Which of the following is the correct plot for the probability density $${\psi ^2}$$ (r) as a function of distance 'r' o

Consider the species CH4, NH$$_4^ + $$ and BH$$_4^ - $$. Choose the correct option with respect to the these species.

4.0 moles of argon and 5.0 moles of PCl5 are introduced into an evacuated flask of 100 litre capacity at 610 K. The syst

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

Given below are two statements. $$\bullet$$ Statement I : In CuSO4 . 5H2O, Cu-O bonds are present. $$\bullet$$ Statement

Number of lone pair(s) of electrons on central atom and the shape BrF3 molecule respectively, are

Sulphur dioxide is one of the components of polluted air. SO2 is also a major contributor to acid rain. The correct and

Which of the following carbocations is most stable?

The stable carbocation formed in the above reaction is

Two isomers (A) and (B) with Molar mass 184 g/mol and elemental composition C, 52.2%; H, 4.9% and Br 42.9% gave benzoic

In Friedel-Crafts alkylation of aniline, one gets

The structure of protein that is unaffected by heating is

A white precipitate was formed when BaCl2 was added to water extract of an inorganic salt. Further, a gas 'X' with chara

A box contains 0.90 g of liquid water in equilibrium with water vapour at 27$$^\circ$$C. The equilibrium vapour pressure

2.2 g of nitrous oxide (N2O) gas is cooled at a constant pressure of 1 atm from 310 K to 270 K causing the compression o

Elevation in boiling point for 1.5 molal solution of glucose in water is 4 K. The depression in freezing point for 4.5 m

The cell potential for the given cell at 298 K Pt| H2 (g, 1 bar) | H+ (aq) || Cu2+ (aq) | Cu(s) is 0.31 V. The pH of the

The equation k = (6.5 $$\times$$ 1012s$$-$$1)e$$-$$26000K/T is followed for the decomposition of compound A. The activat

Spin only magnetic moment of [MnBr6]4$$-$$ is _________ B.M. (round off to the closest integer)

For the reaction given below : CoCl3 . xNH3 + AgNO3 (aq) $$\to$$ If two equivalents of AgCl precipitate out, then the va

The number of chiral alcohol(s) with molecular formula C4H10O is ________.

In the given reaction, the number of sp2 hybridised carbon(s) in compound 'X' is ________.

In the given reaction, The number of $$\pi$$ electrons present in the product 'P' is _________.

Let $$\alpha$$ be a root of the equation 1 + x2 + x4 = 0. Then, the value of $$\alpha$$1011 + $$\alpha$$2022 $$-$$ $$\al

Let arg(z) represent the principal argument of the complex number z. Then, |z| = 3 and arg(z $$-$$ 1) $$-$$ arg(z + 1) =

The value of $$\mathop {\lim }\limits_{x \to 1} {{({x^2} - 1){{\sin }^2}(\pi x)} \over {{x^4} - 2{x^3} + 2x - 1}}$$ is e

Let f be a real valued continuous function on [0, 1] and $$f(x) = x + \int\limits_0^1 {(x - t)f(t)dt} $$. Then, which of

If $$\int\limits_0^2 {\left( {\sqrt {2x} - \sqrt {2x - {x^2}} } \right)dx = \int\limits_0^1 {\left( {1 - \sqrt {1 - {y^

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

Let a triangle ABC be inscribed in the circle $${x^2} - \sqrt 2 (x + y) + {y^2} = 0$$ such that $$\angle BAC = {\pi \ov

The distance of the origin from the centroid of the triangle whose two sides have the equations $$x - 2y + 1 = 0$$ and $

Let A, B, C be three points whose position vectors respectively are $$\overrightarrow a = \widehat i + 4\widehat j + 3\

The probability that a relation R from {x, y} to {x, y} is both symmetric and transitive, is equal to :

The number of values of a $$\in$$ N such that the variance of 3, 7, 12, a, 43 $$-$$ a is a natural number is :

Let  $$\overrightarrow a = \widehat i - 2\widehat j + 3\widehat k$$,   $$\overrightarrow b = \widehat i

Let y = y(x), x > 1, be the solution of the differential equation $$(x - 1){{dy} \over {dx}} + 2xy = {1 \over {x - 1}}$$

Let 3, 6, 9, 12, ....... upto 78 terms and 5, 9, 13, 17, ...... upto 59 terms be two series. Then, the sum of the terms

For real numbers a, b (a > b > 0), let Area $$\left\{ {(x,y):{x^2} + {y^2} \le {a^2}\,and\,{{{x^2}} \over {{a^2}}} + {{{

Let f and g be twice differentiable even functions on ($$-$$2, 2) such that $$f\left( {{1 \over 4}} \right) = 0$$, $$f\l

Let the coefficients of x$$-$$1 and x$$-$$3 in the expansion of $${\left( {2{x^{{1 \over 5}}} - {1 \over {{x^{{1 \over 5

The total number of four digit numbers such that each of first three digits is divisible by the last digit, is equal to

Let $$M = \left[ {\matrix{ 0 & { - \alpha } \cr \alpha & 0 \cr } } \right]$$, where $$\alpha$$ is a non-zer

Let f(x) and g(x) be two real polynomials of degree 2 and 1 respectively. If $$f(g(x)) = 8{x^2} - 2x$$ and $$g(f(x)) = 4

A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10m in t

At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6

Two point charges Q each are placed at a distance d apart. A third point charge q is placed at a distance x from mid-poi

The speed of light in media 'A' and 'B' are $$2.0 \times {10^{10}}$$ cm/s and $$1.5 \times {10^{10}}$$ cm/s respectively

The electric field at a point associated with a light wave is given by E = 200 [sin (6 $$\times$$ 1015)t + sin (9 $$\tim

A capacitor is discharging through a resistor R. Consider in time t1, the energy stored in the capacitor reduces to half

Starting with the same initial conditions, an ideal gas expands from volume V1 to V2 in three different ways. The work d

Two long current carrying conductors are placed to each other at a distance of 8 cm between them. The magnitude of magne

The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased t

The motion of a simple pendulum executing S.H.M. is represented by the following equation. $$y = A\sin (\pi t + \phi )$$

A vessel contains 16g of hydrogen and 128g of oxygen at standard temperature and pressure. The volume of the vessel in c

Given below are two statements : Statement I : The electric force changes the speed of the charged particle and hence ch

A block of mass 40 kg slides over a surface, when a mass of 4 kg is suspended through an inextensible massless string pa

In the given figure, the block of mass m is dropped from the point 'A'. The expression for kinetic energy of block when

A block of mass M placed inside a box descends vertically with acceleration 'a'. The block exerts a force equal to one-f

If the electric potential at any point (x, y, z) m in space is given by V = 3x2 volt. The electric field at the point (1

The combination of two identical cells, whether connected in series or parallel combination provides the same current th

A person can throw a ball upto a maximum range of 100 m. How high above the ground he can throw the same ball?

The Vernier constant of Vernier callipers is 0.1 mm and it has zero error of ($$-$$0.05) cm. While measuring diameter of

A small spherical ball of radius 0.1 mm and density 104 kg m$$-$$3 falls freely under gravity through a distance h befo

In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonan

Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance 2000 $$\Omega$$

A potential barrier of 0.4 V exists across a p-n junction. An electron enters the junction from the n-side with a speed

The displacement current of 4.425 $$\mu$$A is developed in the space between the plates of parallel plate capacitor when

The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is I1. The same rod is be

In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the

An inductor of 0.5 mH, a capacitor of 200 $$\mu$$F and a resistor of 2 $$\Omega$$ are connected in series with a 220 V a