The atomic masses of He and Ne are 4 and 20 a.m.u., respectively. The value of the de Broglie wavelength of He gas at –7

The total number of lone-pairs of electrons in melamine is

The standard enthalpies of formation of CO2(g), H2O(l) and glucose(s) at 25oC are –400 kJ/mol, –300 kJ/mol and –1300 kJ/

The initial rate of hydrolysis of methyl acetate (1M) by a weak acid (HA, 1M) is 1/100th of that of a strong acid (HX, 1

The hyperconjugative stabilities of tert-butyl cation and 2-butene, respectively, are due to

Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at 25oC. For this process, the correct stat

Benzene and naphthalene form an ideal solution at room temperature. For this process, the true statement(s) is(are)

Sulphide ores are common for the metals

KI in acetone, undergoes SN2 reaction with each of P, Q, R and S. The rates of the reaction vary as

The compound that does NOT liberate CO2, on treatment with aqueous sodium bicarbonate solution, is

Consider the following complex ions : P, Q and R. $$P = {[Fe{F_6}]^{3 - }}$$, $$Q = {[V{({H_2}O)_6}]^{2 + }}$$ and $$R =

In the reaction, P + Q $$\to$$ R + S, the time taken for 75% reaction of P is twice the time taken for 50% reaction of P

Concentrated nitric acid, upon long standing, turns yellow-brown due to the formation of

The arrangement of X$$-$$ ions around A+ ion in solid AX is given in the figure (not drawn to scale). If the radius of X

Upon treatment with ammoniacal H2S, the metal ion that precipitates as a sulphide is

The pair(s) of coordination complexes/ions exhibiting the same kind of isomerism is(are)

Among P, Q, R and S, the aromatic compound(s) is(are)

The total number of carboxylic acid groups is the product P is _________.

EDTA4$$-$$ is ethylenediaminetetraacetate ion. The total number of N$$-$$Co$$-$$O bond angles in [Co(EDTA)]1$$-$$ comple

A tetrapeptide has $$-$$COOH group on alanine. This produces glycine (Gly), valine (Val), phenyl alanine (Phe) and alani

Let $$f\left( x \right) = x\sin \,\pi x,\,x > 0.$$ Then for all natural numbers $$n,\,f'\left( x \right)$$ vanishes a

A pack contains $$n$$ cards numbered from $$1$$ to $$n.$$ Two consecutive numbered cards are removed from the pack and t

Let complex numbers $$\alpha \,and\,{1 \over {\overline \alpha }}\,$$ lie on circles $${\left( {x - {x_0}} \right)^2} +

The number of points in $$\left( { - \infty \,\infty } \right),$$ for which $${x^2} - x\sin x - \cos x = 0,$$ is

The coefficient of three consecutive terms of $${\left( {1 + x} \right)^{n + 5}}$$ are in the ratio $$5:10:14.$$ Then $

Consider the set of eight vectors $$V = \left\{ {a\,\hat i + b\,\hat j + c\hat k:a,\,b,\,c\, \in \left\{ { - 1,\,1} \rig

Let $${S_n} = {\sum\limits_{k = 1}^{4n} {\left( { - 1} \right)} ^{{{k\left( {k + 1} \right)} \over 2}}}{k^2}.$$ Then $${

Perpendiculars are drawn from points on the line $\frac{x+2}{2}=\frac{y+1}{-1}=\frac{z}{3}$ to the plane $x+y+$ $z=3$. T

For $$a > b > c > 0,$$ the distance between $$(1, 1)$$ and the point of intersection of the lines $$ax + by + c

A vertical line passing through the point $$(h,0)$$ intersects the ellipse $${{{x^2}} \over 4} + {{{y^2}} \over 3} = 1$$

The value of $$\cot \left( {\sum\limits_{n = 1}^{23} {{{\cot }^{ - 1}}} \left( {1 + \sum\limits_{k = 1}^n {2k} } \right)

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio $$8:15$$ is converted into an open r

For 3 × 3 matrices M and N, which of the following statement(s) is(are) NOT correct?

The area enclosed by the curves $$y = \sin x + {\mathop{\rm cosx}\nolimits} $$ and $$y = \left| {\cos x - \sin x} \right

Let $$f$$ $$:\,\,\left[ {{1 \over 2},1} \right] \to R$$ (the set of all real number) be a positive, non-constant and di

A curve passes through the point $$\left( {1,{\pi \over 6}} \right)$$. Let the slope of the curve at each point $$(x,y

Four persons independently solve a certain problem correctly with probabilities $${1 \over 2},{3 \over 4},{1 \over 4},{1

Of the three independent events $${E_1},{E_2}$$ and $${E_3},$$ the probability that only $${E_1}$$ occurs is $$\alpha ,$

A line $$l$$ passing through the origin is perpendicular to the lines $$$\,{l_1}:\left( {3 + t} \right)\widehat i + \le

Let $\overrightarrow{\mathrm{PR}}=3 \hat{i}+\hat{j}-2 \hat{k}$ and $ \overrightarrow{\mathrm{SQ}}=\hat{i}-3 \hat{j}-4 \h

A uniform circular disc of mass 50 kg and radius 0.4 m is rotating with an angular velocity of 10 rad s-1 about its own

The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is one-third the

The work done on a particle of mass m by a force $$$K\left[ {{x \over {{{\left( {{x^2} + {y^2}} \right)}^{3/2}}}}\wideha

A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to the particle.

A particle of mass m is projected from the ground with an initial speed u0 at an angle $$\alpha $$ with the horizontal.

A bob of mass m, suspended by a string of length l1 is given a minimum velocity required to complete a full circle in th

One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another horizontal thin copp

A solid sphere of radius R and density $$\rho $$ is attached to one end of a mass-less spring of force constant k. The o

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their partial pressure

Two non-conducting solid spheres of radii $$R$$ and $$2R,$$ having uniform volume charge densities $${\rho _1}$$ and $${

In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance $$C.$$ The switch $${S_1

The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero of the Ve

A ray of light travelling in the direction $${1 \over 2}\left( {\widehat i + \sqrt 3 \widehat j} \right)$$ is incident o

Two rectangular blocks, having identical dimensions, can be arranged in either configuration-I or configuration-II as sh

A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30

In the Young's double-slit experiment using a monochromatic light of wavelength $$\lambda$$, the path difference (in ter

A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation y(x, t) =

A particle of mass M and positive charge Q, moving with a constant velocity $${\overrightarrow u _1} = 4\widehat i$$ ms$

The work functions of silver and sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the stopping potenti

A freshly prepared sample of a radioisotope of half-life 1386 s has activity 103 disintegrations per second. Given that