In the following the correct bond order sequence is :

Which one of the following metal complexes is most stable?

The ionic radii of F^$$-$$ and O^2$$-$$ respectively are 1.33$$\mathop A\limits^o $$ and 1.4$$\mathop A\limits^o $$, while the covalent radius of N is 0.74$$\mathop A\limits^o $$.

The correct statement for the ionic radius of N^3$$-$$ from the following is :

The correct decreasing order of densities of the following compounds is :

Consider the above reaction, the product "P" is :

A reaction of benzonitrile with one equivalent CH₃MgBr followed by hydrolysis produces a yellow liquid "P". The compound "P" will give positive _________.

The spin only magnetic moments (in BM) for free Ti³⁺, V²⁺ and Sc³⁺ ions respectively are :

(At.No. Sc : 21, Ti : 22, V : 23)

Which one of the following is correct structure for cytosine?

Identify the species having one $$\pi$$-bond and maximum number of canonical forms from the following :

Which one of the following metals forms interstitial hydride easily?

Maleic anhydride can prepared by :

[where $$Et \Rightarrow - {C_2}{H_5}{}^tBu \Rightarrow {(C{H_3})_3}C - $$]

Consider the above reaction sequence, Product "A" and Product "B" formed respectively are :

What is the major product "P" of the following reaction?

Identify the process in which change in the oxidation state is five :

Which among the following is the strongest acid ?

A system does 200 J of work and at the same time absorbs 150 J of heat. The magnitude of the change in internal energy is ____________ J. (Nearest integer)

An accelerated electron has a speed of 5 $$\times$$ 10⁶ ms^$$-$$1 with an uncertainty of 0.02%. The uncertainty in finding its location while in motion is x $$\times$$ 10^$$-$$9 m. The value of x is ____________. (Nearest integer)

[Use mass of electron = 9.1 $$\times$$ 10^$$-$$31 kg, h =6.63 $$\times$$ 10^$$-$$34 Js, $$\pi$$ = 3.14]

Number of electrons present in 4f orbital of Ho³⁺ ion is ____________. (Given Atomic No. of Ho = 67)

Consider the above chemical reaction. The total number of stereoisomers possible for Product 'P' is _____________.

For a chemical reaction A $$\to$$ B, it was found that concentration of B is increased by 0.2 mol L^$$-$$ in 30 min. The average rate of the reaction is ____________ $$\times$$ 10^$$-$$1 mol L^$$-$$1 h^$$-$$1. (in nearest integer)

Assuming that Ba(OH)₂ is completely ionised in aqueous solution under the given conditions the concentration of H₃O⁺ ions in 0.005 M aqueous solution of Ba(OH)² at 298 K is ______________ $$\times$$ 10^$$-$$12 mol L^$$-$$1. (Nearest integer)

0.8 g of an organic compound was analyzed by Kjeldahl's method for the estimation of nitrogen. If the percentage of nitrogen in the compound was found to be 42%, then ______________ mL of 1 M H₂SO₄ would have been neutralized by the ammonia evolved during the analysis.

When 3.00 g of a substance 'X' is dissolved in 100 g of CCl₄, it raises the boiling point by 0.60 K. The molar mass of the substance 'X' is ______________ g mol^$$-$$1. (Nearest integer).

[Given K_b for CCl₄ is 5.0 K kg mol^$$-$$1]

The sum of all those terms which are rational numbers in the

expansion of (2^1/3 + 3^1/4)¹² is :

The first of the two samples in a group has 100 items with mean 15 and standard deviation 3. If the whole group has 250 items with mean 15.6 and standard deviation $$\sqrt {13.44} $$, then the standard deviation of the second sample is :

If $$f(x) = \left\{ {\matrix{ {\int\limits_0^x {\left( {5 + \left| {1 - t} \right|} \right)dt,} } & {x > 2} \cr {5x + 1,} & {x \le 2} \cr } } \right.$$, then

If the greatest value of the term independent of 'x' in the

expansion of $${\left( {x\sin \alpha + a{{\cos \alpha } \over x}} \right)^{10}}$$ is $${{10!} \over {{{(5!)}^2}}}$$, then the value of 'a' is equal to :

The value of $$\cot {\pi \over {24}}$$ is :

The lowest integer which is greater

than $${\left( {1 + {1 \over {{{10}^{100}}}}} \right)^{{{10}^{100}}}}$$ is ______________.

The value of the

integral $$\int\limits_{ - 1}^1 {\log \left( {x + \sqrt {{x^2} + 1} } \right)dx} $$ is :

Let a, b and c be distinct positive numbers. If the vectors $$a\widehat i + a\widehat j + c\widehat k,\widehat i+\widehat k$$ and $$c\widehat i + c\widehat j + b\widehat k$$ are co-planar, then c is equal to :

If [x] be the greatest integer less than or equal to x,

then $$\sum\limits_{n = 8}^{100} {\left[ {{{{{( - 1)}^n}n} \over 2}} \right]} $$ is equal to :

The number of distinct real roots

of $$\left| {\matrix{ {\sin x} & {\cos x} & {\cos x} \cr {\cos x} & {\sin x} & {\cos x} \cr {\cos x} & {\cos x} & {\sin x} \cr } } \right| = 0$$ in the interval $$ - {\pi \over 4} \le x \le {\pi \over 4}$$ is :

If $$\left| {\overrightarrow a } \right| = 2,\left| {\overrightarrow b } \right| = 5$$ and $$\left| {\overrightarrow a \times \overrightarrow b } \right|$$ = 8, then $$\left| {\overrightarrow a .\,\overrightarrow b } \right|$$ is equal to :

The number of real solutions of the equation, x² $$-$$ |x| $$-$$ 12 = 0 is :

Consider function f : A $$\to$$ B and g : B $$\to$$ C (A, B, C $$ \subseteq $$ R) such that (gof)^$$-$$1 exists, then :

If $$P = \left[ {\matrix{ 1 & 0 \cr {{1 \over 2}} & 1 \cr } } \right]$$, then P⁵⁰ is :

Let X be a random variable such that the probability function of a distribution is given by $$P(X = 0) = {1 \over 2},P(X = j) = {1 \over {{3^j}}}(j = 1,2,3,...,\infty )$$. Then the mean of the distribution and P(X is positive and even) respectively are :

If $${}^n{P_r} = {}^n{P_{r + 1}}$$ and $${}^n{C_r} = {}^n{C_{r - 1}}$$, then the value of r is equal to :

Let y = y(x) be the solution of the differential

equation xdy = (y + x³ cosx)dx with y($$\pi$$) = 0, then $$y\left( {{\pi \over 2}} \right)$$ is equal to :

Consider the function


where P(x) is a polynomial such that P'' (x) is always a constant and P(3) = 9. If f(x) is continuous at x = 2, then P(5) is equal to _____________.

The equation of a circle is Re(z²) + 2(Im(z))² + 2Re(z) = 0, where z = x + iy. A line which passes through the center of the given circle and the vertex of the parabola, x² $$-$$ 6x $$-$$ y + 13 = 0, has y-intercept equal to ______________.

If $$\left( {\overrightarrow a + 3\overrightarrow b } \right)$$ is perpendicular to $$\left( {7\overrightarrow a - 5\overrightarrow b } \right)$$ and $$\left( {\overrightarrow a - 4\overrightarrow b } \right)$$ is perpendicular to $$\left( {7\overrightarrow a - 2\overrightarrow b } \right)$$, then the angle between $$\overrightarrow a $$ and $$\overrightarrow b $$ (in degrees) is _______________.

If a + b + c = 1, ab + bc + ca = 2 and abc = 3, then the value of a⁴ + b⁴ + c⁴ is equal to ______________.

A fair coin is tossed n-times such that the probability of getting at least one head is at least 0.9. Then the minimum value of n is ______________.

If the co-efficient of x⁷ and x⁸ in the expansion of $${\left( {2 + {x \over 3}} \right)^n}$$ are equal, then the value of n is equal to _____________.

The relation between time t and distance x for a moving body is given as t = mx² + nx, where m and n are constants. The retardation of the motion is : (When v stands for velocity)

In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.

A force $$\overrightarrow F = (40\widehat i + 10\widehat j)N$$ acts on a body of mass 5 kg. If the body starts from rest, its position vector $$\overrightarrow r $$ at time t = 10 s, will be :

A prism of refractive index $$\mu$$ and angle of prism A is placed in the position of minimum angle of deviation. If minimum angle of deviation is also A, then in terms of refractive index

Two ions having same mass have charges in the ratio 1 : 2. They are projected normally in a uniform magnetic field with their speeds in the ratio 2 : 3. The ratio of the radii of their circular trajectories is :

A 10 $$\Omega$$ resistance is connected across 220V $$-$$ 50 Hz AC supply. The time taken by the current to change from its maximum value to the rms value is :

A balloon was moving upwards with a uniform velocity of 10 m/s. An object of finite mass is dropped from the balloon when it was at a height of 75 m from the ground level. The height of the balloon from the ground when object strikes the ground was around :

(takes the value of g as 10 m/s²)

If q_f is the free charge on the capacitor plates and q_b is the bound charge on the dielectric slab of dielectric constant k placed between the capacitor plates, then bound charge q_b an be expressed as :

Consider a planet in some solar system which has a mass double the mass of earth and density equal to the average density of earth. If the weight of an object on earth is W, the weight of the same object on that planet will be :

Two ideal electric dipoles A and B, having their dipole moment p₁ and p₂ respectively are placed on a plane with their centres at O as shown in the figure. At point C on the axis of dipole A, the resultant electric field is making an angle of 37$$^\circ$$ with the axis. The ratio of the dipole moment of A and B, $${{{p_1}} \over {{p_2}}}$$ is : (take $$\sin 37^\circ = {3 \over 5}$$)

Two spherical soap bubbles of radii r₁ and r₂ in vacuum combine under isothermal conditions. The resulting bubble has a radius equal to :

The force is given in terms of time t and displacement x by the equation

F = A cos Bx + C sin Dt

The dimensional formula of $${{AD} \over B}$$ is :

An electron moving with speed v and a photon moving with speed c, have same D-Broglie wavelength. The ratio of kinetic energy of electron to that of photon is :

The instantaneous velocity of a particle moving in a straight line is given as $$V = \alpha t + \beta {t^2}$$, where $$\alpha$$ and $$\beta$$ are constants. The distance travelled by the particle between 1s and 2s is :

A ray of light entering from air into a denser medium of refractive index $${4 \over 3}$$, as shown in figure. The light ray suffers total internal reflection at the adjacent surface as shown. The maximum value of angle $$\theta$$ should be equal to :

When radiation of wavelength $$\lambda$$ is incident on a metallic surface, the stopping potential of ejected photoelectrons is 4.8 V. If the same surface is illuminated by radiation of double the previous wavelength, then the stopping potential becomes 1.6 V. The threshold wavelength of the metal is :

Two vectors $$\overrightarrow X $$ and $$\overrightarrow Y $$ have equal magnitude. The magnitude of ($$\overrightarrow X $$ $$-$$ $$\overrightarrow Y $$) is n times the magnitude of ($$\overrightarrow X $$ + $$\overrightarrow Y $$). The angle between $$\overrightarrow X $$ and $$\overrightarrow Y $$ is :

A system consists of two types of gas molecules A and B having same number density 2 $$\times$$ 10²⁵/m³. The diameter of A and B are 10 $$\mathop A\limits^o $$ and 5 $$\mathop A\limits^o $$ respectively. They suffer collision at room temperature. The ratio of average distance covered by the molecule A to that of B between two successive collision is ____________ $$\times$$ 10^$$-$$2

A light beam of wavelength 500 nm is incident on a metal having work function of 1.25 eV, placed in a magnetic field of intensity B. The electrons emitted perpendicular to the magnetic field B, with maximum kinetic energy are bent into circular are of radius 30 cm. The value of B is ___________ $$\times$$ 10^$$-$$7 T.

Given hc = 20 $$\times$$ 10^$$-$$26 J-m, mass of electron = 9 $$\times$$ 10^$$-$$31 kg

A 16 $$\Omega$$ wire is bend to form a square loop. A 9V supply having internal resistance of 1$$\Omega$$ is connected across one of its sides. The potential drop across the diagonals of the square loop is _______________ $$\times$$ 10^$$-$$1 V

Two circuits are shown in the figure (a) & (b). At a frequency of ____________ rad/s the average power dissipated in one cycle will be same in both the circuits.

From the given data, the amount of energy required to break the nucleus of aluminium $$_{13}^{27}$$Al is __________ x $$\times$$ 10^$$-$$3 J.

Mass of neutron = 1.00866 u

Mass of proton = 1.00726 u

Mass of Aluminium nucleus = 27.18846 u

(Assume 1 u corresponds to x J of energy)

(Round off to the nearest integer)

A force of F = (5y + 20)$$\widehat j$$ N acts on a particle. The work done by this force when the particle is moved from y = 0 m to y = 10 m is ___________ J.

A solid disc of radius 20 cm and mass 10 kg is rotating with an angular velocity of 600 rpm, about an axis normal to its circular plane and passing through its centre of mass. The retarding torque required to bring the disc at rest in 10 s is ____________ $$\pi$$ $$\times$$ 10^$$-$$1 Nm.

In a semiconductor, the number density of intrinsic charge carries at 27$$^\circ$$C is 1.5 $$\times$$ 10¹⁶/m³. If the semiconductor is doped with impurity atom, the hole density increases to 4.5 $$\times$$ 10²²/m³. The electron density in the doped semiconductor is ___________ $$\times$$ 10⁹/m³.