120 g of an organic compound that contains only carbon and hydrogen gives 330 g of CO2 and 270 g of water on complete co

The energy of one mole of photons of radiation of wavelength 300 nm is (Given : h = 6.63 $$\times$$ 10$$-$$34 J s, NA =

The correct order of bond orders of $${C_2}^{2 - }$$, $${N_2}^{2 - }$$ and $${O_2}^{2 - }$$ is, respectively

At 25$$^\circ$$C and 1 atm pressure, the enthalpies of combustion are as given below : .tg {border-collapse:collapse;b

For a first order reaction, the time required for completion of 90% reaction is 'x' times the half life of the reaction.

Metals generally melt at very high temperature. Amongst the following, the metal with the highest melting point will be

PCl5 is well known, but NCl5 is not. because,

Transition metal complex with highest value of crystal field splitting ($$\Delta$$0) will be :

Arrange the following carbocations in decreasing order of stability.

Given below are two statements : Statement I : The presence of weaker $$\pi$$-bonds make alkenes less stable than alkane

Which of the following reagents / reactions will convert 'A' to 'B' ?

Hex-4-ene-2-ol on treatment with PCC gives 'A'. 'A' on reaction with sodium hypoiodite gives 'B', which on further heati

The conversion of propan-1-ol to n-butylamine involves the sequential addition of reagents. The correct sequential order

In the flame test of a mixture of salts, a green flame with blue centre was observed. Which one of the following cations

A company dissolves 'x' amount of CO2 at 298 K in 1 litre of water to prepare soda water. X = __________ $$\times$$ 10$$

PCl5 dissociates as PCl5(g) $$\rightleftharpoons$$ PCl3(g) + Cl2(g) 5 moles of PCl5 are placed in a 200 litre vessel whi

The resistance of a conductivity cell containing 0.01 M KCl solution at 298 K is 1750 $$\Omega$$. If the conductivity of

Manganese (VI) has ability to disproportionate in acidic solution. The difference in oxidation states of two ions it for

0.2 g of an organic compound was subjected to estimation of nitrogen by Dumas method in which volume of N2 evolved (at S

Consider the above reaction. The number of $$\pi$$ electrons present in the product 'P' is __________.

In alanylglycyl leucyl alanyl valine, the number of peptide linkages is ___________.

Let $$x * y = {x^2} + {y^3}$$ and $$(x * 1) * 1 = x * (1 * 1)$$. Then a value of $$2{\sin ^{ - 1}}\left( {{{{x^4} + {x^2

The sum of all the real roots of the equation $$({e^{2x}} - 4)(6{e^{2x}} - 5{e^x} + 1) = 0$$ is

Let the system of linear equations x + y + $$\alpha$$z = 2 3x + y + z = 4 x + 2z = 1 have a unique solution (x$$^ * $$,

Let x, y > 0. If x3y2 = 215, then the least value of 3x + 2y is

Let $$f(x) = \left\{ {\matrix{ {{{\sin (x - [x])} \over {x - [x]}}} & {,\,x \in ( - 2, - 1)} \cr {\max \{ 2x,3[|

The value of the integral $$\int\limits_{ - \pi /2}^{\pi /2} {{{dx} \over {(1 + {e^x})({{\sin }^6}x + {{\cos }^6}x)}}} $

A particle is moving in the xy-plane along a curve C passing through the point (3, 3). The tangent to the curve C at the

Let the maximum area of the triangle that can be inscribed in the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over 4}

Let the area of the triangle with vertices A(1, $$\alpha$$), B($$\alpha$$, 0) and C(0, $$\alpha$$) be 4 sq. units. If th

The number of distinct real roots of the equation x7 $$-$$ 7x $$-$$ 2 = 0 is

A random variable X has the following probability distribution : .tg {border-collapse:collapse;border-spacing:0;} .tg

If the shortest distance between the lines $${{x - 1} \over 2} = {{y - 2} \over 3} = {{z - 3} \over \lambda }$$ and $${{

Let $$\widehat a$$ and $$\widehat b$$ be two unit vectors such that $$|(\widehat a + \widehat b) + 2(\widehat a \times \

If $$y = {\tan ^{ - 1}}\left( {\sec {x^3} - \tan {x^3}} \right),{\pi \over 2}

Let $$\lambda$$$$^ * $$ be the largest value of $$\lambda$$ for which the function $${f_\lambda }(x) = 4\lambda {x^3} -

Let S = {z $$\in$$ C : |z $$-$$ 3| $$\le$$ 1 and z(4 + 3i) + $$\overline z $$(4 $$-$$ 3i) $$\le$$ 24}. If $$\alpha$$ + i

Let $$S = \left\{ {\left( {\matrix{ { - 1} & a \cr 0 & b \cr } } \right);a,b \in \{ 1,2,3,....100\} } \right

The number of 7-digit numbers which are multiples of 11 and are formed using all the digits 1, 2, 3, 4, 5, 7 and 9 is __

The sum of all the elements of the set $$\{ \alpha \in \{ 1,2,.....,100\} :HCF(\alpha ,24) = 1\} $$ is __________.

The remainder on dividing 1 + 3 + 32 + 33 + ..... + 32021 by 50 is _________.

The area (in sq. units) of the region enclosed between the parabola y2 = 2x and the line x + y = 4 is __________.

Let a circle C : (x $$-$$ h)2 + (y $$-$$ k)2 = r2, k > 0, touch the x-axis at (1, 0). If the line x + y = 0 intersects t

Let the hyperbola $$H:{{{x^2}} \over {{a^2}}} - {y^2} = 1$$ and the ellipse $$E:3{x^2} + 4{y^2} = 12$$ be such that the

Let P1 be a parabola with vertex (3, 2) and focus (4, 4) and P2 be its mirror image with respect to the line x + 2y = 6.

Identify the pair of physical quantities that have same dimensions:

The distance between Sun and Earth is R. The duration of year if the distance between Sun and Earth becomes 3R will be :

A stone of mass m, tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the strin

Two identical charged particles each having a mass 10 g and charge 2.0 $$\times$$ 10$$-$$7C are placed on a horizontal

Two massless springs with spring constants 2 k and 9 k, carry 50 g and 100 g masses at their free ends. These two masses

What will be the most suitable combination of three resistors A = 2$$\Omega$$, B = 4$$\Omega$$, C = 6$$\Omega$$ so that

The soft-iron is a suitable material for making an electromagnet. This is because soft-iron has

A proton, a deutron and an $$\alpha$$-particle with same kinetic energy enter into a uniform magnetic field at right ang

Given below are two statements : Statement I : The reactance of an ac circuit is zero. It is possible that the circuit c

Potential energy as a function of r is given by $$U = {A \over {{r^{10}}}} - {B \over {{r^5}}}$$, where r is the interat

An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding fo

A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated by the f

A 100 g of iron nail is hit by a 1.5 kg hammer striking at a velocity of 60 ms$$-$$1. What will be the rise in the tempe

If the charge on a capacitor is increased by 2 C, the energy stored in it increases by 44%. The original charge on the c

A long cylindrical volume contains a uniformly distributed charge of density $$\rho$$. The radius of cylindrical volume

An electric bulb is rated as 200 W. What will be the peak magnetic field at 4 m distance produced by the radiations comi

The light of two different frequencies whose photons have energies 3.8 eV and 1.4 eV respectively, illuminate a metallic

Two light beams of intensities in the ratio of 9 : 4 are allowed to interfere. The ratio of the intensity of maxima and

In Bohr's atomic model of hydrogen, let K, P and E are the kinetic energy, potential energy and total energy of the elec

A body is projected from the ground at an angle of 45$$^\circ$$ with the horizontal. Its velocity after 2s is 20 ms$$-$$

Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfer

In the given circuit, the value of current IL will be ____________ mA. (When RL = 1k$$\Omega$$)

A ray of light is incident at an angle of incidence 60$$^\circ$$ on the glass slab of refractive index $$\sqrt3$$. After

A circular coil of 1000 turns each with area 1m2 is rotated about its vertical diameter at the rate of one revolution pe

A monoatomic gas performs a work of $${Q \over {4}}$$ where Q is the heat supplied to it. The molar heat capacity of the