If a rocket runs on a fuel (C15H30) and liquid oxygen, the weight of oxygen required and CO2 released for every litre of

Consider the following pairs of electrons (A) (a) n = 3, $$l$$ = 1, m1 = 1, ms = + $${1 \over 2}$$    &nb

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For a reaction at equilibrium A(g) $$\rightleftharpoons$$ B(g) + $${1 \over 2}$$ C(g) the relation between dissociation

Given below are two statements : Statement I : Emulsions of oil in water are unstable and sometimes they separate into t

Given below are the oxides: Na2O, As2O3, N2O, NO and Cl2O7 Number of amphoteric oxides is :

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The highest industrial consumption of molecular hydrogen is to produce compounds of element :

Which of the following statements are correct? (A) Both LiCl and MgCl2 are soluble in ethanol. (B) The oxides Li2O and M

Identify the correct statement for B2H6 from those given below : (A) In B2H6, all B-H bonds are equivalent. (B) In B2H6,

The most stable trihalide of nitrogen is :

Which one of the following elemental forms is not present in the enamel of the teeth?

In the given reaction sequence, the major product 'C' is :

Two statements are given below : Statement I : The melting point of monocarboxylic acid with even number of carbon atoms

Which of the following is an example of conjugated diketone?

The major product of the above reactions is :

Which of the following is an example of polyester?

A polysaccharide 'X' on boiling with dil H2SO4 at 393 K under 2-3 atm pressure yields 'Y'. 'Y' on treatment with bromine

Which of the following is not a broad spectrum antibiotic?

During the qualitative analysis of salt with cation y2+, addition of a reagent (X) to alkaline solution of the salt give

Atoms of element X form hcp lattice and those of element Y occupy $${2 \over 3}$$ of its tetrahedral voids. The percenta

2O3(g) $$\rightleftharpoons$$ 3O2(g) At 300 K, ozone is fifty percent dissociated. The standard free energy change at th

The osmotic pressure of blood is 7.47 bar at 300 K. To inject glucose to a patient intravenously, it has to be isotonic

The cell potential for the following cell Pt |H2(g)|H+ (aq)|| Cu2+ (0.01 M)|Cu(s) is 0.576 V at 298 K. The pH of the sol

The rate constants for decomposition of acetaldehyde have been measured over the temperature range 700 - 1000 K. The dat

The difference in oxidation state of chromium in chromate and dichromate salts is ___________.

In the cobalt-carbonyl complex : [Co2(CO)8], number of Co-Co bonds is "X" and terminal CO ligands is "Y". X + Y = ______

A 0.166 g sample of an organic compound was digested with conc. H2SO4 and then distilled with NaOH. The ammonia gas evol

Number of electrophilic centres in the given compound is _______________.

The major product 'A' of the following given reaction has _____________ sp2 hybridized carbon atoms.

Let $$A = \{ z \in C:1 \le |z - (1 + i)| \le 2\} $$ and $$B = \{ z \in A:|z - (1 - i)| = 1\} $$. Then, B :

The remainder when 32022 is divided by 5 is :

The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius

Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and n white balls. One bag is chosen a

Let x2 + y2 + Ax + By + C = 0 be a circle passing through (0, 6) and touching the parabola y = x2 at (2, 4). Then A + C

The number of values of $$\alpha$$ for which the system of equations : x + y + z = $$\alpha$$ $$\alpha$$x + 2$$\alpha$$y

If the sum of the squares of the reciprocals of the roots $$\alpha$$ and $$\beta$$ of the equation 3x2 + $$\lambda$$x $$

The set of all values of k for which $${({\tan ^{ - 1}}x)^3} + {({\cot ^{ - 1}}x)^3} = k{\pi ^3},\,x \in R$$, is the int

Let S = {$$\sqrt{n}$$ : 1 $$\le$$ n $$\le$$ 50 and n is odd}. Let a $$\in$$ S and $$A = \left[ {\matrix{ 1 & 0 & a \

For the function $$f(x) = 4{\log _e}(x - 1) - 2{x^2} + 4x + 5,\,x > 1$$, which one of the following is NOT correct?

If the tangent at the point (x1, y1) on the curve $$y = {x^3} + 3{x^2} + 5$$ passes through the origin, then (x1, y1) do

The sum of absolute maximum and absolute minimum values of the function $$f(x) = |2{x^2} + 3x - 2| + \sin x\cos x$$ in t

If $$\{ {a_i}\} _{i = 1}^n$$, where n is an even integer, is an arithmetic progression with common difference 1, and $$\

If x = x(y) is the solution of the differential equation $$y{{dx} \over {dy}} = 2x + {y^3}(y + 1){e^y},\,x(1) = 0$$; the

Let $$\lambda x - 2y = \mu $$ be a tangent to the hyperbola $${a^2}{x^2} - {y^2} = {b^2}$$. Then $${\left( {{\lambda \o

Let $$\widehat a$$, $$\widehat b$$ be unit vectors. If $$\overrightarrow c $$ be a vector such that the angle between $$

If a random variable X follows the Binomial distribution B(33, p) such that $$3P(X = 0) = P(X = 1)$$, then the value of

The domain of the function $$f(x) = {{{{\cos }^{ - 1}}\left( {{{{x^2} - 5x + 6} \over {{x^2} - 9}}} \right)} \over {{{\l

Let $$S = \left\{ {\theta \in [ - \pi ,\pi ] - \left\{ { \pm \,\,{\pi \over 2}} \right\}:\sin \theta \tan \theta + \t

The number of choices for $$\Delta \in \{ \wedge , \vee , \Rightarrow , \Leftrightarrow \} $$, such that $$(p\Delta q)

The number of one-one functions f : {a, b, c, d} $$\to$$ {0, 1, 2, ......, 10} such that 2f(a) $$-$$ f(b) + 3f(c) + f(d

In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct. There are

Let $$A\left( {{3 \over {\sqrt a }},\sqrt a } \right),\,a > 0$$, be a fixed point in the xy-plane. The image of A in y-a

Let a line having direction ratios, 1, $$-$$4, 2 intersect the lines $${{x - 7} \over 3} = {{y - 1} \over { - 1}} = {{z

The number of points where the function $$f(x) = \left\{ {\matrix{ {|2{x^2} - 3x - 7|} & {if} & {x \le - 1} \cr

Let $$f(\theta ) = \sin \theta + \int\limits_{ - \pi /2}^{\pi /2} {(\sin \theta + t\cos \theta )f(t)dt} $$. Then the v

Let $$\mathop {Max}\limits_{0\, \le x\, \le 2} \left\{ {{{9 - {x^2}} \over {5 - x}}} \right\} = \alpha $$ and $$\mathop

If two tangents drawn from a point ($$\alpha$$, $$\beta$$) lying on the ellipse 25x2 + 4y2 = 1 to the parabola y2 = 4x a

Let S be the region bounded by the curves y = x3 and y2 = x. The curve y = 2|x| divides S into two regions of areas R1,

If the shortest distance between the lines $$\overrightarrow r = \left( { - \widehat i + 3\widehat k} \right) + \lambda

The bulk modulus of a liquid is 3 $$\times$$ 1010 Nm$$-$$2. The pressure required to reduce the volume of liquid by 2% i

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A)

Two identical cells each of emf 1.5 V are connected in parallel across a parallel combination of two resistors each of r

Identify the pair of physical quantities which have different dimensions:

A projectile is projected with velocity of 25 m/s at an angle $$\theta$$ with the horizontal. After t seconds its inclin

A block of mass 10 kg starts sliding on a surface with an initial velocity of 9.8 ms$$-$$1. The coefficient of friction

A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string

A vertical electric field of magnitude 4.9 $$\times$$ 105 N/C just prevents a water droplet of a mass 0.1 g from falling

A particle experiences a variable force $$\overrightarrow F = \left( {4x\widehat i + 3{y^2}\widehat j} \right)$$ in a h

The approximate height from the surface of earth at which the weight of the body becomes $${1 \over 3}$$ of its weight o

A resistance of 40 $$\Omega$$ is connected to a source of alternating current rated 220 V, 50 Hz. Find the time taken by

The equations of two waves are given by : y1 = 5 sin 2$$\pi$$(x - vt) cm y2 = 3 sin 2$$\pi$$(x $$-$$ vt + 1.5) cm These

A plane electromagnetic wave travels in a medium of relative permeability 1.61 and relative permittivity 6.44. If magnit

Choose the correct option from the following options given below :

Nucleus A is having mass number 220 and its binding energy per nucleon is 5.6 MeV. It splits in two fragments 'B' and 'C

A baseband signal of 3.5 MHz frequency is modulated with a carrier signal of 3.5 GHz frequency using amplitude modulatio

A Carnot engine whose heat sinks at 27$$^\circ$$C, has an efficiency of 25%. By how many degrees should the temperature

A parallel plate capacitor is formed by two plates each of area 30$$\pi$$ cm2 separated by 1 mm. A material of dielectri

The magnetic field at the centre of a circular coil of radius r, due to current I flowing through it, is B. The magnetic

Two metallic blocks M1 and M2 of same area of cross-section are connected to each other (as shown in figure). If the the

0.056 kg of Nitrogen is enclosed in a vessel at a temperature of 127$$^\circ$$C. Th amount of heat required to double th

Two identical thin biconvex lens of focal length 15 cm and refractive index 1.5 are in contact with each other. The spac

A transistor is used in common-emitter mode in an amplifier circuit. When a signal of 10 mV is added to the base-emitter

As shown in the figure an inductor of inductance 200 mH is connected to an AC source of emf 220 V and frequency 50 Hz. T

Sodium light of wavelengths 650 nm and 655 nm is used to study diffraction at a single slit of aperture 0.5 mm. The dist

When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted el

From the top of a tower, a ball is thrown vertically upward which reaches the ground in 6 s. A second ball thrown vertic

A ball of mass 100 g is dropped from a height h = 10 cm on a platform fixed at the top of a vertical spring (as shown in

In a potentiometer arrangement, a cell gives a balancing point at 75 cm length of wire. This cell is now replaced by ano

A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10 g are put one on the top of the