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

The increasing order of basicity 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 most appropriate reagent for conversion of C2H5CN into CH3CH2CH2NH2 is

The structure of PCl5 in the solid state 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

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

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 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

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 :

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

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}}}}

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

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

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

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

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 :

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

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

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

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

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

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}

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

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

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

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

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

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

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

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

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