is perpendicular to the line $$3 x+y=3$$. Its $$y$$-intercept is

The distance between the foci of a hyperbola is 16 and its eccentricity is $$\sqrt{2}$$. Its equation is

If $$\lim _\limits{x \rightarrow 0} \frac{\sin (2+x)-\sin (2-x)}{x}=A \cos B$$, then the values of $$A$$ and $$B$$ respectively are

If $$n$$ is even and the middle term in the expansion of $$\left(x^2+\frac{1}{x}\right)^n$$ is $$924 x^6$$, then $$n$$ is equal to

$$n$$th term of the series $$1+\frac{3}{7}+\frac{5}{7^2}+\frac{1}{7^2}+\ldots$$ is

$$f: R \rightarrow R$$ and $$g:[0, \infty) \rightarrow R$$ defined by $$f(x)=x^2$$ and $$g(x)=\sqrt{x}$$. Which one of the following is not true?

Let $$f: R \rightarrow R$$ be defined by $$f(x)=3 x^2-5$$ and $$g: R \rightarrow R$$ by $$g(x)=\frac{x}{x^2+1}$$, then $$g \circ f$$ is

Let the relation $$R$$ be defined in $$N$$ by $$a R b$$, if $$3 a+2 b=27$$, then $$R$$ is

Let $$f(x)=\sin 2 x+\cos 2 x$$ and $$g(x)=x^2-1$$ then $$g(f(x))$$ is invertible in the domain

The contrapositive of the statement.

"If two lines do not intersect in the same plane, then they are parallel." is

The mean of 100 observations is 50 and their standard deviation is 5. Then, the sum of squares of all observations is

If $$x\left[\begin{array}{l}3 \\ 2\end{array}\right]+y\left[\begin{array}{r}1 \\ -1\end{array}\right]=\left[\begin{array}{l}15 \\ 5\end{array}\right]$$, then the value of $$x$$ and $$y$$ are

If $$A$$ and $$B$$ are two matrices, such that $$A B=B$$ and $$B A=A$$, then $$A^2+B^2$$ equals to

If $$A=\left[\begin{array}{cc}2-k & 2 \\ 1 & 3-k\end{array}\right]$$ is singular matrix, then the value of $$5 k-k^2$$ is equal to

The area of a triangle with vertices $$(-3,0)$$, $$(3,0)$$ and $$(0, k)$$ is 9 sq units, find the value of $$k$$ is

If $$\Delta=\left|\begin{array}{ccc}1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2\end{array}\right|$$ and $$\Delta_1=\left|\begin{array}{ccc}1 & 1 & 1 \\ b c & c a & a b \\ a & b & c\end{array}\right|$$, then

If $$\sin ^{-1}\left(\frac{2 a}{1+a^2}\right)+\cos ^{-1}\left(\frac{1-a^2}{1+a^2}\right)=\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)$$ where $$a, x \in(0,1)$$, then the value of $$x$$ is

The value of $$\cot ^{-1}\left[\frac{\sqrt{1-\sin x}+\sqrt{1+\sin x}}{\sqrt{1-\sin x}-\sqrt{1+\sin x}}\right]$$, where $$x \in\left(0, \frac{\pi}{4}\right)$$ is

The function $$f(x)=\cot x$$ is discontinuous on every point of the set

If the function is $$f(x)=\frac{1}{x+2}$$, then the point of discontinuity of the composite function $$y=f(f(x))$$ is

If $$y=a \sin x+b \cos x$$, then $$y^2+\left(\frac{d y}{d x}\right)^2$$ is a

If $$f(x)=1+n x+\frac{n(n-1)}{2} x^2+\frac{n(n-1)(n-2)}{6} x^3+\ldots+x^n$$, then $$f^n(1)$$ is equal to :

If $$A=\left[\begin{array}{cc}1 & \tan \alpha / 2 \\ -\tan \alpha / 2 & 1\end{array}\right]$$ and $$A B=I$$, then $$B$$ is equal to

If $$u=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)$$ and $$v=\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)$$, then $$\frac{d u}{d v}$$ is

The distance '$$s$$' in meters travelled by a particle in '$$t$$' seconds is given by $$s=\frac{2 t^3}{3}-18 t+\frac{5}{3}$$. The acceleration when the particle comes to rest is :

A particle moves along the curve $$\frac{x^2}{16}+\frac{y^2}{4}=1$$. When the rate of change of abscissa is 4 times that of its ordinate, then the quadrant in which the particle lies is

An enemy fighter jet is flying along the curve, given by $$y=x^2+2$$. A soldier is placed at $$(3,2)$$ wants to shoot down the jet when it is nearest to him. Then, the nearest distance is

$$\int\limits_2^8 \frac{5^{\sqrt{10-x}}}{5^{\sqrt{x}}+5^{\sqrt{10-x}}} d x \text { is equals to :}$$

$$\int \sqrt{\operatorname{cosec} x-\sin x} d x$$ is equals to

If $$f(x)$$ and $$g(x)$$ are two functions with $$g(x)=x-\frac{1}{x}$$ and $$f \circ g(x)=x^3-\frac{1}{x^3}$$, then $$f^{\prime}(x)$$ is equals to

A circular plate of radius $$5 \mathrm{~cm}$$ is heated. Due to expansion, its radius increase at the rate of $$0.05 \mathrm{~cm} / \mathrm{s}$$. The rate at which its area is increasing when the radius is $$5.2 \mathrm{~cm}$$ is

$$\int_{-2}^0\left(x^3+3 x^2+3 x+3+(x+1) \cos (x+1)\right) d x$$ is equals to

$$\int\limits_0^\pi \frac{x \tan x}{\sec x \cdot \operatorname{cosec} x} d x$$ is equals to

$$\int \sqrt{5-2 x+x^2} d x$$ is equals to

$$\int \frac{1}{1+3 \sin ^2 x+8 \cos ^2 x} d x$$ is equals to

If a curve passes through the point $$(1,1)$$ and at any point $$(x, y)$$ on the curve, the product of the slope of its tangent and $$x$$ coordinate of the point is equal to the $$y$$ coordinate of the point, then the curve also passes through the point

The degree of the differential equation $$1+\left(\frac{d y}{d x}\right)^2+\left(\frac{d^2 y}{d x^2}\right)^2=\sqrt[3]{\frac{d^2 y}{d x^2}+1}$$ is

If $$|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|$$, then

The component of $$\hat{\mathbf{i}}$$ in the direction of the vector $$\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$$ is

In the interval $$(0, \pi / 2)$$ area lying between the curves $$y=\tan x$$ and $$y=\cot x$$ and the $$X$$-axis is

The area of the region bounded by the line $$y=x+1$$ and the lines $$x=3$$ and $$x=5$$ is

For a point object, which of the following always produces virtual image in air?

For a given pair of transparent media, the critical angle for which colour is maximum?

An equiconvex lens made of glass of refractive index $$\frac{3}{2}$$ has focal length $$f$$ in air. It is completely immersed in water of refractive index $$\frac{4}{3}$$. The percentage change in the focal length is

A point object is moving at a constant speed of 1 ms$$^{-1}$$ along the principal axis of a convex lens of focal length 10 cm. The speed of the image is also 1 ms$$^{-1}$$, when the object is at ............. cm from the optical centre of the lens.

When light propagates through a given homogeneous medium, the velocities of

Total impedance of a series $$L$$-$$C$$-$$R$$ circuit varies with angular frequency of the $$\mathrm{AC}$$ source connected to it as shown in the graph. The quality factor $$Q$$ of the series $$L$$-$$C$$-$$R$$ circuit is

The ratio of the magnitudes of electric field to the magnetic field of an electromagnetic wave is of the order of

A 60 W source emits monochromatic light of wavelength 662.5 nm. The number of photons emitted per second is

In an experiment to study photoelectric effect the observed variation of stopping potential with frequency of incident radiation is as shown in the figure. The slope and $$y$$-intercept are respectively

In the Rutherford's alpha scattering experiment, as the impact parameter increases, the scattering angle of the alpha particle

Three energy levels of hydrogen atom and the corresponding wavelength of the emitted radiation due to different electron transition are as shown. Then,

An unpolarised light of intensity $$I$$ is passed through two polaroids kept one after the other with their planes parallel to each other. The intensity of light emerging from second polaroid is $$\frac{I}{4}$$. The angle between the pass axes of the polaroids is

In the Young's double slit experiment, the intensity of light passing through each of the two double slits is $$2 \times 10^{-2} \mathrm{~Wm}^{-2}$$. The screen-slit distance is very large in comparison with slit-slit distance. The fringe width is $$\beta$$. The distance between the central maximum and a point $$P$$ on the screen is $$x=\frac{\beta}{3}$$. Then, the total light intensity at the point is

A radioactive sample has half-life of 3 years. The time required for the activity of the sample to reduce to $$\frac{1}{5}$$th of its initial value is about

When a $$p$$-$$n$$ junction diode is in forward bias, which type of charge carriers flows in the connecting wire?

A full-wave rectifier with diodes $$D_1$$ and $$D_2$$ is used to rectify $$50 \mathrm{~Hz}$$ alternating voltage. The diode $$D_1$$ conducts ......... times in one second.

A truth table for the given circuit is

The energy gap of an LED is $$2.4 \mathrm{~eV}$$. When the LED is switched ON, the momentum of the emitted photons is

In the following equation representing $$\beta^{-}$$ decay, the number of neutrons in the nucleus $$X$$ is

$${ }_{83}^{210} \mathrm{Bi} \longrightarrow X+e^{-1}+\bar{v}$$

A nucleus with mass number 220 initially at rest emits an alpha particle. If the $$Q$$ value of reaction is $$5.5 ~\mathrm{MeV}$$. Calculate the value of kinetic energy of alpha particle

A particle is in uniform circular motion, related to one complete revolution of the particle, which among the statements is incorrect?

A body of mass $$10 \mathrm{~kg}$$ is kept on a horizontal surface. The coefficient of kinetic friction between the body and the surface is 0.5. A horizontal force of $$60 \mathrm{~N}$$ is applied on the body. The resulting acceleration of the body is about

A ball of mass $$0.2 \mathrm{~kg}$$ is thrown vertically down from a height of $$10 \mathrm{~m}$$. It collides with the floor and loses $$50 \%$$ of its energy and then rises back to the same height. The value of its initial velocity is

The moment of inertia of a rigid body about an axis

Seven identical discs are arranged in a planar pattern, so as to touch each other as shown in the figure. Each disc has mass $$m$$ radius $$R$$. What is the moment of inertia of system of six discs about an axis passing through the centre of central disc and normal to plane of all discs?

The true length of a wire is $$3.678 \mathrm{~cm}$$. When the length of this wire is measured using instrument $$A$$, the length of the wire is $$3.5 \mathrm{~cm}$$. When the length of the wire is measured using instrument $$B$$, it is found to have length $$3.38 \mathrm{~cm}$$. Then, the

A body is moving along a straight line with initial velocity $$v_0$$. Its acceleration $$a$$ is constant. After $$t$$ seconds, its velocity becomes $$v$$. The average velocity of the body over the given time interval is

A closed water tank has cross-sectional area $$A$$. It has a small hole at a depth of $$h$$ from the free surface of water. The radius of the hole is $$r$$ so that $$r \ll \sqrt{\frac{A}{\pi}}$$. If $$p_o$$ is the pressure inside the tank above water level and $$p_a$$ is the atmospheric pressure, the rate of flow of the water coming out of the hole is ( $$\rho$$ is density of water)

$$100 \mathrm{~g}$$ of ice at $$0^{\circ} \mathrm{C}$$ is mixed with $$100 \mathrm{~g}$$ of water at $$100^{\circ} \mathrm{C}$$. The final temperature of the mixture is

[Take, $$L_f=3.36 \times 10^5 \mathrm{~J} \mathrm{~kg}^{-1}$$ and $$S_w=4.2 \times 10^3 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1} \text { ] }$$

The $$p$$-$$V$$ diagram of a Carnot's engine is shown in the graph below. The engine uses 1 mole of an ideal gas as working substance. From the graph, the area enclosed by the $$p$$-$$V$$ diagram is [The heat supplied to the gas is 8000 J]

When a planet revolves around the Sun, in general, for the planet

A stretched wire of a material whose young's modulus $$Y=2 \times 10^{11} ~\mathrm{Nm}^{-2}$$ has poisson's ratio 0.25 . Its lateral strain $$\varepsilon_l=10^{-3}$$. The elastic energy density of the wire is

The speed of sound in an ideal gas at a given temperature $$T$$ is $$v$$. The rms speed of gas molecules at that temperature is $$v_{\text {rms }}$$. The ratio of the velocities $$v$$ and $$v_{\text {rms }}$$ for helium and oxygen gases are $$X$$ and $$X^{\prime}$$ respectively. Then, $$\frac{X}{X^{\prime}}$$ is equal to

A positively charged glass rod is brought near uncharged metal sphere, which is mounted on an insulated stand. If the glass rod is removed, the net charge on the metal sphere is

In the situation shown in the diagram, magnitude, if $$q < < |Q|$$ and $$r >>>a$$. The net force on the free charge $$-q$$ and net torque on it about $$O$$ at the instant shown are respectively.

($$p=2 a Q$$ is the dipole moment)

Pressure of ideal gas at constant volume is proportional to .........

A block of mass $$m$$ is connected to a light spring of force constant $$k$$. The system is placed inside a damping medium of damping constant $$b$$. The instantaneous values of displacement, acceleration and energy of the block are $$x, a$$ and $$E$$ respectively. The initial amplitude of oscillation is $$A$$ and $$\omega^{\prime}$$ is the angular frequency of oscillations. The incorrect expression related to the damped oscillations is

Five capacitance each of value $$1 ~\mu \mathrm{F}$$ are connected as shown in the figure. The equivalent capacitance between $$A$$ and $$B$$ is

A uniform electric field vector $$\mathbf{E}$$ exists along horizontal direction as shown. The electric potential at $$A$$ is $$V_A$$. A small point charge $$q$$ is slowly taken from $$A$$ to $$B$$ along the curved path as shown. The potential energy of the charge when it is at point $$B$$ is

A parallel plate capacitor of capacitance $$C_1$$ with a dielectric slab in between its plates is connected to a battery. It has a potential difference $$V_1$$ across its plates. When the dielectric slab is removed, keeping the capacitor connected to the battery, the new capacitance and potential difference are $$C_2$$ and $$V_2$$ respectively, Then

A cubical Gaussian surface has side of length $$a=10 \mathrm{~cm}$$. Electric field lines are parallel to $$X$$-axis as shown in figure. The magnitudes of electric fields through surfaces $$A B C D$$ and $$E F G H$$ are $$6 ~\mathrm{kNC}^{-1}$$ and $$9 \mathrm{~kNC}^{-1}$$ respectively. Then, the total charge enclosed by the cube is

[Take, $$\varepsilon_0=9 \times 10^{-12} \mathrm{~Fm}^{-1}$$ ]

Electric field at a distance $$r$$ from an infinitely long uniformly charged straight conductor, having linear charge density $$\lambda$$ is $$E_1$$. Another uniformly charged conductor having same linear charge density $$\lambda$$ is bent into a semicircle of radius $$r$$. The electric field at its centre is $$E_2$$. Then

A wire of resistance $$R$$ is connected across a cell of emf $$(\varepsilon)$$ and internal resistance $$(r)$$. The current through the circuit is $$I$$. In time $$t$$, the work done by the battery to establish the current $$I$$ is

For a given electric current the drift velocity of conduction electrons in a copper wire is $$v_d$$ and their mobility is $$\mu$$. When the current is increased at constant temperature

Ten identical cells each emf $$2 \mathrm{~V}$$ and internal resistance $$1 ~\Omega$$ are connected in series with two cells wrongly connected. A resistor of $$10 ~\Omega$$ is connected to the combination. What is the current through the resistor?

The equivalent resistance between the points A and B in the following circuit is

A charged particle is subjected to acceleration in a cyclotron as shown. The charged particle undergoes increase in its speed

The resistance of a carbon resistor is $$4.7 ~\mathrm{k} \Omega \pm 5 \%$$. The colour of the third band is

The four bands of a colour coded resistor are of the colours grey, red, gold and gold. The value of the resistance of the resistor is

A positively charged particle $$q$$ of mass $m$ is passed through a velocity selector. It moves horizontally rightward without deviation along the line $$y=\frac{2 m v}{q B}$$ with a speed $$v$$. The electric field is vertically downwards and magnetic field is into the plane of paper. Now, the electric field is switched off at $$t=0$$. The angular momentum of the charged particle about origin $$O$$ at $$t=\frac{\pi m}{q B}$$ is

The Curie temperature of cobalt and iron are $$1400 \mathrm{~K}$$ and $$1000 \mathrm{~K}$$ respectively. At $$T=1600 \mathrm{~K}$$, the ratio of magnetic susceptibility of cobalt to that of iron is

The torque acting on a magnetic dipole placed in uniform magnetic field is zero, when the angle between the dipole axis and the magnetic field is .........

The horizontal component of Earth's magnetic field at a place is $$3 \times 10^{-5} \mathrm{~T}$$. If the dip at that place is $$45^{\circ}$$, the resultant magnetic field at that place is

A proton and an alpha-particle moving with the same velocity enter a uniform magnetic field with their velocities perpendicular to the magnetic field. The ratio of radii of their circular paths is

A moving coil galvanometer is converted into an ammeter of range 0 to $$5 \mathrm{~mA}$$. The galvanometer resistance is $$90 \Omega$$ and the shunt resistance has a value of $$10 \Omega$$. If there are 50 divisions in the galvanometer-turned-ammeter on either sides of zero, its current sensitivity is

A square loop of side $$2 \mathrm{~cm}$$ enters a magnetic field with a constant speed of $$2 \mathrm{~cm} \mathrm{~s}^{-1}$$ as shown. The front edge enters the field at $$t=0 \mathrm{~s}$$. Which of the following graph correctly depicts the induced emf in the loop?

(Take clockwise direction positive)

In series $$L C R$$ circuit at resonance, the phase difference between voltage and current is

An ideal transformer has a turns ratio of 10. When the primary is connected to $$220 \mathrm{~V}, 50 \mathrm{~Hz}$$ as source, the power output is

The current in a coil changes from $$2 \mathrm{~A}$$ to $$5 \mathrm{~A}$$ in $$0.3 \mathrm{~s}$$. The magnitude of emf induced in the coil is $$1.0 \mathrm{~V}$$. The value of self-inductance of the coil is

A metallic rod of length $$1 \mathrm{~m}$$ held along east-west direction is allowed to fall down freely. Given horizontal component of earth's magnetic field $$B_H=3 \times 10^{-5} \mathrm{~T}$$. the emf induced in the rod at an instant $$t=2 \mathrm{~s}$$ after it is released is

(Take, $$g=10 \mathrm{~ms}^{-2}$$ )