Pure water freezes at $$273$$ $$K$$ and $$1$$ bar. The addition of $$34.5$$ $$g$$ of ethanol to $$500$$ $$g$$ of water c

The product $$S$$ is

The order of basicity among the following compounds is

$$Y$$ and $$Z$$ are, respectively

Which of the following combination will produce $${H_2}$$ gas ?

For the following compounds, the correct statement(s) with respect to nucleophilic substitution reaction is (are)

For the following cell, $$Zn\left( s \right)\left| {ZnS{O_4}\left( {aq} \right)} \right|\left| {CuS{O_4}\left( {aq} \rig

The standard state Gibbs free energies of formation of $$C$$(graphite) and $$C$$(diamond) at $$T=298$$ $$K$$ are $${\Del

The order of the oxidation state of the phosphorous atom in $${H_3}P{O_2},{H_3}P{O_4},{H_3}P{O_3}$$ and $${H_4}{P_2}{O_

For a reaction taking place in a container in equilibrium with its surroundings, the effect of temperature on its equili

The correct statement(s) about surface properties is (are)

In a bimolecular reaction, the steric factor $$P$$ was experimentally determined to be $$4.5.$$ The correct option(s) am

Among the following, the correct statement(s) is (are)

The options(s) with only amphoteric oxides is (are)

Compounds $$P$$ and $$R$$ upon ozonolysis produce $$Q$$ and $$S,$$ respectively. The molecular formula of $$Q$$ and $$S$

$$W$$ and $$X$$ are, respectively

The reactions, $$Q$$ to $$R$$ and $$R$$ to $$S,$$ are

The major product of the following reaction is

If f : R $$ \to $$ R is a twice differentiable function such that f"(x) > 0 for all x$$ \in $$R, and $$f\left( {{1 \o

If y = y(x) satisfies the differential equation$${8\sqrt x \left( {\sqrt {9 + \sqrt x } } \right)dy = {{\left( {\sqrt {4

How many 3 $$ \times $$ 3 matrices M with entries from {0, 1, 2} are there, for which the sum of the diagonal entries of

Three randomly chosen nonnegative integers x, y and z are found to satisfy the equation x + y + z = 10. Then the probabi

Let S = {1, 2, 3, .........., 9}. For k = 1, 2, .........., 5, let Nk be the number of subsets of S, each containing fiv

Let O be the origin and let PQR be an arbitrary triangle. The point S is such that$$\overrightarrow{OP}$$ . $$\overright

The equation of the plane passing through the point (1, 1, 1) and perpendicular to the planes 2x + y $$-$$ 2z = 5 and 3x

f : R $$ \to $$ R is a differentiable function such that f'(x) > 2f(x) for all x$$ \in $$R, and f(0) = 1 then

If $$I = \sum\nolimits_{k = 1}^{98} {\int_k^{k + 1} {{{k + 1} \over {x(x + 1)}}} dx} $$, then

If the line x = $$\alpha $$ divides the area of region R = {(x, y) $$ \in $$R2 : x3 $$ \le $$ y $$ \le $$ x, 0 $$ \le $$

Let $$\alpha $$ and $$\beta $$ be non zero real numbers such that $$2(\cos \beta - \cos \alpha ) + \cos \alpha \cos \be

Let $$f(x) = {{1 - x(1 + |1 - x|)} \over {|1 - x|}}\cos \left( {{1 \over {1 - x}}} \right)$$for x $$ \ne $$ 1. Then

If $$g(x) = \int_{\sin x}^{\sin (2x)} {{{\sin }^{ - 1}}} (t)\,dt$$, then

If $$f(x) = \left| {\matrix{ {\cos 2x} & {\cos 2x} & {\sin 2x} \cr { - \cos x} & {\cos x} & { -

If the triangle PQR varies, then the minimum value of cos(P + Q) + cos(Q + R) + cos(R + P) is

|$$\overrightarrow{OX}$$ $$ \times $$ $$\overrightarrow{OY}$$| = ?

a12 = ?

If a4 = 28, then p + 2q =

A point charge $$+Q$$ is placed just outside an imaginary hemispherical surface of radius $$R$$ as shown in the figure.

Two coherent monochromatic point sources $${S_1}$$ and $${S_2}$$ of wavelength $$\lambda = 600\,nm$$ are placed symmetr

The instantaneous voltages at three terminals marked $$X,Y$$ and $$Z$$ are given by $${V_x} = {V_0}\,\sin \,\omega t,$

A uniform magnetic field $$B$$ exist in the region between $$x=0$$ and $$x = {{3R} \over 2}$$ (region $$2$$ in the figur

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of

A rocket is launched normal to the surface of the Earth, away from the sun, along the line joining the Sun and the Earth

Three vectors $$\overrightarrow P ,\overrightarrow Q $$ and $$\overrightarrow R $$ are shown in the figure. Let $$S$$ b

A symmetric star shaped conducting wire loop is carrying a steady state current $${\rm I}$$ as shown in the figure. The

A photoelectric material having work-function $${\phi _0}$$ is illuminated with light of wavelength $$\lambda \left( {\l

Consider regular polygons with number of sides $$n=3,4,5....$$ as shown in the figure. The center of mass of all the pol

Consider an expanding sphere of instantaneous radius R whose total mass remains constant. The expansion is such that the

A wheel of radius R and mass M is placed at the bottom of a fixed step of height R as shown in the figure. A constant fo

A rigid uniform bar AB of length L is slipping from its vertical position on a frictionless floor (as shown in the figur

A source of constant voltage V is connected to a resistance R and two ideal inductors L1 and L2 through a switch S as sh

In Process 1, the energy stored in the capacitor EC and heat dissipated across resistance ED are related by

In Process 2, total energy dissipated across the resistance ED is

The total kinetic energy of the ring is

The minimum value of $$\omega$$0 below which the ring will drop down is