The first and second ionisation enthalpies of a metal are 496 and 4560 kJ mol–1, respectively. How many moles of HCl and

Which of the following reactions will not produce a racemic product?

In the following reaction A is :

The correct order of the spin-only magnetic moments of the following complexes is : (I) [Cr(H2O)6]Br2 (II) Na4[Fe(CN)6]

Which of the following has the shortest C-Cl bond?

In the figure shown below reactant A (represented by square) is in equilibrium with product B (represented by circle). T

The decreasing order of basicity of the following amines is :

The solubility product of Cr(OH)3 at 298 K is 6.0 × 10–31. The concentration of hydroxide ions in a saturated solution o

5 g of zinc is treated separately with an excess of (a) dilute hydrochloric acid and (b) aqueous sodium hydroxide. The r

Consider the following reactions, The compound [P] is :

A, B and C are three biomolecules. The results of the tests performed on them are given below: $$ \begin{array}{|l|l|l|l

The reaction of H3N3B3Cl3 (A) with LiBH4 in tetrahydrofuran gives inorganic benzene (B). Further, the reaction of (A) wi

The isomer(s) of [Co(NH3)4Cl2] that has/have a Cl–Co–Cl angle of 90°, is/are :

The number of sp2 hybrid orbitals in a molecule of benzene is :

The true statement amongst the following is :

A cylinder containing an ideal gas (0.1 mol of 1.0 dm3) is in thermal equilibrium with a large volume of 0.5 molal aqueo

A sample of milk splits after 60 min. at 300 K and after 40 min. at 400 K when the population of lactobacillus acidophil

The sum of the total number of bonds between chromium and oxygen atoms in chromate and dichromate ions is ____________.

10.30 mg of O2 is dissolved into a liter of sea water of density 1.03 g/mL. The concentration of O2 in ppm is__________.

Consider the following reactions The mass percentage of carbon in A is ______.

Let [t] denote the greatest integer $$ \le $$ t and $$\mathop {\lim }\limits_{x \to 0} x\left[ {{4 \over x}} \right] = A

The following system of linear equations 7x + 6y – 2z = 0 3x + 4y + 2z = 0 x – 2y – 6z = 0, has

Let a, b $$ \in $$ R, a $$ \ne $$ 0 be such that the equation, ax2 – 2bx + 5 = 0 has a repeated root $$\alpha $$, which

A random variable X has the following probability distribution : .tg {border-collapse:collapse;border-spacing:0;width:

If $$x = 2\sin \theta - \sin 2\theta $$ and $$y = 2\cos \theta - \cos 2\theta $$, $$\theta \in \left[ {0,2\pi } \righ

Given : $$f(x) = \left\{ {\matrix{ {x\,\,\,\,\,,} & {0 \le x < {1 \over 2}} \cr {{1 \over 2}\,\,\,\,,} &a

If $$x = \sum\limits_{n = 0}^\infty {{{\left( { - 1} \right)}^n}{{\tan }^{2n}}\theta } $$ and $$y = \sum\limits_{n = 0

If A = {x $$ \in $$ R : |x| < 2} and B = {x $$ \in $$ R : |x – 2| $$ \ge $$ 3}; then :

If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes conta

Let a function ƒ : [0, 5] $$ \to $$ R be continuous, ƒ(1) = 3 and F be defined as : $$F(x) = \int\limits_1^x {{t^2}g(t)d

If $${{dy} \over {dx}} = {{xy} \over {{x^2} + {y^2}}}$$; y(1) = 1; then a value of x satisfying y(x) = e is :

If $$\int {{{d\theta } \over {{{\cos }^2}\theta \left( {\tan 2\theta + \sec 2\theta } \right)}}} = \lambda \tan \theta

If z be a complex number satisfying |Re(z)| + |Im(z)| = 4, then |z| cannot be :

Let a – 2b + c = 1. If $$f(x)=\left| {\matrix{ {x + a} & {x + 2} & {x + 1} \cr {x + b} & {x + 3} &am

In the expansion of $${\left( {{x \over {\cos \theta }} + {1 \over {x\sin \theta }}} \right)^{16}}$$, if $${\ell _1}$$ i

The number of terms common to the two A.P.'s 3, 7, 11, ....., 407 and 2, 9, 16, ....., 709 is ______.

Let $$\overrightarrow a $$, $$\overrightarrow b $$ and $$\overrightarrow c $$ be three vectors such that $$\left| {\over

Let an be the nth term of a G.P. of positive terms. $$\sum\limits_{n = 1}^{100} {{a_{2n + 1}} = 200} $$ and $$\sum\limit

Let ƒ and g be differentiable functions on R such that fog is the identity function. If for some a, b $$ \in $$ R, g'(a)

If the curves, x2 – 6x + y2 + 8 = 0 and x2 – 8y + y2 + 16 – k = 0, (k > 0) touch each other at a point, then the larg

A wire of length L and mass per unit length 6.0 × 10–3 kgm–1 is put under tension of 540 N. Two consecutive frequencies

A spring mass system (mass m, spring constant k and natural length $$l$$) rest in equilibrium on a horizontal disc. The

A rod of length L has non-uniform linear mass density given by $$\rho $$(x) = $$a + b{\left( {{x \over L}} \right)^2}$$

An electron gun is placed inside a long solenoid of radius R on its axis. The solenoid has n turns/length and carries a

A plane electromagnetic wave is propagating along the direction $${{\widehat i + \widehat j} \over {\sqrt 2 }}$$ , with

A small spherical droplet of density d is floating exactly half immersed in a liquid of density $$\rho $$ and surface te

A small circular loop of conducting wire has radius a and carries current I. It is placed in a uniform magnetic field B

The current i in the network is :

In LC circuit the inductance L = 40 mH and capacitance C = 100 $$\mu $$F. If a voltage V(t) = 10sin(314t) is applied to

There is a small source of light at some depth below the surface of water (refractive index = $${4 \over 3}$$) in a tank

Two gases-argon (atomic radius 0.07 nm, atomic weight 40) and xenon (atomic radius 0.1 nm, atomic weight 140) have the s

A particle of mass m is projected with a speed u from the ground at an angle $$\theta = {\pi \over 3}$$ w.r.t. horizon

A particle starts from the origin at t = 0 with an initial velocity of 3.0 $$\widehat i$$ m/s and moves in the x-y plane

The energy required to ionise a hydrogen like ion in its ground state is 9 Rydbergs. What is the wavelength of the radia

Two identical capacitors A and B, charged to the same potential 5V are connected in two different circuits as shown belo

A uniformly thick wheel with moment of inertia I and radius R is free to rotate about its centre of mass (see fig). A ma

Planet A has mass M and radius R. Planet B has half the mass and half the radius of Planet A. If the escape velocities f

For the four sets of three measured physical quantities as given below. Which of the following options is correct ? (i)

Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored

An electron of mass m and magnitude of charge |e| initially at rest gets accelerated by a constant electric field E. The

Starting at temperature 300 K, one mole of an ideal diatomic gas ($$\gamma $$ = 1.4) is first compressed adiabatically f

In a meter bridge experiment S is a standard resistance. R is a resistance wire. It is found that balancing length is $$

The circuit shown below is working as a 8 V dc regulated voltage source. When 12 V is used as input, the power dissipate

In a Young's double slit experiment 15 fringes are observed on a small portion of the screen when light of wavelength 50

An electric field $$\overrightarrow E = 4x\widehat i - \left( {{y^2} + 1} \right)\widehat j$$ N/C passes through the bo