Given below are two statements : Statement I : Boron is extremely hard indicating its high lattice energy. Statement II

The density of alkali metals is in the order :

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The two products formed in above reaction are -

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The bond order and magnetic property of acetylide ion are same as that of

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

'A' in the above reaction is:

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Given below are two statement: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathbf

A metal chloride contains $$55.0 \%$$ of chlorine by weight . $$100 \mathrm{~mL}$$ vapours of the metal chloride at STP

Four gases A, B, C and D have critical temperatures $$5.3,33.2,126.0$$ and $$154.3 \mathrm{~K}$$ respectively. For their

Correct statements for the given reaction are : A. Compound '$$\mathrm{B}$$' is aromatic B. The completion of above rea

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The incorrect statement regarding the reaction given below is

For lead storage battery pick the correct statements A. During charging of battery, $$\mathrm{PbSO}_{4}$$ on anode is co

Given below are two statements : Statement I : $$\mathrm{SbCl}_{5}$$ is more covalent than $$\mathrm{SbCl}_{3}$$ Stateme

In the following reaction 'A' is

The major product 'P' formed in the following sequence of reactions is

In the given reaction cycle X, Y and Z respectively are :

In an oligopeptide named Alanylglycylphenyl alanyl isoleucine, the number of $$\mathrm{sp}^{2}$$ hybridised carbons is _

80 mole percent of $$\mathrm{MgCl}_{2}$$ is dissociated in aqueous solution. The vapour pressure of $$1.0 ~\mathrm{molal

Values of work function (W$$_0$$) for a few metals are given below .tg {border-collapse:collapse;border-spacing:0;} .t

At $$600 \mathrm{~K}$$, the root mean square (rms) speed of gas $$\mathrm{X}$$ (molar mass $$=40$$ ) is equal to the mos

Three organic compounds A, B and $$\mathrm{C}$$ were allowed to run in thin layer chromatography using hexane and gave t

The value of $$x$$ in compound 'D' is _________.

The mass of NH$$_3$$ produced when 131.8 kg of cyclohexanecarbaldehyde undergoes Tollen's test is ________ kg. (Nearest

The reaction $$2 \mathrm{NO}+\mathrm{Br}_{2} \rightarrow 2 \mathrm{NOBr}$$ takes places through the mechanism given belo

An analyst wants to convert $$1 \mathrm{~L} \mathrm{~HCl}$$ of $$\mathrm{pH}=1$$ to a solution of $$\mathrm{HCl}$$ of $$

One mole of an ideal gas at $$350 \mathrm{~K}$$ is in a $$2.0 \mathrm{~L}$$ vessel of thermally conducting walls, which

Two dice A and B are rolled. Let the numbers obtained on A and B be $$\alpha$$ and $$\beta$$ respectively. If the varia

Let $$A=\left[\begin{array}{cc}1 & \frac{1}{51} \\ 0 & 1\end{array}\right]$$. If $$\mathrm{B}=\left[\begin{array}{cc}1 &

Let $$y=y(x), y > 0$$, be a solution curve of the differential equation $$\left(1+x^{2}\right) \mathrm{d} y=y(x-y) \math

Let the lines $$l_{1}: \frac{x+5}{3}=\frac{y+4}{1}=\frac{z-\alpha}{-2}$$ and $$l_{2}: 3 x+2 y+z-2=0=x-3 y+2 z-13$$ be co

If $$\frac{1}{n+1}{ }^{n} \mathrm{C}_{n}+\frac{1}{n}{ }^{n} \mathrm{C}_{n-1}+\ldots+\frac{1}{2}{ }^{n} \mathrm{C}_{1}+{

Let $$ $$ be a sequence such that $$a_{1}+a_{2}+\ldots+a_{n}=\frac{n^{2}+3 n}{(n+1)(n+2)}$$. If $$28 \sum_\limits{k=1}^{

The number of five digit numbers, greater than 40000 and divisible by 5 , which can be formed using the digits $$0,1,3,5

Let $$\mathrm{C}$$ be the circle in the complex plane with centre $$\mathrm{z}_{0}=\frac{1}{2}(1+3 i)$$ and radius $$r=1

Among the two statements $$(\mathrm{S} 1):(p \Rightarrow q) \wedge(p \wedge(\sim q))$$ is a contradiction and $$(\mathrm

Let $$a, b, c$$ be three distinct real numbers, none equal to one. If the vectors $$a \hat{i}+\hat{\mathrm{j}}+\hat{\mat

Let $$\lambda \in \mathbb{Z}, \vec{a}=\lambda \hat{i}+\hat{j}-\hat{k}$$ and $$\vec{b}=3 \hat{i}-\hat{j}+2 \hat{k}$$. Let

If the point $$\left(\alpha, \frac{7 \sqrt{3}}{3}\right)$$ lies on the curve traced by the mid-points of the line segmen

Let $$\alpha, \beta$$ be the roots of the quadratic equation $$x^{2}+\sqrt{6} x+3=0$$. Then $$\frac{\alpha^{23}+\beta^{2

Let $$\mathrm{P}\left(\frac{2 \sqrt{3}}{\sqrt{7}}, \frac{6}{\sqrt{7}}\right), \mathrm{Q}, \mathrm{R}$$ and $$\mathrm{S}$

The sum, of the coefficients of the first 50 terms in the binomial expansion of $$(1-x)^{100}$$, is equal to

If the local maximum value of the function $$f(x)=\left(\frac{\sqrt{3 e}}{2 \sin x}\right)^{\sin ^{2} x}, x \in\left(0,

Let the plane P: $$4 x-y+z=10$$ be rotated by an angle $$\frac{\pi}{2}$$ about its line of intersection with the plane $

The area of the region enclosed by the curve $$y=x^{3}$$ and its tangent at the point $$(-1,-1)$$ is :

In a triangle ABC, if $$\cos \mathrm{A}+2 \cos \mathrm{B}+\cos C=2$$ and the lengths of the sides opposite to the angles

Let $$\mathrm{D}$$ be the domain of the function $$f(x)=\sin ^{-1}\left(\log _{3 x}\left(\frac{6+2 \log _{3} x}{-5 x}\ri

Let $$\mathrm{D}_{\mathrm{k}}=\left|\begin{array}{ccc}1 & 2 k & 2 k-1 \\ n & n^{2}+n+2 & n^{2} \\ n & n^{2}+n & n^{2}+n+

Let the digits a, b, c be in A. P. Nine-digit numbers are to be formed using each of these three digits thrice such that

Two circles in the first quadrant of radii $$r_{1}$$ and $$r_{2}$$ touch the coordinate axes. Each of them cuts off an i

A fair $$n(n > 1)$$ faces die is rolled repeatedly until a number less than $$n$$ appears. If the mean of the number of

If $$\int_\limits{-0.15}^{0.15}\left|100 x^{2}-1\right| d x=\frac{k}{3000}$$, then $$k$$ is equal to ___________.

The number of relations, on the set $$\{1,2,3\}$$ containing $$(1,2)$$ and $$(2,3)$$, which are reflexive and transitive

Let the plane $$x+3 y-2 z+6=0$$ meet the co-ordinate axes at the points A, B, C. If the orthocenter of the triangle $$\m

Let $$[x]$$ be the greatest integer $$\leq x$$. Then the number of points in the interval $$(-2,1)$$, where the function

Let the positive numbers $$a_{1}, a_{2}, a_{3}, a_{4}$$ and $$a_{5}$$ be in a G.P. Let their mean and variance be $$\fra

Let $$I(x)=\int \sqrt{\frac{x+7}{x}} \mathrm{~d} x$$ and $$I(9)=12+7 \log _{e} 7$$. If $$I(1)=\alpha+7 \log _{e}(1+2 \sq

A particle is executing simple harmonic motion (SHM). The ratio of potential energy and kinetic energy of the particle w

Given below are two statements: Statement I : A truck and a car moving with same kinetic energy are brought to rest by a

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Given below are two statements: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathb

In an n-p-n common emitter (CE) transistor the collector current changes from 5 $$\mathrm{mA}$$ to $$16 \mathrm{~mA}$$ f

The ratio of escape velocity of a planet to the escape velocity of earth will be:- Given: Mass of the planet is 16 times

Two satellites $$\mathrm{A}$$ and $$\mathrm{B}$$ move round the earth in the same orbit. The mass of $$\mathrm{A}$$ is t

An engine operating between the boiling and freezing points of water will have A. efficiency more than 27%. B. efficienc

Three forces $$F_{1}=10 \mathrm{~N}, F_{2}=8 \mathrm{~N}, \mathrm{~F}_{3}=6 \mathrm{~N}$$ are acting on a particle of ma

A body cools from $$80^{\circ} \mathrm{C}$$ to $$60^{\circ} \mathrm{C}$$ in 5 minutes. The temperature of the surroundin

An ice cube has a bubble inside. When viewed from one side the apparent distance of the bubble is $$12 \mathrm{~cm}$$. W

A proton and an $$\alpha$$-particle are accelerated from rest by $$2 \mathrm{~V}$$ and $$4 \mathrm{~V}$$ potentials, res

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

Given below are two statements: Statement I : The diamagnetic property depends on temperature. Statement II : The induce

A wire of resistance $$160 ~\Omega$$ is melted and drawn in a wire of one-fourth of its length. The new resistance of th

A ball is thrown vertically upward with an initial velocity of $$150 \mathrm{~m} / \mathrm{s}$$. The ratio of velocity a

If the r. m.s speed of chlorine molecule is $$490 \mathrm{~m} / \mathrm{s}$$ at $$27^{\circ} \mathrm{C}$$, the r. m. s s

A $$12.5 \mathrm{~eV}$$ electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral li

The amplitude of $$15 \sin (1000 \pi \mathrm{t})$$ is modulated by $$10 \sin (4 \pi \mathrm{t})$$ signal. The amplitude

Given below are two statements: Statement I : When the frequency of an a.c source in a series LCR circuit increases, the

To maintain a speed of 80 km/h by a bus of mass 500 kg on a plane rough road for 4 km distance, the work done by the eng

64 identical drops each charged upto potential of $$10 ~\mathrm{mV}$$ are combined to form a bigger drop. The potential

For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is $$\frac{x}{5}$$. The v

The current flowing through a conductor connected across a source is $$2 \mathrm{~A}$$ and 1.2 $$\mathrm{A}$$ at $$0^{\c

A compass needle oscillates 20 times per minute at a place where the dip is $$30^{\circ}$$ and 30 times per minute where

Glycerin of density $$1.25 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}$$ is flowing through the conical section of pipe

Two convex lenses of focal length $$20 \mathrm{~cm}$$ each are placed coaxially with a separation of $$60 \mathrm{~cm}$$

For a certain organ pipe, the first three resonance frequencies are in the ratio of $$1:3:5$$ respectively. If the frequ

A common example of alpha decay is $${ }_{92}^{238} \mathrm{U} \longrightarrow{ }_{90}^{234} \mathrm{Th}+{ }_{2} \mathrm

A conducting circular loop is placed in a uniform magnetic field of $$0.4 \mathrm{~T}$$ with its plane perpendicular to