120 g of an organic compound that contains only carbon and hydrogen gives 330 g of CO₂ and 270 g of water on complete combustion. The percentage of carbon and hydrogen, respectively are

The energy of one mole of photons of radiation of wavelength 300 nm is

(Given : h = 6.63 $$\times$$ 10^$$-$$34 J s, N_A = 6.02 $$\times$$ 10²³ mol^$$-$$1, c = 3 $$\times$$ 10⁸ m s^$$-$$1)

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

At 25$$^\circ$$C and 1 atm pressure, the enthalpies of combustion are as given below :

The enthalpy of formation of ethane is

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

(Given : ln 10 = 2.303 and log 2 = 0.3010)

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

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 alkanes.

Statement II : The strength of the double bond is greater than that of carbon-carbon single bond.

In the light of the above statements, choose the correct answer from the options given below :

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 heating with soda lime gives 'C'. The compound 'C' is :

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

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

A company dissolves 'x' amount of CO₂ at 298 K in 1 litre of water to prepare soda water. X = __________ $$\times$$ 10^$$-$$3 g. (nearest integer)

(Given : partial pressure of CO₂ at 298 K = 0.835 bar.

Henry's law constant for CO₂ at 298 K = 1.67 kbar.

Atomic mass of H, C and O is 1, 12, and 6 g mol^$$-$$1, respectively)

PCl₅ dissociates as

PCl₅(g) $$\rightleftharpoons$$ PCl₃(g) + Cl₂(g)

5 moles of PCl₅ are placed in a 200 litre vessel which contains 2 moles of N₂ and is maintained at 600 K. The equilibrium pressure is 2.46 atm. The equilibrium constant K_p for the dissociation of PCl₅ is __________ $$\times$$ 10^$$-$$3. (nearest integer)

(Given : R = 0.082 L atm K^$$-$$1 mol^$$-$$1; Assume ideal gas behaviour)

The resistance of a conductivity cell containing 0.01 M KCl solution at 298 K is 1750 $$\Omega$$. If the conductivity of 0.01 M KCl solution at 298 K is 0.152 $$\times$$ 10^$$-$$3 S cm^$$-$$1, then the cell constant of the conductivity cell is ____________ $$\times$$ 10^$$-$$3 cm^$$-$$1.

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

0.2 g of an organic compound was subjected to estimation of nitrogen by Dumas method in which volume of N₂ evolved (at STP) was found to be 22.400 mL. The percentage of nitrogen in the compound is _________. [nearest integer]

(Given : Molar mass of N₂ is 28 g mol^$$-$$1. Molar volume of N₂ at STP : 22.4 L)

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 $$2{\sin ^{ - 1}}\left( {{{{x^4} + {x^2} - 2} \over {{x^4} + {x^2} + 2}}} \right)$$ is :

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$$^ * $$, y$$^ * $$, z$$^ * $$). If ($$\alpha$$, x$$^ * $$), (y$$^ * $$, $$\alpha$$) and (x$$^ * $$, $$-$$y$$^ * $$) are collinear points, then the sum of absolute values of all possible values of $$\alpha$$ is

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

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

where [t] denotes greatest integer $$\le$$ t. If m is the number of points where $$f$$ is not continuous and n is the number of points where $$f$$ is not differentiable, then the ordered pair (m, n) is :

The value of the integral

$$\int\limits_{ - \pi /2}^{\pi /2} {{{dx} \over {(1 + {e^x})({{\sin }^6}x + {{\cos }^6}x)}}} $$ is equal to

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 point P meets the x-axis at Q. If the y-axis bisects the segment PQ, then C is a parabola with :

Let the maximum area of the triangle that can be inscribed in the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over 4} = 1,\,a > 2$$, having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the y-axis, be $$6\sqrt 3 $$. Then the eccentricity of the ellipse is :

Let the area of the triangle with vertices A(1, $$\alpha$$), B($$\alpha$$, 0) and C(0, $$\alpha$$) be 4 sq. units. If the points ($$\alpha$$, $$-$$$$\alpha$$), ($$-$$$$\alpha$$, $$\alpha$$) and ($$\alpha$$², $$\beta$$) are collinear, then $$\beta$$ is equal to :

The number of distinct real roots of the equation

x⁷ $$-$$ 7x $$-$$ 2 = 0 is

A random variable X has the following probability distribution :

The value of P(1 < X < 4 | X $$\le$$ 2) is equal to :

If the shortest distance between the lines $${{x - 1} \over 2} = {{y - 2} \over 3} = {{z - 3} \over \lambda }$$ and $${{x - 2} \over 1} = {{y - 4} \over 4} = {{z - 5} \over 5}$$ is $${1 \over {\sqrt 3 }}$$, then the sum of all possible value of $$\lambda$$ is :

Let $$\widehat a$$ and $$\widehat b$$ be two unit vectors such that $$|(\widehat a + \widehat b) + 2(\widehat a \times \widehat b)| = 2$$. If $$\theta$$ $$\in$$ (0, $$\pi$$) is the angle between $$\widehat a$$ and $$\widehat b$$, then among the statements :

(S1) : $$2|\widehat a \times \widehat b| = |\widehat a - \widehat b|$$

(S2) : The projection of $$\widehat a$$ on ($$\widehat a$$ + $$\widehat b$$) is $${1 \over 2}$$

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

Let $$\lambda$$$$^ * $$ be the largest value of $$\lambda$$ for which the function $${f_\lambda }(x) = 4\lambda {x^3} - 36\lambda {x^2} + 36x + 48$$ is increasing for all x $$\in$$ R. Then $${f_{{\lambda ^ * }}}(1) + {f_{{\lambda ^ * }}}( - 1)$$ is equal to :

Let S = {z $$\in$$ C : |z $$-$$ 3| $$\le$$ 1 and z(4 + 3i) + $$\overline z $$(4 $$-$$ 3i) $$\le$$ 24}. If $$\alpha$$ + i$$\beta$$ is the point in S which is closest to 4i, then 25($$\alpha$$ + $$\beta$$) is equal to ___________.

Let $$S = \left\{ {\left( {\matrix{ { - 1} & a \cr 0 & b \cr } } \right);a,b \in \{ 1,2,3,....100\} } \right\}$$ and let $${T_n} = \{ A \in S:{A^{n(n + 1)}} = I\} $$. Then the number of elements in $$\bigcap\limits_{n = 1}^{100} {{T_n}} $$ is ___________.

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 the circle C at P and Q such that the length of the chord PQ is 2, then the value of h + k + r is equal to ___________.

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 length of latus rectum of H is equal to the length of latus rectum of E. If $${e_H}$$ and $${e_E}$$ are the eccentricities of H and E respectively, then the value of $$12\left( {e_H^2 + e_E^2} \right)$$ is equal to ___________.

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. Then the directrix of P₂ is x + 2y = ____________.

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 string is

Two identical charged particles each having a mass 10 g and charge 2.0 $$\times$$ 10^$$-$$7C are placed on a horizontal table with a separation of L between them such that they stay in limited equilibrium. If the coefficient of friction between each particle and the table is 0.25, find the value of L. [Use g = 10 ms^$$-$$2]

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 oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be :

What will be the most suitable combination of three resistors A = 2$$\Omega$$, B = 4$$\Omega$$, C = 6$$\Omega$$ so that $$\left( {{{22} \over 3}} \right)$$$$\Omega$$ is equivalent resistance of combination?

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 angle to magnetic field. The ratio of the radii of their respective circular paths is :

Given below are two statements :

Statement I : The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an inductor.

Statement II : In ac circuit, the average power delivered by the source never becomes zero.

In the light of the above statements, choose the correct answer from the options given below.

Potential energy as a function of r is given by $$U = {A \over {{r^{10}}}} - {B \over {{r^5}}}$$, where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be :

An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the motion. The ratio of time of ascent to the time of descent will be equal to : [Use g = 10 ms^$$-$$2].

A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated by the fly wheel in the next second, will be :

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 temperature of the nail if one fourth of energy of the hammer goes into heating the nail?

[Specific heat capacity of iron = 0.42 Jg^$$-$$1 $$^\circ$$C^$$-$$1]

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

A long cylindrical volume contains a uniformly distributed charge of density $$\rho$$. The radius of cylindrical volume is R. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is :

An electric bulb is rated as 200 W. What will be the peak magnetic field at 4 m distance produced by the radiations coming from this bulb? Consider this bulb as a point source with 3.5% efficiency.

The light of two different frequencies whose photons have energies 3.8 eV and 1.4 eV respectively, illuminate a metallic surface whose work function is 0.6 eV successively. The ratio of maximum speeds of emitted electrons for the two frequencies respectively will be :

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

In Bohr's atomic model of hydrogen, let K, P and E are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level :

A body is projected from the ground at an angle of 45$$^\circ$$ with the horizontal. Its velocity after 2s is 20 ms^$$-$$1. The maximum height reached by the body during its motion is __________ m. (use g = 10 ms^$$-$$2)

Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by $$y = (10\cos \pi x\sin {{2\pi t} \over T})$$ cm

The amplitude of the particle at $$x = {4 \over 3}$$ cm will be ___________ cm.

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

A ray of light is incident at an angle of incidence 60$$^\circ$$ on the glass slab of refractive index $$\sqrt3$$. After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray is 4$$\sqrt3$$ cm. The thickness of the glass slab is __________ cm.

A circular coil of 1000 turns each with area 1m² is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of 0.07T. The maximum voltage generation will be ___________ V.

A monoatomic gas performs a work of $${Q \over {4}}$$ where Q is the heat supplied to it. The molar heat capacity of the gas will be ______________ R during this transformation. Where R is the gas constant.