In dilute aqueous H2SO4, the complex diaquodioxalatoferrate(II) is oxidized by $$MnO_4^-$$. For this reaction, the ratio

A closed vessel with rigid walls contains 1 mol of $${}_{92}^{238}U$$ and 1 mol of air at 298 K. Considering complete de

The molar conductivity of a solution of a weak acid HX (0.01 M) is 10 times smaller than the molar conductivity of a sol

When O2 is adsorbed on a metallic surface, electron transfer occurs from the metal to O2. The true statement(s) regardin

Paragraph When 100 mL of 1.0 M KCl was mixed with 100 mL of 1.0 M NaOH in an insulated beaker at constant pressure, a te

Paragraph When 100 mL of 1.0 M HCl was mixed with 100 mL of 1.0 M NaOH in an insulated beaker at constant pressure, a te

The number of hydroxyl group(s) in Q is ___________.

Among the following the number of reactions that produces benzaldehyde is _________.

In the complex acetylbromidodicarbonylbis(triethylphosphine) iron(II), the number of Fe-C bond(s) is ___________.

Among the complex ions, [Co(NH2-CH2-CH2-NH2)2Cl2]+, [CrCl2(C2O4)2]3$$-$$, [Fe(H2O)4)OH)2]+, [Fe(NH3)2(CN)4]$$-$$, [Co(NH

Three moles of B2H6 are completely reacted with methanol. The number of moles of boron containing product formed is ____

In the following reactions, the product S is

The major product U in the following reactions is

In the following reactions, the major product W is

The correct statements regarding (i) HClO, (ii) HClO2, (iii) HClO3 and (iv) HClO4 is (are)

The pairs of ions where BOTH the ions are precipitated upon passing H2S gas in presence of dilute HCl, is(are)

Under hydrolytic conditions, the compounds used for preparation of linear polymer and for chain termination, respectivel

One mole of a monoatomic real gas satisfies the equation p(V $$-$$ b) = RT where b is a constant. The relationship of in

In the following reactions Compound X is

In the following reactions The major compound Y is

Let $$S$$ be the set of all non-zero real numbers $$\alpha $$ such that the quadratic equation $$\alpha {x^2} - x + \alp

For any integer k, let $${a_k} = \cos \left( {{{k\pi } \over 7}} \right) + i\,\,\sin \left( {{{k\pi } \over 7}} \right)$

Suppose that $$\overrightarrow p ,\overrightarrow q $$ and $$\overrightarrow r $$ are three non-coplanar vectors in $${R

Let $${n_1}$$ and $${n_2}$$ be the number of red and black balls, respectively, in box $${\rm I}$$. Let $${n_3}$$ and $

Let $${n_1}$$ and $${n_2}$$ be the number of red and black balls, respectively, in box $${\rm I}$$. Let $${n_3}$$ and $

Let $$f:R \to R$$ be a continuous odd function, which vanishes exactly at one point and $$f\left( 1 \right) = {1 \over {

Suppose that all the terms of an arithmetic progression (A.P) are natural numbers. If the ratio of the sum of the first

The coefficient of $${x^9}$$ in the expansion of (1 + x) (1 + $${x^2)}$$ (1 + $${x^3}$$) ....$$(1 + {x^{100}})$$ is

Let $${E_1}$$ and $${E_2}$$ be two ellipses whose centres are at the origin. The major axes of $${E_1}$$ and $${E_2}$$ l

Consider the hyperbola $$H:{x^2} - {y^2} = 1$$ and a circle $$S$$ with center $$N\left( {{x_2},0} \right)$$. Suppose tha

Suppose that the foci of the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 5} = 1$$ are $$\left( {{f_1},0} \right)$$ and

If $$\alpha $$ $$ = 3{\sin ^{ - 1}}\left( {{6 \over {11}}} \right)$$ and $$\beta = 3{\cos ^{ - 1}}\left( {{4 \over 9}}

Let $$f, g :$$ $$\left[ { - 1,2} \right] \to R$$ be continuous functions which are twice differentiable on the interval

Let $$f\left( x \right) = 7{\tan ^8}x + 7{\tan ^6}x - 3{\tan ^4}x - 3{\tan ^2}x$$ for all $$x \in \left( { - {\pi \over

The option(s) with the values of a and $$L$$ that satisfy the following equation is (are) $$${{\int\limits_0^{4\pi } {{

Let $$f'\left( x \right) = {{192{x^3}} \over {2 + {{\sin }^4}\,\pi x}}$$ for all $$x \in R\,\,$$ with $$f\left( {{1 \ove

Let $$F:R \to R$$ be a thrice differentiable function. Suppose that $$F\left( 1 \right) = 0,F\left( 3 \right) = - 4$$

Let $$F:R \to R$$ be a thrice differentiable function. Suppose that $$F\left( 1 \right) = 0,F\left( 3 \right) = - 4$$

If $$\alpha = \int\limits_0^1 {\left( {{e^{9x + 3{{\tan }^{ - 1}}x}}} \right)\left( {{{12 + 9{x^2}} \over {1 + {x^2}}}}

Let m and n be two positive integers greater than 1. If $$$\mathop {\lim }\limits_{\alpha \to 0} \left( {{{{e^{\cos \le

Consider a uniform spherical charge distribution of radius $${R_1}$$ centred at the origin $$O.$$ In this distribution,

A spherical body of radius R consists of a fluid of constant density and is in equilibrium under its own gravity. If P(r

The densities of two solid spheres A and B of the same radii R vary with radial distance r as $${\rho _A}(r) = k\left( {

The energy of a system as a function of time t is given as E(t) = $${A^2}\exp \left( { - \alpha t} \right)$$, where $$\a

In terms of potential difference V, electric current I, permittivity $${\varepsilon _0}$$, permeability $${\mu _0}$$ and

Four harmonic waves of equal frequencies and equal intensities I0 have phase angles 0, $${\pi \over 3},{{2\pi } \over 3

For a radioactive material, its activity A and rate of change of its activity R are defined as $$A = - {{dN} \over {dt}

A monochromatic beam of light is incident at 60$$^\circ$$ on one face of an equilateral prism of refractive index n and

In the following circuit, the current through the resistor R(=2$$\Omega$$) is I amperes. The value of I is :

An electron in an excited state of Li2+ ion has angular momentum $${{3h} \over {2\pi }}$$. The de Broglie wavelength of

A large spherical mass M is fixed at one position and two identical masses m are kept on a line passing through the cent

In plotting stress versus strain curves for two materials P and Q, a student by mistake puts strain on the y-axis and st

A parallel plate capacitor having plates of area S and plate separation d, has capacitance C1 in air. When two dielectri

An ideal monoatomic gas is confined in a horizontal cylinder by a spring loaded piston (as shown in the figure). Initial

A fission reaction is given by $$_{92}^{236}U \to _{54}^{140}Xe + _{38}^{94}Sr + x + y$$, where x and y are two particle

Two spheres P and Q for equal radii have densities $$\rho$$1 and $$\rho$$2, respectively. The spheres are connected by a

For two structures namely S1 with n1 = $${{\sqrt {45} } \over 4}$$ and n2 = $${3 \over 2}$$, and S2 with n1 = $${8 \over

If two structures of same cross-sectional area, but different numeral apertures NA1 and NA2 (NA2 < NA1) are joined lo

Consider two different metallic strips (1 and 2) of the same material. Their lengths are the same, widths are w1 and w2

Consider two different metallic strips (1 and 2) of same dimensions (length l, width w and thickness d) with carrier den