The species having bond order different from that in CO is :

Among the following the paramagnetic compound is:

Extraction of zinc from zinc blende is achieved by

In the following reaction,

The structure of the major 'X' is

The reagent(s) for the following conversion,

The number of structural isomers for C$$_6$$H$$_{14}$$ is :

The percentage of p-character in the orbitals forming P-P bonds in P$$_4$$ is

When 20 g of naphthoic acid (C$$_{11}$$H$$_{8}$$O$$_{2}$$) is dissolved in 50 g of benzene in 50 g of benzene (K$$_f$$ = 1.72 K kg mol$$^{-1}$$), a freezing point depression of 2 K is observed. The van't Hoff factor (i) is :

The value of log$$_{10}$$ K for a reaction $A \rightleftharpoons B$ is

(Given : $${\Delta _r}H{^\circ _{298\,K}} = - 54.07$$ kJ mol$$^{-1}$$, $${\Delta _r}S{^\circ _{298\,K}} = 10$$ J K$$^{-1}$$ mol$$^{-1}$$ and R = 8.314 J K$$^{-1}$$ mol$$^{-1}$$; 2.303 $$\times$$ 8.314 $$\times$$ 298 = 5705)

Statement 1 : Boron always forms covalent bond.

Statement 2 : The small size of B$$^{3+}$$ favours formation of covalent bond.

Statement 1 : In water, orthoboric acid behaves as a weak monobasic acid.

Statement 2 : In water, orthoboric acid acts as a proton donor.

Statement 1 : p-Hydroxybenzoic acid has a lower boiling point than o-hydroxybenzoic acid.

Statement 2 : o-Hydroxybenzoic acid has intramolecular hydrogen bonding.

Statement 1 : Micelles are formed by surfactant molecules above the critical micellar concentration (CMC).

Statement 2 : The conductivity of a solution having surfactant molecules decreases sharply at the CMC.

Argon is used in arc welding because of its

The structure of XeO$$_3$$

XeF$$_4$$ and XeF$$_6$$ are expected to be

The total number of moles of chlorine gas evolved is :

If the cathode is a Hg electrode, the maximum weight (g) of amalgam formed from this solution is:

The total charge (coulombs) required for complete electrolysis is:

Match the complexes in Column I with their properties listed in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 $$\times$$ 4 matrix given in the ORS.

Match the chemical substances in Column I with type of polymers/type of bonds in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 $$\times$$ 4 matrix given in the ORS.

Match gases under specified conditions listed in Column I with their properties/laws in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 $$\times$$ 4 matrix given in the ORS.

Let $$\alpha,\beta$$ be the roots of the equation $$x^2-px+r=0$$ and $$\frac{\alpha}{2},2\beta$$ be the roots of the equation $$x^2-qx+r=0$$. Then the value of r is

Let $$f(x)$$ be differentiable on the interval (0, $$\infty$$) such that $$f(1)=1$$, and $$\mathop {\lim }\limits_{t \to x} {{{t^2}f(x) - {x^2}f(t)} \over {t - x}} = 1$$ for each $$x > 0$$. Then $$f(x)$$ is

One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is

The tangent to the curve $$y=e^x$$ drawn at the point ($$c,e^c$$) intersects the line joining the points ($$c-1,e^{c-1}$$) and ($$c+1,e^{c+1}$$)

$$\mathop {\lim }\limits_{x \to {\pi \over 4}} {{\int\limits_2^{{{\sec }^2}x} {f(t)\,dt} } \over {{x^2} - {{{\pi ^2}} \over {16}}}}$$ equal

A hyperbola, having the transverse axis of the length $$2\sin \theta $$, is confocal with the ellipse $$3{x^2} + 4{y^2} = 12$$. Then its equation is

The number of distinct real values of $$\lambda$$, for which the vectors $$ - {\lambda ^2}\widehat i + \widehat j + \widehat k,\widehat i - {\lambda ^2}\widehat j + \widehat k$$ and $$\widehat i + \widehat j - {\lambda ^2}\widehat k$$ are coplanar, is :

A man walks a distance of 3 units from the origin towards the north-east (N 45$$^\circ$$E) direction. From there, he walks a distance of 4 units towards the north-west (N 45$$^\circ$$W) direction to reach a point P. Then the position of P in the Argand plane is

The number of solutions of the pair of equations

$$2{\sin ^2}\theta - \cos 2\theta = 0$$

$$2{\cos ^2}\theta - 3\sin \theta = 0$$

in the interval $$[0,2\pi]$$ is

Let H$$_1$$, H$$_2$$, ..., H$$_n$$ be mutually exclusive and exhaustive events with P(H$$_i$$) > 0, i = 1, 2, ..., n. Let E be any other event with 0 < P(E) < 1.

Statement 1 : P(H$$_i$$ | E) > P(E | H$$_i$$). P(H$$_i$$) for $$i=1,2,...,n$$.

Statement 2 : $$\sum\limits_{i = 1}^n {P({H_i}) = 1} $$.

Tangents are drawn from the point (17, 7) to the circle $$x^2+y^2=169$$.

Statement 1 : The tangents are mutually perpendicular.

Statement 2 : The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is $$x^2+y^2=338$$

Let the vector $$\overrightarrow {PQ} ,\overrightarrow {QR} ,\overrightarrow {RS} ,\overrightarrow {ST} ,\overrightarrow {TU} $$ and $$\overrightarrow {UP} $$, represent the sides of a regular hexagon.

Statement 1 : $$\overrightarrow {PQ} \times \left( {\overrightarrow {RS} + \overrightarrow {ST} } \right) \ne \overrightarrow 0 $$

Statement 2 : $$\overrightarrow {PQ} \times \overrightarrow {RS} = \overrightarrow 0 $$ and $$\overrightarrow {PQ} \times \overrightarrow {ST} \ne \overrightarrow 0 $$

Let F(x) be an indefinite integral of $$\sin^2x$$.

Statement 1 : The function F(x) satisfies F($$x+\pi$$) = F($$x$$) for all real x.

Statement 2 : $${\sin ^2}(x + \pi ) = {\sin ^2}x$$ for all real x.

The sum V$$_1$$ + V$$_2$$ + ... + V$$_n$$ is

T$$_r$$ is always

Which one of the following is a correct statement?

The ratio of the areas of the triangles PQS and PQR is

The radius of the circumcircle of the triangle PRS is

The radius of the incircle of the triangle PQR is

Consider the following linear equations

$$ax + by + cz = 0$$

$$bx + cy + az = 0$$

$$cx + ay + bz = 0$$

Match the conditions/expressions in Column I with statements in Column II.

In the following [x] denotes the greatest integer less than or equal to x.

Match the functions in Column I with the properties Column II.

Match the integrals in Column I with the values in Column II.

A resistance of 2 $$\Omega$$ is connected across one gap of a metre-bridge (the length of the wire is 100 cm) and an unknown resistance, greater than 2 $$\Omega$$, is connected across the other gap. When these resistance are interchanged, the balance point shifts by 20 cm. Neglecting any corrections, the unknown resistance is

In an experiment to determine the focal length (f) of a concave mirror by the u-v method, a student places the object pin A on the principal axis at a distance x form the pole P. The student looks at the pin and its inverted image form a distance keeping his/her eye in line with PA. When the student shifts his/her eye towards left, the image appears to the right, oh the object pin. Then,

Two particles of mass m each are tied at the ends of a light string of length 2a. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance 'a' form the centre P (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force F. As a result, the particles move towards each other on the surface. The magnitude of acceleration, with the separation between them becomes 2x, is

A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinder are initially electrically neutral.

Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then,

A circuit is connected as shown in the figure with the switch S open. When the switch is closed, the total amount of charge that flows from Y to X is

A ray of light travelling in water in incident on its surface open to air. The angle of incidence is $$\theta$$, which is less than the critical angle. Then there will be

In the option given below, let E denote the rest mass energy of a nucleus and n a neutron. The correct option is

The largest wavelength in the ultraviolet region of the hydrogen spectrum is 122 nm. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is

Statement 1 :

A block of mass m starts moving on a rough horizontal surface with a velocity v. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of 30$$^\circ$$ with the horizontal and the same block is made to go up on the surface with the same initial velocity v. The decrease in the mechanical energy in the second situation is smaller than that in the first situation.

Statement 2 :

The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.

Statement 1 :

In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.

Statement 2 :

In an elastic collision, the linear momentum of the system is conserved.

The ratio $${{{x_1}} \over {{x_2}}}$$ is

When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is

The loss of kinetic energy during the above process is :

The piston is now pulled out slowly and held at a distance 2L from the top. The pressure in the cylinder between its top and the piston will then be

While the piston is at a distance 2L from the top, the hole at the top is sealed. The piston is then released, to a position where it can stay in equilibrium. In this condition, the distance of the piston from the top is :

The piston is taken completely out of the cylinder. The hole at the top is sealed. A water tank is brought below the cylinder and put in a position so that the water surface in the tank is at the same level as the top of the cylinder as shown in the figure. The density of the water is $$\rho$$. In equilibrium, the height H of the water column in the cylinder satisfies

Some physical quantities are given in Column I and some possible SI units in which these quantities may be expressed are given in Column II. Match the physical quantities in Column I with the units in Column II and indicate your answer by darkening appropriate bubbles in the 4 $$\times$$ 4 matrix given in the ORS.

Column I gives certain situations in which a straight metallic wire of resistance R is used and Column II gives some resulting effects. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the 4 $$\times$$ 4 matrix given in the ORS.

Some laws/processes are given in Column I. Match these with the physical phenomena given in Column II and indicate your answer by darkening appropriate bubbles in the 4 $$\times$$ 4 matrix given in the ORS.

Statement 1 :

The formula connecting u, v and f for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature.

Statement 2 :

Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.

Statement 1 :

If the accelerating potential in an X-ray tube is increased, the wavelengths of the characteristic X-rays do not change.

Statement 2 :

When an electron beam strikes the target in an X-ray tube, part of the kinetic energy is converted into X-ray energy.