Hyperconjugation involves overlapping of the following orbitals:

The major product of the following reaction is:

Aqueous solutions of Na$$_2$$S$$_2$$O$$_3$$ on reaction with Cl$$_2$$ gives:

Native silver metal forms a water soluble complex with a dilute aqueous solution of NaCN in the presence of:

Under the same reaction conditions, initial concentration of 1.386 mol dm$$^{-3}$$ of a substance becomes half in 40 seconds and 20 seconds through first order and zero order kinetics, respectively. Ratio $$\left( {{{{k_1}} \over {{k_0}}}} \right)$$ of the rate constants for first order ($$k_1$$) and zero order ($$k_0$$) of the reactions is:

2.5 mL of $$\frac{2}{5}$$M weak monoacidic base (K$$_b$$ = 1 $$\times$$ 10$$^{-12}$$ at 25$$^\circ$$C) is titrated with $$\frac{2}{15}$$M HCl in water at 25$$^\circ$$C. The concentration of H$$^+$$ at equivalence point is (K$$_w$$ = 1 $$\times$$ 10$$^{-14}$$ at 25$$^\circ$$C).

The correct statement(s) about the compound given below is(are):

The correct statement(s) concerning the structures E, F and G is(are) :

A solution of colourless salt H on boiling with excess NaOH produces a non-flammable gas. The gas evolution ceases after sometime. Upon addition of Zn dust to the same solution, the gas evolution restarts. The colourless salt(s) H is(are):

A gas described by van Der Waals equation

Statement 1 : Bromobenzene upon reaction with Br$$_2$$/Fe gives 1, 4-dibromobenzene as the major product.

and

Statement 2: In bromobenzene, the inductive effect of the bromo group is more dominant than the mesomeric effect in directing the incoming electrophile.

Statement 1 : Pb$$^{4+}$$ compounds are stronger oxidising agents than Sn$$^{4+}$$ compounds.

and

Statement 2 : The higher oxidation states for the group 14 elements are more stable for the heavier members of the group due to 'inert pair effect'.

Statement 1 : For every chemical reaction at equilibrium, standard Gibbs energy of reaction is zero.

and

Statement 2 : At constant temperature and pressure, chemical reactions are spontaneous in the direction of decreasing Gibbs energy.

The structure of the product I is :

The structure of compounds J and K, respectively, are:

The structure of product L is :

Among the following, the correct statement is:

Among the following, the correct statement is :

White phosphorus on reaction with NaOH gives PH$$_3$$ as one of the products. This is a:

The freezing point of the solution M is :

The vapour pressure of the solution M is :

Water is added to the solution M such that the fraction of water in the solution becomes 0.9 mole. The boiling point of this solution is:

The number of elements in the set $$A \cap B \cap C$$ is

Let $${L_1},$$ $${L_2},$$ $${L_3}$$ be the lines of intersection of the planes $${P_2}$$ and $${P_3},$$ $${P_3}$$ and $${P_1},$$ $${P_1}$$ and $${P_2},$$ respectively.

STATEMENT - 1Z: At least two of the lines $${L_1},$$ $${L_2}$$ and $${L_3}$$ are non-parallel and

STATEMENT - 2: The three planes doe not have a common point.

$$\int\limits_{ - 1}^1 {g'\left( x \right)dx = } $$

The area of the region bounded by the curve $$y=f(x),$$ the
$$x$$-axis, and the lines $$x=a$$ and $$x=b$$, where $$ - \infty < a < b < - 2,$$ is :

If $$f\left( { - 10\sqrt 2 } \right) = 2\sqrt 2 ,$$ then $$f''\left( { - 10\sqrt 2 } \right) = $$

STATEMENT - 1: $$\mathop {\lim }\limits_{x \to 0} \,\,\left[ {g\left( x \right)\cot x - g\left( 0 \right)\cos ec\,x} \right] = f''\left( 0 \right)$$ and

STATEMENT - 2: $$f'\left( 0 \right) = g\left( 0 \right)$$

Let z be any point $$A \cap B \cap C$$ and let w be any point satisfying $$\left| {w - 2 - i} \right| < 3\,$$. Then, $$\left| z \right| - \left| w \right| + 3$$ lies between :

Let z be any point in $$A \cap B \cap C$$

Then, $${\left| {z + 1 - i} \right|^2} + {\left| {z - 5 - i} \right|^2}$$ lies between :

Points E and F are given by

Equations of the sides QR, RP are

The equation of circle C is

Let a and b be non-zero real numbers. Then, the equation

$$(a{x^2} + b{y^2} + c)({x^2} - 5xy + 6{y^2}) = 0$$ represents :

Let $$g(x) = {{{{(x - 1)}^n}} \over {\log {{\cos }^m}(x - 1)}};0 < x < 2,m$$ and $$n$$ are integers, $$m \ne 0,n > 0$$, and let $$p$$ be the left hand derivative of $$|x - 1|$$ at $$x = 1$$. If $$\mathop {\lim }\limits_{x \to {1^ + }} g(x) = p$$, then

The total number of local maxima and local minima of the function

$$f(x) = \left\{ {\matrix{ {{{(2 + x)}^3},} & { - 3 < x \le - 1} \cr {{x^{2/3}},} & { - 1 < x < 2} \cr } } \right.$$ is

Consider the system of equations:

$$x-2y+3z=-1$$

$$-x+y-2z=k$$

$$x-3y+4z=1$$

Statement - 1 : The system of equations has no solution for $$k\ne3$$.

and

Statement - 2 : The determinant $$\left| {\matrix{ 1 & 3 & { - 1} \cr { - 1} & { - 2} & k \cr 1 & 4 & 1 \cr } } \right| \ne 0$$, for $$k \ne 3$$.

Student I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a simple pendulum. They use different length of the pendulum and/or record time for different number of oscillations. The observations area shown in the table.

Least count for length = 0.1 cm

Least count for time = 0.1 s

If E_I, E_II and E_III are the percentage errors in g, i.e., $$\left(\frac{\triangle g}g\times100\right)$$ for students I, II and III, respectively,then

Figure shows three resistor configurations R1, R2 and R3 connected to 3 V battery. If the power dissipated by the configuration R1, R2 and R3 is P1, P2 and P3, respectively, then

Which one of the following statements is WRONG in the context of X-rays generated from a X-ray tube?

Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is 60$$^\circ$$). In the position of minimum deviation, the angle of refraction will be :

An ideal gas is expanding such that PT$$^2$$ = constant. The coefficient of volume expansion of the gas is

A spherically symmetric gravitational system of particles has a mass density

$$\rho = \left\{ {\matrix{ {{\rho _0}} & {for} & {r \le R} \cr 0 & {for} & {r > R} \cr } } \right.$$

Where $$\rho_0$$ is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed V as a function of distance $$r(0 < r < \infty)$$ from the centre of the system is represented by

Two balls, having linear momenta $${\overrightarrow p _1} = p\widehat i$$ and $${\overrightarrow p _2} = - p\widehat i$$, undergo a collision in free space. There is no external force acting on the balls. Let $${\overrightarrow {p'} _1}$$ and $${\overrightarrow {p'} _2}$$ be their final momenta. The following option(s) is (are) NOT ALLOWED for any non-zero value of $$p,{a_1},{a_2},{b_1},{b_2},{c_1}$$ and $${c_2}$$ :

Assume that the nuclear binding energy per nucleon (B/A) versus mass number (A) is as shown in the figure. Use this plot to choose the correct choice(s) given below.

A particle of mass m and charge q, moving with velocity v enters Region II normal to the boundary as shown in the figure. Region II has a uniform magnetic field B perpendicular to the plane of the paper. The length of the Region II is $$l$$. Choose the correct choice (s).

In a Young's double slit experiment, the separation between the two slits is d and the wavelength of the light is $$\lambda$$. The intensity of light falling on slit 1 is four times the intensity of light falling on slit 2. Choose the correct choice(s).

STATEMENT - 1

In a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance.

and

STATEMENT - 2

Resistance of a metal increases with increase in temperature.

STATEMENT - 1

An astronaut in an orbiting space station above the Earth experiences weightlessness.

and

STATEMENT - 2

An object moving around the Earth under the influence of Earth's gravitational force is in a state of 'free-fall'.

STATEMENT - 1 :

Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.

and

STATEMENT - 2 :

By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.

STATEMENT - 1 :

The stream of water flowing at high speed from a garden hose pipe tends to spread line a fountain when held vertically up, but tends to narrow down when held vertically down.

and

STATEMENT - 2 :

In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.

As the bubble moves upwards, besides the buoyancy force the following forces are acting on it

When the gas bubble is at a height y from the bottom, its temperature is :

The buoyancy force acting on the gas bubble is (Assume R is the universal gas constant)

The quantum number n of the state finally populated in He$$^+$$ ions is :

The wavelength of light emitted in the visible region by He$$^+$$ ions after collisions with H atoms is

The ratio of the kinetic energy of the $$n=2$$ electron for the H atom to that of He$$^+$$ ion is

The speed of the block at point B immediately after it strikes the second incline is

The speed of the block at point C, immediately before it leaves the second incline is

If collision between the block and the incline is completely elastic, then the vertical (upward) component of the velocity of the block at point B, immediately after it strikes the second incline is