'A' in the given reaction is

When the hydrogen ion concentration [H$$^+$$] changes by a factor of 1000, the value of pH of the solution __________

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What is the mass ratio of ethylene glycol ($$\mathrm{C_2H_6O_2}$$, molar mass = 62 g/mol) required for making 500 g of 0

Find out the major product from the following reaction.

The isomeric deuterated bromide with molecular formula $$\mathrm{C_4H_8DBr}$$ having two chiral carbon atoms is

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A. Ammonium salts produce haze in atmosphere. B. Ozone gets produced when atmospheric oxygen reacts with chlorine radica

Statement I : Dipole moment is a vector quantity and by convention it is depicted by a small arrow with tail on the nega

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A chloride salt solution acidified with dil.HNO$$_3$$ gives a curdy white precipitate, [A], on addition of AgNO$$_3$$. [

Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R Assertion A : Butyl

Potassium dichromate acts as a strong oxidizing agent in acidic solution. During this process, the oxidation state chang

28.0 L of CO$$_2$$ is produced on complete combustion of 16.8 L gaseous mixture of ethene and methane at 25$$^\circ$$C a

The number of pairs of the solutions having the same value of the osmotic pressure from the following is _________. (Ass

A first order reaction has the rate constant, $$\mathrm{k=4.6\times10^{-3}~s^{-1}}$$. The number of correct statement/s

$$Pt(s)|{H_2}(g)(1\,bar)|{H^ + }(aq)(1\,M)||{M^{3 + }}(aq),{M^ + }(aq)|Pt(s)$$ The $$\mathrm{E_{cell}}$$ for the given c

The number of given orbitals which have electron density along the axis is _________ $$\mathrm{p_x,p_y,p_z,d_{xy},d_{yz}

Total number of moles of AgCl precipitated on addition of excess of AgNO$$_3$$ to one mole each of the following complex

Number of compounds giving (i) red colouration with ceric ammonium nitrate and also (ii) positive iodoform test from the

Number of hydrogen atoms per molecule of a hydrocarbon A having 85.8% carbon is __________ (Given : Molar mass of A = 84

The equations of two sides of a variable triangle are $$x=0$$ and $$y=3$$, and its third side is a tangent to the parabo

The foot of perpendicular of the point (2, 0, 5) on the line $${{x + 1} \over 2} = {{y - 1} \over 5} = {{z + 1} \over {

The number of functions $$f:\{ 1,2,3,4\} \to \{ a \in Z|a| \le 8\} $$ satisfying $$f(n) + {1 \over n}f(n + 1) = 1,\fora

Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that $$N-2,\sqrt{3N},N+2$

If the function $$f(x) = \left\{ {\matrix{ {(1 + |\cos x|)^{\lambda \over {|\cos x|}}} & , & {0 is continuous at $$

Let A, B, C be 3 $$\times$$ 3 matrices such that A is symmetric and B and C are skew-symmetric. Consider the statements

The shortest distance between the lines $$x+1=2y=-12z$$ and $$x=y+2=6z-6$$ is :

Let T and C respectively be the transverse and conjugate axes of the hyperbola $$16{x^2} - {y^2} + 64x + 4y + 44 = 0$$.

Let the function $$f(x) = 2{x^3} + (2p - 7){x^2} + 3(2p - 9)x - 6$$ have a maxima for some value of $$x 0$$. Then, the

Let $$z$$ be a complex number such that $$\left| {{{z - 2i} \over {z + i}}} \right| = 2,z \ne - i$$. Then $$z$$ lies on

The integral $$16\int\limits_1^2 {{{dx} \over {{x^3}{{\left( {{x^2} + 2} \right)}^2}}}} $$ is equal to

Let $$f:\mathbb{R}\to\mathbb{R}$$ be a function defined by $$f(x) = {\log _{\sqrt m }}\{ \sqrt 2 (\sin x - \cos x) + m -

The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1, 3, 5, 7, 9 without repetition,

Let $$y=y(t)$$ be a solution of the differential equation $${{dy} \over {dt}} + \alpha y = \gamma {e^{ - \beta t}}$$ whe

Let $$A = \left[ {\matrix{ {{1 \over {\sqrt {10} }}} & {{3 \over {\sqrt {10} }}} \cr {{{ - 3} \over {\sqrt {10}

$$\sum\limits_{k = 0}^6 {{}^{51 - k}{C_3}} $$ is equal to :

Let $$f(x) = 2{x^n} + \lambda ,\lambda \in R,n \in N$$, and $$f(4) = 133,f(5) = 255$$. Then the sum of all the positive

25% of the population are smokers. A smoker has 27 times more chances to develop lung cancer than a non smoker. A person

A triangle is formed by X-axis, Y-axis and the line $$3x+4y=60$$. Then the number of points P(a, b) which lie strictly i

The remainder when (2023)$$^{2023}$$ is divided by 35 is __________.

If $$\int\limits_{{1 \over 3}}^3 {|{{\log }_e}x|dx = {m \over n}{{\log }_e}\left( {{{{n^2}} \over e}} \right)} $$, where

Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges.

For the two positive numbers $$a,b,$$ if $$a,b$$ and $$\frac{1}{18}$$ are in a geometric progression, while $$\frac{1}{a

If the shortest distance between the line joining the points (1, 2, 3) and (2, 3, 4), and the line $${{x - 1} \over 2} =

Let $$\alpha \in\mathbb{R}$$ and let $$\alpha,\beta$$ be the roots of the equation $${x^2} + {60^{{1 \over 4}}}x + a = 0

The light rays from an object have been reflected towards an observer from a standard flat mirror, the image observed by

A particle executes simple harmonic motion between $$x=-A$$ and $$x=+A$$. If time taken by particle to go from $$x=0$$ t

The distance travelled by a particle is related to time t as $$x=4\mathrm{t}^2$$. The velocity of the particle at t=5s i

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A wire of length 1m moving with velocity 8 m/s at right angles to a magnetic field of 2T. The magnitude of induced emf,

Consider a block kept on an inclined plane (incline at 45$$^\circ$$) as shown in the figure. If the force required to ju

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Every planet revolves around the sun in an elliptical orbit :- A. The force acting on a planet is inversely proportional

Two objects are projected with same velocity 'u' however at different angles $$\alpha$$ and $$\beta$$ with the horizonta

The graph between two temperature scales P and Q is shown in the figure. Between upper fixed point and lower fixed point

A point charge of 10 $$\mu$$C is placed at the origin. At what location on the X-axis should a point charge of 40 $$\mu$

The resistance of a wire is 5 $$\Omega$$. It's new resistance in ohm if stretched to 5 times of it's original length wil

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Statement I : When a Si sample is doped with Boron, it becomes P type and when doped by Arsenic it becomes N-type semi c

According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molec

A body of mass is taken from earth surface to the height h equal to twice the radius of earth (R$$_e$$), the increase in

For a moving coil galvanometer, the deflection in the coil is 0.05 rad when a current of 10 mA is passes through it. If

Given below are two statements : Statement I : Stopping potential in photoelectric effect does not depend on the power o

The energy levels of an atom is shown in figure. Which one of these transitions will result in the emission of a photon

Two long parallel wires carrying currents 8A and 15A in opposite directions are placed at a distance of 7 cm from each o

A capacitor has capacitance 5$$\mu$$F when it's parallel plates are separated by air medium of thickness d. A slab of ma

An object is placed on the principal axis of convex lens of focal length 10cm as shown. A plane mirror is placed on the

Two cells are connected between points A and B as shown. Cell 1 has emf of 12 V and internal resistance of 3$$\Omega$$.

A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance R = 80$$\Omega$$, a

If a solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius. Then the ratio of moment of inertia of the

A body of mass 1 kg collides head on elastically with a stationary body of mass 3 kg. After collision, the smaller body

A spherical drop of liquid splits into 1000 identical spherical drops. If u$$_\mathrm{i}$$ is the surface energy of the