A commercially sold conc. HCl is 35% HCl by mass. If the density of this commercial acid is 1.46 g/mL, the molarity of t

If the radius of the 3rd Bohr's orbit of hydrogen atom is r3 and the radius of 4th Bohr's orbit is r4. Then :

Consider the ions/molecule O$$_2^ + $$, O2, O$$_2^ - $$, O$$_2^ {2-} $$ For increasing bond order the correct option is

The $${\left( {{{\partial E} \over {\partial T}}} \right)_P}$$ of different types of half cells are as follows: .tg {b

Choose the correct stability order of group 13 elements in their + 1 oxidation state :

Given below are two statements : Statement I : In 'Lassaigne's Test', when both nitrogen and sulphur are present in an o

(C7H5O2)2 $$\buildrel {hv} \over \longrightarrow $$ [X] $$\to$$ 2C6H5 + 2CO2 Consider the above reaction and identify t

Consider the above reaction sequence and identify the product B.

Which will have the highest enol content?

Among the following structures, which will show the most stable enamine formation? (Where Me is $$-$$CH3)

Which statement is not true with respect to nitrate ion test?

For complete combustion of methanol CH3OH(I) + $${3 \over 2}$$O2(g) $$\to$$ CO2(g) + 2H2O(I) the amount of heat produced

A 0.5 percent solution of potassium chloride was found to freeze at $$-$$0.24$$^\circ$$C. The percentage dissociation of

50 mL of 0.1 M CH3COOH is being titrated against 0.1 M NaOH. When 25 mL of NaOH has been added, the pH of the solution w

A flask is filled with equal moles of A and B. The half lives of A and B are 100 s and 50 s respectively and are indepen

The spin-only magnetic moment value of the most basic oxide of vanadium among V2O3, V2O4 and V2O5 is _____________ B.M.

The spin-only magnetic moment value of an octahedral complex among CoCl3.4NH3, NiCl2.6H2O and PtCl4.2HCl, which upon rea

On complete combustion 0.30 g of an organic compound gave 0.20 g of carbon dioxide and 0.10 g of water. The percentage o

Compound 'P' on nitration with dil. HNO3 yields two isomers (A) and (B). These isomers can be separated by steam distill

The number of oxygens present in a nucleotide formed from a base, that is present only in RNA is ___________.

Let $$f(x) = {{x - 1} \over {x + 1}},\,x \in R - \{ 0, - 1,1\} $$. If $${f^{n + 1}}(x) = f({f^n}(x))$$ for all n $$\in$$

Let $$A = \left\{ {z \in C:\left| {{{z + 1} \over {z - 1}}} \right|

The ordered pair (a, b), for which the system of linear equations 3x $$-$$ 2y + z = b 5x $$-$$ 8y + 9z = 3 2x + y + az =

The remainder when (2021)2023 is divided by 7 is :

$$\mathop {\lim }\limits_{x \to {1 \over {\sqrt 2 }}} {{\sin ({{\cos }^{ - 1}}x) - x} \over {1 - \tan ({{\cos }^{ - 1}}x

Let f, g : R $$\to$$ R be two real valued functions defined as $$f(x) = \left\{ {\matrix{ { - |x + 3|} & , & {x 1 and

The sum of the absolute minimum and the absolute maximum values of the function f(x) = |3x $$-$$ x2 + 2| $$-$$ x in the

The area bounded by the curve y = |x2 $$-$$ 9| and the line y = 3 is :

Let R be the point (3, 7) and let P and Q be two points on the line x + y = 5 such that PQR is an equilateral triangle.

If the two lines $${l_1}:{{x - 2} \over 3} = {{y + 1} \over {-2}},\,z = 2$$ and $${l_2}:{{x - 1} \over 1} = {{2y + 3} \o

The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8. If M is the mean deviation of the numbers about t

Let $$f(x) = 2{\cos ^{ - 1}}x + 4{\cot ^{ - 1}}x - 3{x^2} - 2x + 10$$, $$x \in [ - 1,1]$$. If [a, b] is the range of the

The sum of the cubes of all the roots of the equation $${x^4} - 3{x^3} - 2{x^2} + 3x + 1 = 0$$ is _________.

There are ten boys B1, B2, ......., B10 and five girls G1, G2, ........, G5 in a class. Then the number of ways of formi

Let f(x) = max {|x + 1|, |x + 2|, ....., |x + 5|}. Then $$\int\limits_{ - 6}^0 {f(x)dx} $$ is equal to __________.

Let the solution curve y = y(x) of the differential equation $$(4 + {x^2})dy - 2x({x^2} + 3y + 4)dx = 0$$ pass through t

If $${\sin ^2}(10^\circ )\sin (20^\circ )\sin (40^\circ )\sin (50^\circ )\sin (70^\circ ) = \alpha - {1 \over {16}}\sin

Let A = {n $$\in$$ N : H.C.F. (n, 45) = 1} and Let B = {2k : k $$\in$$ {1, 2, ......., 100}}. Then the sum of all the el

The value of the integral $${{48} \over {{\pi ^4}}}\int\limits_0^\pi {\left( {{{3\pi {x^2}} \over 2} - {x^3}} \right){{

Let $$A = \sum\limits_{i = 1}^{10} {\sum\limits_{j = 1}^{10} {\min \,\{ i,j\} } } $$ and $$B = \sum\limits_{i = 1}^{10}

Let $$S = (0,2\pi ) - \left\{ {{\pi \over 2},{{3\pi } \over 4},{{3\pi } \over 2},{{7\pi } \over 4}} \right\}$$. Let $$y

An expression for a dimensionless quantity P is given by $$P = {\alpha \over \beta }{\log _e}\left( {{{kt} \over {\beta

A person is standing in an elevator. In which situation, he experiences weight loss?

An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero?

A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio of the centrip

A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 rads$$-$$1 in a horizontal pl

The variation of acceleration due to gravity (g) with distance (r) from the center of the earth is correctly represented

Time period of a simple pendulum in a stationary lift is 'T'. If the lift accelerates with $${g \over 6}$$ vertically up

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving

Two capacitors having capacitance C1 and C2 respectively are connected as shown in figure. Initially, capacitor C1 is ch

Given below two statements : One is labelled as Assertion (A) and other is labelled as Reason (R). Assertion (A) : Non-p

The magnetic flux through a coil perpendicular to its plane is varying according to the relation $$\phi = (5{t^3} + 4{t

An aluminium wire is stretched to make its length, 0.4% larger. The percentage change in resistance is :

A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to t

If Electric field intensity of a uniform plane electromagnetic wave is given as $$E = - 301.6\sin (kz - \omega t){\wide

In free space, an electromagnetic wave of 3 GHz frequency strikes over the edge of an object of size $${\lambda \over {

An electron with speed v and a photon with speed c have the same de-Broglie wavelength. If the kinetic energy and moment

The I-V characteristics of a p-n junction diode in forward bias is shown in the figure. The ratio of dynamic resistance,

A fighter jet is flying horizontally at a certain altitude with a speed of 200 ms$$-$$1. When it passes directly overhea

A ball of mass 0.5 kg is dropped from the height of 10 m. The height, at which the magnitude of velocity becomes equal t

The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a

The elongation of a wire on the surface of the earth is 10$$-$$4 m. The same wire of same dimensions is elongated by 6 $

A 10 $$\Omega$$, 20 mH coil carrying constant current is connected to a battery of 20 V through a switch. Now after swit

A light ray is incident, at an incident angle $$\theta$$1, on the system of tow plane mirrors M1 and M2 having an inclin

In a vernier callipers, each cm on the main scale is divided into 20 equal parts. If tenth vernier scale division coinci

As per the given circuit, the value of current through the battery will be ____________ A.

A 110 V, 50 Hz, AC source is connected in the circuit (as shown in figure). The current through the resistance 55 $$\Ome

An ideal fluid of density 800 kgm$$-$$3, flows smoothly through a bent pipe (as shown in figure) that tapers in cross-se