The compound(s) formed upon combustion of sodium metal in excess air is (are)

Given that the abundances of isotopes 54Fe, 56Fe and 57Fe are 5%, 90% and 5%, respectively, the atomic mass of Fe is :

The term that corrects for the attractive forces present in a real gas in the van der Waals equation is

Among the electrolytes Na$$_2$$SO$$_4$$, CaCl$$_2$$, Al$$_2$$(SO$$_4$$)$$_3$$ and NH$$_4$$Cl, the most effective coagula

The Henry's law constant for the solubility of N$$_2$$ gas in water at 298 K is 1.0 $$\times$$ 10$$^5$$ atm. The mole fr

The reaction of P$$_4$$ with X leads selectively to P$$_4$$O$$_6$$. The X is

The correct acidity order of the following is

Among cellulose, poly(vinyl chloride), nylon and natural rubber, the polymer in which the intermolecular force of attrac

The IUPAC name of the following compound is

The correct statement(s) regarding defects in solids is (are)

The compound(s) that exhibit(s) geometrical isomerism is(are)

The correct statement(s) about the compound $$\mathrm{H_3C(HO)HC-CH=CH-CH(OH)CH_3~~(X)}$$ is (are)

The compound X is

The compound Y is

The compound Z is

The structure of the carbonyl compound P is

The structures of the products Q and R, respectively, are

The structure of the product S is

Match each of the diatomic molecules in Column I with its property/properties in Column II: .tg {border-collapse:colla

Match each of the compounds in Column I with its characteristic reaction(s) in Column II. .tg {border-collapse:collaps

Let $$z = \,\cos \,\theta \, + i\,\sin \,\theta $$ . Then the value of $$\sum\limits_{m = 1}^{15} {{\mathop{\rm Im}\noli

Let $$z = x + iy$$ be a complex number where x and y are integers. Then the area of the rectangle whose vertices are the

Let $$P(3,2,6)$$ be a point in space and $$Q$$ be a point on the line $$$\widehat r = \left( {\widehat i - \widehat j +

If $$\overrightarrow a ,\overrightarrow b ,\overrightarrow c $$ and $$\overrightarrow d $$ are unit vectors such that $$

The probability that $$X\ge3$$ equals :

The conditional probability that $$X\ge6$$ given $$X>3$$ equals :

The probability that X = 3 equals

Area of the region bounded by the curve $$y = {e^x}$$ and lines $$x=0$$ and $$y=e$$ is

Let $$f$$ be a non-negative function defined on the interval $$[0,1]$$. If $$\int\limits_0^x {\sqrt {1 - {{(f'(t))}^2}d

Match the conics in Column I with the statements/expressions in Column II : .tg {border-collapse:collapse;border-spaci

In a triangle $$ABC$$ with fixed base $$BC$$, the vertex $$A$$ moves such that $$$\cos \,B + \cos \,C = 4{\sin ^2}{A \o

The line passing through the extremity $$A$$ of the major axis and extremity $$B$$ of the minor axis of the ellipse $${x

Tangents drawn from the point P (1, 8) to the circle $${x^2}\, + \,{y^2}\, - \,6x\, - 4y\, - 11 = 0$$ touch the circl

The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, i

If $${{{{\sin }^4}x} \over 2} + {{{{\cos }^4}x} \over 3} = {1 \over 5},$$ then

Match the statements/expressions in Column I with the open intervals in Column II : .tg {border-collapse:collapse;bord

Let $$L = \mathop {\lim }\limits_{x \to 0} {{a - \sqrt {{a^2} - {x^2}} - {{{x^2}} \over 4}} \over {{x^4}}},a > 0$$. If

The number of matrices in A is

The number of matrices A in A for which the system of linear equations $$A\left[ {\matrix{ x \cr y \cr z \

The number of matrices A in A for which the system of linear equations $$A\left[ {\matrix{ x \cr y \cr z \

A block of base 10 cm × 10 cm and height 15 cm is kept on an inclined plane. The coefficient of friction between them is

Look at the drawing given in the figure below which has been drawn with ink of uniform line-thickness. The mass of ink u

The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular ma

Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. T

A disk of radius $${a \over 4}$$ having a uniformly distributed charge 6C is placed in the xy-plane with its centre at (

Three concentric metallic spherical shells of radii $$R,2R,3R$$ are given charges $$Q_1,Q_2,Q_3$$, respectively. It is f

The $$x$$-$$t$$ graph of a particle undergoing simple harmonic motion is shown in the figure. The acceleration of the pa

A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive index of water is 4/3. A fi

For the circuit shown in the figure

$$C_V$$ and $$C_P$$ denote the molar specific heat capacities of a gas at constant volume and constant pressure, respect

A student performed the experiment of determination of focal length of a concave mirror by $$u$$-$$v$$ method using an o

If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one ca

The allowed energy for the particle for a particular value of $$n$$ is proportional to

If the mass of the particle is $$m=1.0\times10^{-30}$$ kg and $$a=6.6$$ nm, the energy of the particle in its ground sta

The speed of the particle, that can take discrete values, is proportional to

In the core of nuclear fusion reactor, the gas becomes plasma because of

Assume that two deuteron nuclei in the core of fusion reactor at temperature T are moving towards each other, each with

Results of calculations for four different designs of a fusion reactor using D-D reaction are given below. Which of thes

Column II shows five systems in which two objects are labelled as X and Y. Also in each case a point P is shown. Column

Six point charges, each of the same magnitude q, are arranged in different manners as shown in Column II. In each case,