For a first-order reaction A $$\to$$ P, the temperature (T) dependent rate constant (k) was found to follow the equation

The spin only magnetic moment value (in Bohr magneton units) of Cr(CO)$$_6$$ is

In the following carbocation, H/CH$$_3$$ that is most likely to migrate to the positively charged carbon is :

The correct stability order of the following resonance structures is

For the reduction of NO$$_3^ - $$ ion in an aqueous solution, E$$^0$$ is + 0.96 V. Values of E$$^0$$ for some metal ions

Among the following, the state function(s) is(are)

In the reaction $$\mathrm{2X+B_2H_6\to[BH_2(X)_2]^+[BH_4]^-}$$ the amine(s) X is(are) :

The nitrogen oxide(s) that contain(s) N-N bond(s) is(are)

The correct statement(s) about the following sugar X and Y is(are)

Match each of the reactions given in Column I with the corresponding product(s) given in Column II: .tg {border-collap

Match each of the compounds given in Column I with the reaction(s), that they can undergo, given in Column II. .tg {bo

In a constant volume calorimeter, 3.5 g of a gas with molecular weight 28 was burnt in excess oxygen at 298.0 K. The tem

At 400 K, the root mean square (rms) speed of a gas X (molecular weight = 40) is equal to the most probable speed of gas

The dissociation constant of a substituted benzoic acid at 25$$^\circ$$C is 1.0 $$\times$$ 10$$^{-4}$$. The pH of a 0.01

The total number of $$\alpha$$ and $$\beta$$ particles emitted in the nuclear reaction $$_{92}^{238}U \to _{82}^{214}Pb$

The oxidation number of Mn in the product of alkaline oxidative fusion of MnO$$_2$$ is ___________.

The number of water molecule(s) directly bonded to the centre in CuSO$$_4$$ . 5H$$_2$$O is __________.

The coordination number of Al in the crystalline state of AlCl$$_3$$ is ___________.

The total number of cyclic structural as well as stereoisomers possible for a compound with the molecular formula C$$_5$

For $$0 < \theta < {\pi \over 2},$$ the solution (s) of $$$\sum\limits_{m = 1}^6 {\cos ec\,\left( {\theta + {{

Let $$\left( {x,\,y,\,z} \right)$$ be points with integer coordinates satisfying the system of homogeneous equation: $$

The smallest value of $$k$$, for which both the roots of the equation $$${x^2} - 8kx + 16\left( {{k^2} - k + 1} \right)

If the sum of first $$n$$ terms of an A.P. is $$c{n^2}$$, then the sum of squares of these $$n$$ terms is

The centres of two circles $${C_1}$$ and $${C_2}$$ each of unit radius are at a distance of 6 units from each other. Let

The normal at a point $$P$$ on the ellipse $${x^2} + 4{y^2} = 16$$ meets the $$x$$- axis $$Q$$. If $$M$$ is the mid poin

The tangent $$PT$$ and the normal $$PN$$ to the parabola $${y^2} = 4ax$$ at a point $$P$$ on it meet its axis at points

An ellipse intersects the hyperbola $$2{x^2} - 2{y^2} = 1$$ orthogonally. The eccentricity of the ellipse is reciprocal

If the function $$f(x) = {x^3} + {e^{x/2}}$$ and $$g(x) = {f^{ - 1}}(x)$$, then the value of $$g'(1)$$ is _________.

Let ABC and ABC' be two non-congruent triangles with sides AB = 4, AC = AC' = 2$$\sqrt2$$ and angle B = 30$$^\circ$$. Th

For the function $$$f\left( x \right) = x\cos \,{1 \over x},x \ge 1,$$$

Let $$p(x)$$ be a polynomial of degree $$4$$ having extremum at $$x = 1,2$$ and $$\mathop {\lim }\limits_{x \to 0} \lef

The maximum value of the function $$f(x) = 2{x^3} - 15{x^2} + 36x - 48$$ on the set $$A = \{ x|{x^2} + 20 \le 9x|\} $$ i

If $${I_n} = \int\limits_{ - \pi }^\pi {{{\sin nx} \over {(1 + {\pi ^x})\sin x}}dx,n = 0,1,2,} $$ .... then

Let $$f:R \to R$$ be a continuous function which satisfies $$f(x) = \int\limits_0^x {f(t)dt} $$. Then, the value of $$f(

A line with positive direction cosines passes through the point P(2, $$-$$1, 2) and makes equal angles with the coordina

Match the statements/expressions in Column I with the values given in Column II: .tg {border-collapse:collapse;border-

Match the statements/expressions in Column I with the values given in Column II: .tg {border-collapse:collapse;border-

The locus of the orthocentre of the triangle formed by the lines $$(1 + p)x - py + p(1 + p) = 0, $$ $$(1 + q)x - qy + q(

A piece of wire is bent in the shape of a parabola y = kx2 (y-axis vertical) with a bead of mass m on it. The bead can s

Photoelectric effect experiments are performed using three different metal plates p, q and r having work functions $$\ph

The mass M shown in the figure below oscillates in simple harmonic motion with amplitude A. The amplitude of the point P

A uniform rod of length L and mass M is pivoted at the centre. Its two ends are attached to two springs of equal spring

The figure shows the PV plot of an ideal gas taken through a cycle ABCDA. The part ABC is a semicircle and CDA is half o

Under the influence of the Coulomb field of charge +Q, a charge $$-$$q is moving around it in an elliptical orbit. Find

Two metallic rings A and B, identical in shape and size but having different resistivities $$\rho_A$$ and $$\rho_B$$, ar

A sphere is rolling without slipping on a fixed horizontal plane surface. In the figure below, A is the point of contact

A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonance

Column II gives certain systems undergoing a process. Column I suggests changes in some of the parameters related to the

Column I shows four situations of standard Young's double slit arrangement with the screen placed far away from the slit

A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses 0.

Two soap bubbles A and B are kept in a closed chamber where the air is maintained at pressure 8 N/m$$^2$$. The radii of

A steady current I goes through a wire loop PQR having shape of a right angle triangle wit6h PQ = 3, PR = 4x and QR = 5x

A cylindrical vessel of height 500 mm has an orifice (small hole) at its bottom. The orifice is initially closed and wat

A 20 cm long string, having a mass of 1.0 g, is fixed at both the ends. The tension in the string is 0.5 N. The string i

A solid sphere of radius R has a charge Q distributed in its volume with a charge density $$\rho = K{r^a}$$, where K an

A metal rod AB of length 10x has its one end A in ice at 0$$^\circ$$C and the other end B in water at 100$$^\circ$$C. If

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. These have masses m, 2m and m