The increasing order of the acidity of the $$\alpha $$-hydrogen of the following compounds is :

A flask contains a mixture of compounds A and B. Both compounds decompose by first-order kinetics. The half-lives for A

The increasing order of basicity of the following compounds is :

The difference between the radii of 3rd and 4th orbits of Li2+ is R1 . The difference between the radii of 3rd and 4th o

The structure of PCl5 in the solid state is :

The most appropriate reagent for conversion of C2H5CN into CH3CH2CH2NH2 is

Which of the following derivatives of alcohols is unstable in an aqueous base?

The correct electronic configuration and spin-only magnetic moment (BM) of Gd3+ (Z = 64), respectively, are :

In the following reaction sequence the major products A and B are :

Which of the following is not an essential amino acid :

Consider the following reaction: N2O4(g) ⇌ 2NO2(g); $$\Delta $$Ho = +58 kJ For each of the following cases (a, b), the d

The values of the crystal field stabilization energies for a high spin d6 metal ion in octahedral and tetrahedral fields

The total number of coordination sites in ethylenediaminetetraacetate (EDTA4–) is _____.

A soft drink was bottled with a partial pressure of CO2 of 3 bar over the liquid at room temperature. The partial press

An oxidation-reduction reaction in which 3 electrons are transferred has a $$\Delta $$Gº of 17.37 kJ mol–1 at 25 oC. The

The number of chiral carbon(s) present in peptide, Ile-Arg-Pro, is _____.

The minimum number of moles of O2 required for complete combustion of 1 mole of propane and 2 moles of butane is _____.

The potential energy curve for the H2 molecule as a function of internuclear distance is :

In the sixth period, the orbitals that are filled are :

The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the w

If the line, 2x - y + 3 = 0 is at a distance $${1 \over {\sqrt 5 }}$$ and $${2 \over {\sqrt 5 }}$$ from the lines 4x - 2

The natural number m, for which the coefficient of x in the binomial expansion of $${\left( {{x^m} + {1 \over {{x^2}}}}

If $$\alpha $$ is positive root of the equation, p(x) = x2 - x - 2 = 0, then $$\mathop {\lim }\limits_{x \to {\alpha ^ +

If $$\int {\left( {{e^{2x}} + 2{e^x} - {e^{ - x}} - 1} \right){e^{\left( {{e^x} + {e^{ - x}}} \right)}}dx} $$ = $$g\left

Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three o

If the co-ordinates of two points A and B are $$\left( {\sqrt 7 ,0} \right)$$ and $$\left( { - \sqrt 7 ,0} \right)$$ res

Let $$f(x) = x.\left[ {{x \over 2}} \right]$$, for -10< x < 10, where [t] denotes the greatest integer function.

Let $$\lambda \in $$ R . The system of linear equations 2x1 - 4x2 + $$\lambda $$x3 = 1 x1 - 6x2 + x3 = 2 $$\lambda $$x1

If $${3^{2\sin 2\alpha - 1}}$$, 14 and $${3^{4 - 2\sin 2\alpha }}$$ are the first three terms of an A.P. for some $$\al

If the minimum and the maximum values of the function $$f:\left[ {{\pi \over 4},{\pi \over 2}} \right] \to R$$, define

A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percenta

The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2, 4, 10, 12, 14, then the

If the point P on the curve, 4x2 + 5y2 = 20 is farthest from the point Q(0, -4), then PQ2 is equal to:

If the four complex numbers $$z,\overline z ,\overline z - 2{\mathop{\rm Re}\nolimits} \left( {\overline z } \right)$$

If the function $$f\left( x \right) = \left\{ {\matrix{ {{k_1}{{\left( {x - \pi } \right)}^2} - 1,} & {x \le \pi

If (a, b, c) is the image of the point (1, 2, -3) in the line $${{x + 1} \over 2} = {{y - 3} \over { - 2}} = {z \over {

The value of $$\int\limits_{{{ - \pi } \over 2}}^{{\pi \over 2}} {{1 \over {1 + {e^{\sin x}}}}dx} $$ is:

If S is the sum of the first 10 terms of the series $${\tan ^{ - 1}}\left( {{1 \over 3}} \right) + {\tan ^{ - 1}}\left(

If y = y(x) is the solution of the differential equation $${{5 + {e^x}} \over {2 + y}}.{{dy} \over {dx}} + {e^x} = 0$$

The product of the roots of the equation 9x2 - 18|x| + 5 = 0 is :

A particle of mass 200 MeV/c2 collides with a hydrogen atom at rest. Soon after the collision the particle comes to rest

A compound microscope consists of an objective lens of focal length 1 cm and an eyepiece of focal length 5 cm with a sep

A force $$\overrightarrow F = \left( {\widehat i + 2\widehat j + 3\widehat k} \right)$$ N acts at a point $$\left( {4\w

With increasing biasing voltage of a photodiode, the photocurrent magnitude :

A physical quantity z depends on four observables a, b, c and d, as z = $${{{a^2}{b^{{2 \over 3}}}} \over {\sqrt c {d^3}

Two capacitors of capacitances C and 2C are charged to potential differences V and 2V, respectively. These are then conn

A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped f

Assume that the displacement(s) of air is proportional to the pressure difference ($$\Delta $$p) created by a sound wave

A hollow spherical shell at outer radius R floats just submerged under the water surface. The inner radius of the shell

An electron is constrained to move along the y-axis with a speed of 0.1 c (c is the speed of light) in the presence of e

A wheel is rotating freely with an angular speed $$\omega $$ on a shaft. The moment of inertia of the wheel is I and the

A bullet of mass 5 g, travelling with a speed of 210 m/s, strikes a fixed wooden target. One half of its kinetic energy

For a concave lens of focal length f, the relation between object and image distances u and v, respectively, from its po

Two concentric circular coils, C1 and C2 are placed in the XY plane. C1 has 500 turns, and a radius of 1 cm. C2 has 200

A square loop of side 2$$a$$, and carrying current I, is kept in XZ plane with its centre at origin. A long wire carryin

Number of molecules in a volume of 4 cm3 of a perfect monoatomic gas at some temperature T and at a pressure of 2 cm of

A balloon is moving up in air vertically above a point A on the ground. When it is at a height h1, a girl standing at a

A galvanometer of resistance G is converted into a voltmeter of range 0 – 1 V by connecting a resistance R1 in series wi

In a resonance tube experiment when the tube is filled with water up to a height of 17.0 cm from bottom, it resonates wi

The value of the acceleration due to gravity is g1 at a height h = $${R \over 2}$$ (R = radius of the earth) from the su

An electrical power line, having a total resistance of 2 $$\Omega $$, delivers 1 kW at 220 V. The efficiency of the tran

A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point like piece o

Three different processes that can occur in an ideal monoatomic gas are shown in the P vs V diagram. The paths are label