When 1 mole of gas is heated at constant volume, the temperature rises form $$273 \mathrm{~K}$$ to $$546 \mathrm{~K}$$.

Oxidation state of iodine in I$$_3^-$$ is

What is the total number of atoms in BCC crystal lattice having $$1.8 \times 10^{20}$$ unit cells?

Identify the product B in the following sequence of reactions?

What is the volume occupied by 16 g methane gas at STP?

The $$\left[\mathrm{OH}^{-}\right]$$ in a solution is $$1 \times 10^{-12} \mathrm{~mol} \mathrm{~dm}{ }^{-3}$$. What is

Which among the following statements is true for Galvanic cell?

Identify the product $$(\mathrm{X})$$ formed in the following reaction. $$\mathrm{C}_6 \mathrm{H}_5 \mathrm{OH}+\mathrm{

Which of the following is NOT true for alkaline earth metals?

Which of the following is NOT formed when a mixture of methyl bromide and n-propyl bromide is treated with sodium metal

Which element among the following is ferromagnetic?

Which of following enzymes is useful in conversion of glucose to fructose?

Which of the following reagents is used in the reaction shown below? Benzoyl chloride $$\stackrel{?}{\longrightarrow}$$

What is vapour pressure of a solution when $$2 \mathrm{~mol}$$ of a non-volatile solute are dissolved in $$20 \mathrm{~m

Which among following amines has lowest $$\mathrm{pK}_{\mathrm{b}}$$ values?

Which of following elements forms crosslinks in vulcanization of SBR rubber?

What will be the concentration of solution of electrolyte if it's molar conductivity and conductivity are respectively 2

Identify cationic complex from following.

Which property from following is NOT exhibited by interstitial compounds?

Which among the following salt solution in water shows pH greater than 7?

What is the percentage of unoccupied volume in BCC structure?

What type of isomers are the ethoxy ethane and methoxy propane?

What is the value of $$\mathrm{\Delta H-\Delta U}$$ for the formation of 2 moles of ammonia from $$\mathrm{H_{2(g)}}$$ a

What is the density of an element (At mass 100 g mol$$^{-1}$$) having BCC structure with edge length 400 pm?

In which of the following salts, the solubility increases appreciably with increase in temperature?

What is effective atomic number of cobalt in [Co(NH$$_3$$)$$_6$$]$$^{3+}$$ if Co(Z = 27) ?

Which among the following is NOT an example of one-dimensional nanostructure?

For a first order reaction, intercept of the graph between $$\mathrm{\log\frac{[A]_o}{[A]_t}}$$(Y-axis) and conc. (X-axi

The pH of 0.005 M KOH is 9.95. Calculate the [OH$$^-$$] ?

Which of the following reactions is a Wurtz - Fittig reaction?

Which among the following noble gases reacts with fluorine to give crystalline fluorides?

Identify the name of following reaction. Toluene + chromyl chloride $$\stackrel{\mathrm{CS}_2}{\longrightarrow}$$ comple

What is the half-life of a first order reaction if time required to decrease concentration of reactant from 1.0 M to 0.2

Which among the following is obtained as major product $$\mathrm{x}$$ in the reaction stated below? Anisole $$\mathrm{\m

Which among the following statements about ozone depletion is NOT true?

Which free radical initiator is used for polymerization of tetrafluoro ethylene?

Chlorobenzene on heating with concentrated HNO$$_3$$ in presence of concentrated H$$_2$$SO$$_4$$ gives

What is the boiling point of 0.5 molal aqueous solution of sucrose if 0.1 molal aqueous solution of glucose boils at 100

Identify the product formed when tertiary butyl bromide reacts with alcoholic NH$$_3$$ solution?

Which among the following gases is adsorbed to greater extent at similar conditions of temperature and pressure if the a

What is the rate of disappearance of B in following reaction? $$2 \mathrm{A}+\mathrm{B} \rightarrow 3 \mathrm{C}$$, if r

Which reagent oxidizes glucose to saccharic acid?

Two moles of an ideal gas are expanded isothermally from $$15 \mathrm{dm}^3$$ to $$20 \mathrm{dm}^3$$. If the amount of

Which from following statements is NOT correct for heterolysis?

Which among the following molecules exhibits strong London forces?

What is the number of moles of electrons passed when current of 5 ampere is passed through a solution of FeCl$$_3$$ for

What is the formal charge of oxygen atom in carbon monoxide?

Which isomer of C$$_6$$H$$_{14}$$ has highest boiling point?

What is the wavelength for a wave having frequency 50 Hz?

Identify the product formed when benzoyl chloride is reduced by hydrogen using palladium catalyst poisoned with barium s

If $$\mathrm{(m+3 n)(3 m+n)=4 h^2}$$, then the acute angle between the lines represented by $$\mathrm{m x^2+2 h x y+n y^

$$\text{I} : y^{\prime}=\frac{y+x}{x} ; \quad \text { II }: y^{\prime}=\frac{x^2+y}{x^3} ; \quad \text { III }: y^{\prim

The differential equation of the family of circles touching $$y$$-axis at the origin is

The mean of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2 and 6, then the ot

If $$\overline{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}, \overline{\mathrm{b}}=3 \hat{\mathrm{

If $$\mathrm{p}$$ is the length of the perpendicular from origin to the line whose intercepts on the axes are a and $$b$

The abscissa of the points, where the tangent to the curve $$y=x^3-3 x^2-9 x+5$$ is parallel to $$X$$ axis are

$$\int \frac{1}{x^{\frac{1}{2}}+x^{\frac{1}{3}}} d x=$$

If $$A=\left[\begin{array}{ccc}\cos \theta & -\sin \theta & 0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1\end{array}\r

$$\int[\sin |\log x|+\cos |\log x|] d x=$$

$$\int\limits_5^{10} \frac{d x}{(x-1)(x-2)}=$$

The direction cosines $$\ell, \mathrm{m}, \mathrm{n}$$ of the line $$\frac{\mathrm{x}+2}{2}=\frac{2 \mathrm{y}-5}{3} ; \

an urn contains 9 balls of which 3 are red, 4 are blue and 2 are green. Three balls are drawn at random from the urn. Th

If $${\pi \over 2}

Equation of the plane passing through the point (2, 0, 5) and parallel to the vectors $$\widehat i - \widehat j + \wideh

If $$A=\left[\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1\end{array}\right]$$ and $$A^{-1}=\frac{1}{2}\left[\be

For all real $$x$$, the minimum value of the function $$f(x)=\frac{1-x+x^2}{1+x+x^2}$$ is

The objective function $$z=4 x+5 y$$ subjective to $$2 x+y \geq 7 ; 2 x+3 y \leq 15 ; y \leq 3, x \geq 0 ; y \geq 0$$ ha

The co-ordinates of the point $$\mathrm{P} \equiv(1,2,3)$$ and $$\mathrm{O} \equiv(0,0,0)$$, then the direction cosines

$$\int\limits_{{{ - \pi } \over 2}}^{{\pi \over 2}} {{{\cos x} \over {1 + {e^x}}}dx = } $$

The equation of the plane containing the line $$\frac{x+1}{-3}=\frac{y-3}{2}=\frac{z+2}{1}$$ and the point $$(0,7,-7)$$

If the lines $$x^2-4xy+y^2=0$$ make angles $$\alpha$$ and $$\beta$$ with positive direction X-axis, then $$\cot^2\alpha+

It is observed that $$25 \%$$ of the cases related to child labour reported to the police station are solved. If 6 new c

For X ~ B(n, p), if p = 0.6, E(X) = 6, then Var(X) =

The equation of a line passing through $$(3,-1,2)$$ and perpendicular to the lines $$\bar{r}=(\hat{i}+\hat{j}-\hat{k})+\

$$\begin{aligned} & \text { } f(x)=\frac{\sqrt{1+p x}-\sqrt{1-p x}}{x} \text {, if } 1 \leq x is continuous in the inter

The function $$f(x)=\log (1+x)-\frac{2 x}{2+x}$$ is increasing on

If $$A=\left[\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{array}\right]$$, then $$A^{-1}=$$

The equation of circle with centre at $$(2,-3)$$ and the circumference $$10 \pi$$ units is

If y = 2 sin x + 3 cos x and y + A$$\mathrm{\frac{d^2y}{dx^2}}$$ = B, then the values of A, B are respectively

The number of solutions of cos2$$\theta$$ = sin$$\theta$$ in (0, 2$$\pi$$) are

If $$y=\tan ^{-1}\left[\frac{1}{1+x+x^2}\right]+\tan ^{-1}\left[\frac{1}{x^2+3 x+3}\right], x>0$$, then $$\frac{d y}{d x

If $$z(2-i)=(3+i)$$, then $$z^{38}=$$, ( where $$z=x+i y$$)

The area bounded by the parabola $$y^2=x$$, the straight line $$y=4$$ and $$Y$$ axis is

If $$\sin ^{-1}\left(\frac{3}{5}\right)+\cos ^{-1}\left(\frac{12}{13}\right)=\sin ^{-1} \alpha$$, then $$\alpha=$$

If $$\lim _\limits{x \rightarrow 5} \frac{x^k-5^k}{x-5}=500$$, then the value of $$k$$, where $$k \in N$$ is

The logical statement (p $$\to$$ q) $$\wedge$$ (q $$\to$$ ~p) is equivalent to

For a set of five true or false questions, no student has written the all correct answers and no two students have given

The general solution of the differential equation. $$\left(\frac{y}{x}\right) \cos \left(\frac{y}{x}\right) d x-\left[\l

If the half life period of a substance is 5 years, then the total amount of the substance left after 15 years, when init

A bakerman sells 5 types of cakes. Profit due to sale of each type of cake is respectively ₹ 2.5, ₹ 3 , ₹ 1.5 and ₹ 1. T

If $$m$$ is order and $$n$$ is degree of the differential equation $$\left(\frac{d^2 y}{d x^2}\right)^5+4 \frac{\left(\f

If $$\theta+\phi=\alpha$$ and $$\tan \theta=k \tan \phi($$ where $$K>1)$$, then the value of $$\sin (\theta-\phi)$$ is

With usual notations, perimeter of a triangle $$A B C$$ is 6 times the arithmetic mean of sine of its angles. If $$\math

If p $$\to$$ (~p $$\vee$$ q) is false, then the truth values of p and q are, respectively

If $$|\bar{a} \times \bar{b}|^2+(\bar{a} \cdot \bar{b})^2=144$$ and $$|\bar{a}|=4$$, then $$|\bar{b}|=$$

Let A = {10, 11, 12, 14, 26} and let f : A $$\to$$ N be such that f(a) = highest prime factor of a, where a $$\in$$ A, t

If $$\int {{{5\tan x} \over {\tan x - 2}}dx = x + a\log |\sin x - 2\cos x| + c} $$, then a = (Where c is constant of int

The area of the parallelogram with vertices A(1, 2, 3), B(1, 3, a), C(3, 8, 6) and D(3, 7, 3) is $$\sqrt{265}$$ sq. unit

If $$y = {\tan ^{ - 1}}\left\{ {{{a\cos x - b\sin x} \over {b\cos x + a\sin x}}} \right\}$$, then $${{dy} \over {dx}}$$

Under isothermal conditions, two soap bubbles of radii '$$r_1$$' and '$$r_2$$' combine to form a single soap bubble of

Two identical parallel plate air capacitors are connected in series to a battery of emf '$$\mathrm{V}$$'. If one of the

In LCR series resonant circuit, at resonance, voltage across 'L' and 'C' will cancel each other because they are

Two coherent sources of wavelength '$$\lambda$$' produce steady interference pattern. The path difference corresponding

In a capillary tube having area of cross-section A, water rises to a height 'h'. If cross-sectional area is reduced to $

Water rises upto a height $$10 \mathrm{~cm}$$ in a capillary tube. It will rise to a height which is much more than $$10

A moving coil galvanometer is converted into an ammeter, reading upto $$0.04 \mathrm{~A}$$ by connecting a shunt of resi

The inductive reactance of a coil is R$$\Omega$$. If the inductance of a coil is doubled and frequency of a.c. supply is

For a body of mass '$$m$$', the acceleration due to gravity at a distance '$$R$$' from the surface of the earth is $$\le

What is the ratio of the velocity of sound in hydrogen $$\left(\gamma=\frac{7}{5}\right)$$ to that in helium $$\left(\ga

A particle performs rotational motion with an angular momentum 'L'. If frequency of rotation is doubled and its kinetic

Equation of two simple harmonic waves are given by $${Y_1} = 2\sin 8\pi \left( {{t \over {0.2}} - {x \over 2}} \right)m$

A current through 1 $$\Omega$$ resistance in the following circuit is

Three bodies P, Q and R have masses 'm' kg, '2m' kg and '3m' kg respectively. If all the bodies have equal kinetic energ

Equal volumes of two gases are kept in different containers having densities in the ratio 1 : 16. They exert equal press

In Young's experiment, fringes are obtained on a screen placed at a distance $$75 \mathrm{~cm}$$ from the slits. When th

Combination of NAND gates is shown in the figure. It is equivalent to

A molecule of mass 'm' moving with velocity 'v' makes 5 elastic collisions with a wall of container per second. The chan

In thermodynamics, for an isochoric process, which one of the following statement is INCORRECT?

The ratio of energy required to raise a satellite of mass '$$m$$' to height '$$h$$' above the earth's surface to that re

When a piece of polythene is rubbed with wool, a negative charge of $$4 \times 10^{-7} \mathrm{C}$$ is developed on the

Ratio centripetal acceleration for an electron revolving in 3rd and 5th Bohr orbit of hydrogen atom is

In an ideal junction diode, the current flowing through PQ is

LED is manufactured using zinc selenide then it emits.

If '$$\mathrm{E}$$' is the kinetic energy per mole of an ideal gas and '$$\mathrm{T}$$' is the absolute temperature, the

A child is sitting on a swing which performs S.H.M. It has minimum and maximum heights from ground $$0.75 \mathrm{~cm}$$

The north pole of a long horizontal bar magnet is being brought towards closed circuit consisting of a coil. The directi

The wave number of the last line of the Balmer series in the hydrogen spectrum will be $$\left(\right.$$ Rydberg's cons

The refractive index of glass is 1.5 and that of water is 1.33 . The critical angle for a ray of light going from glass

A, B and C are three parallel conductors of equal lengths carrying currents $$\mathrm{I}, \mathrm{I}$$ and $$2 \mathrm{I

Three pure inductors each of inductance 6H are connected as shown in the figure. Their equivalent inductance between the

A body at rest falls through a height 'h' with velocity 'V'. If it has to fall down further for its velocity to become t

A convex lens is dipped in a liquid whose refractive index is equal to refractive index of lens material. Then its focal

Photoemission from metal surface takes place for frequencies '$$v_1$$' and '$$v_2$$' of incident rays $$\left(v_1>v_2\ri

The angle of banking '$$\theta$$' for a meter gauge railway line is given by $$\theta=\tan ^{-1}\left(\frac{1}{20}\right

Three rings each of mass 'M' and radius 'R' are arranged as shown in the figure. The moment of inertia of system about

The instantaneous value of an alternating current is given by $$\mathrm{i}=50 \sin (100 \pi \mathrm{t})$$. It will achie

A proton and alpha particle are accelerated through the same potential difference. The ratio of the de-Broglie wavelengt

Two rods of same length and material are joined end to end. They transfer heat in 8 second. When they are joined in para

A pendulum clock is running fast. To correct its time, we should

A pipe closed at one end has length $$0.8 \mathrm{~m}$$. At its open end $$0.5 \mathrm{~m}$$ long uniform string is vibr

Two coherent sources 'P' and 'Q' produce interference at point 'A' on the screen, where there is a dark band which is fo

The equation of simple harmonic wave produced in the string under tension $$0.4 \mathrm{~N}$$ is given by $$\mathrm{y=4

A condenser of capacity '$$\mathrm{C}_1$$' is charged to potential '$$\mathrm{V}_1$$' and then disconnected. Uncharged c

In a step up transformer, which one of the following statements is correct?

Magnetic moment of revolving electron of charge (e) and mass (m) in terms of angular momentum (L) of electron is :

A particle is performing S.H.M. with maximum velocity '$$v$$'. If the amplitude is tripled and periodic time is doubled

A big water drop is divided into 8 equal droplets. $$\Delta \mathrm{P}_{\mathrm{s}}$$ and $$\Delta \mathrm{P}_{\mathrm{B

A hollow metal sphere has a radius 'r'. The potential difference between a point on its surface and at a point at a dist

The magnetic flux near the axis and inside the air core solenoid of length $$60 \mathrm{~cm}$$ carrying current '$$\math