The number of radial and angular nodes in 4d orbital are, respectively

Match List-I with List-II

Choose the most appropriate answer from the options given below :

Which of the following elements is considered as a metalloid?

The oxide which contains an odd electron at the nitrogen atom is :

Which one of the following is an example of disproportionation reaction ?

The most common oxidation state of Lanthanoid elements is +3. Which of the following is likely to deviate easily from +3 oxidation state?

The correct order of nucleophilicity is

Oxidation of toluene to benzaldehyde can be easily carried out with which of the following reagents?

The major product in the following reaction

Halogenation of which one of the following will yield m-substituted product with respect to methyl group as a major product?

The reagent, from the following, which converts benzoic acid to benzaldehyde in one step is

The final product 'A' in the following reaction sequence

Which statement is NOT correct for p-toluenesulphonyl chloride?

The final product 'C' in the following series of reactions

Which one of the following is a water soluble vitamin, that is not excreted easily?

CNG is an important transportation fuel. When 100 g CNG is mixed with 208 g oxygen in vehicles, it leads to the formation of CO₂ and H₂O and produces large quantity of heat during this combustion, then the amount of carbon dioxide, produced in grams is ____________. [nearest integer]

[Assume CNG to be methane]

Amongst SF₄, XeF₄, CF₄ and H₂O, the number of species with two lone pairs of electrons is _____________.

A fish swimming in water body when taken out from the water body is covered with a film of water of weight 36 g. When it is subjected to cooking at 100$$^\circ$$C, then the internal energy for vaporization in kJ mol^$$-$$1 is ___________. [nearest integer]

[Assume steam to be an ideal gas. Given $$\Delta$$_vapH$$^\Theta $$ for water at 373 K and 1 bar is 41.1 kJ mol^$$-$$1 ; R = 8.31 J K^$$-$$1 mol^$$-$$1]

The osmotic pressure exerted by a solution prepared by dissolving 2.0 g of protein of molar mass 60 kg mol^$$-$$1 in 200 mL of water at 27$$^\circ$$C is ______________ Pa. [integer value]

(use R = 0.083 L bar mol^$$-$$1 K^$$-$$1)

40% of HI undergoes decomposition to H₂ and I₂ at 300 K. $$\Delta$$G$$^\Theta $$ for this decomposition reaction at one atmosphere pressure is __________ J mol^$$-$$1. [nearest integer]

(Use R = 8.31 J K^$$-$$1 mol^$$-$$1 ; log 2 = 0.3010, ln 10 = 2.3, log 3 = 0.477)

Cu(s) + Sn²⁺ (0.001M) $$\to$$ Cu²⁺ (0.01M) + Sn(s)

The Gibbs free energy change for the above reaction at 298 K is x $$\times$$ 10^$$-$$1 kJ mol^$$-$$1. The value of x is __________. [nearest integer]

[Given : $$E_{C{u^{2 + }}/Cu}^\Theta = 0.34\,V$$ ; $$E_{S{n^{2 + }}/Sn}^\Theta = - 0.14\,V$$ ; F = 96500 C mol^$$-$$1]

Catalyst A reduces the activation energy for a reaction by 10 kJ mol^$$-$$1 at 300 K. The ratio of rate constants, $${{{}^kT,\,Catalysed} \over {{}^kT,\,Uncatalysed}}$$ is e^x. The value of x is ___________. [nearest integer]

[Assume that the pre-exponential factor is same in both the cases. Given R = 8.31 J K^$$-$$1 mol^$$-$$1]

Reaction of [Co(H₂O)₆]²⁺ with excess ammonia and in the presence of oxygen results into a diamagnetic product. Number of electrons present in t_2g-orbitals of the product is ___________.

The moles of methane required to produce 81 g of water after complete combustion is _____________ $$\times$$ 10^$$-$$2 mol. [nearest integer]

Let f : R $$\to$$ R be defined as f (x) = x $$-$$ 1 and g : R $$-$$ {1, $$-$$1} $$\to$$ R be defined as $$g(x) = {{{x^2}} \over {{x^2} - 1}}$$.

Then the function fog is :

If the system of equations

$$\alpha$$x + y + z = 5, x + 2y + 3z = 4, x + 3y + 5z = $$\beta$$

has infinitely many solutions, then the ordered pair ($$\alpha$$, $$\beta$$) is equal to :

$$\mathop {\lim }\limits_{x \to 0} {{\cos (\sin x) - \cos x} \over {{x^4}}}$$ is equal to :

Let f(x) = min {1, 1 + x sin x}, 0 $$\le$$ x $$\le$$ 2$$\pi $$. If m is the number of points, where f is not differentiable and n is the number of points, where f is not continuous, then the ordered pair (m, n) is equal to

Consider a cuboid of sides 2x, 4x and 5x and a closed hemisphere of radius r. If the sum of their surface areas is a constant k, then the ratio x : r, for which the sum of their volumes is maximum, is :

The area of the region bounded by y² = 8x and y² = 16(3 $$-$$ x) is equal to:

If $$\int {{1 \over x}\sqrt {{{1 - x} \over {1 + x}}} dx = g(x) + c} $$, $$g(1) = 0$$, then $$g\left( {{1 \over 2}} \right)$$ is equal to :

If $$y = y(x)$$ is the solution of the differential equation

$$x{{dy} \over {dx}} + 2y = x\,{e^x}$$, $$y(1) = 0$$ then the local maximum value

of the function $$z(x) = {x^2}y(x) - {e^x},\,x \in R$$ is :

If the solution of the differential equation

$${{dy} \over {dx}} + {e^x}\left( {{x^2} - 2} \right)y = \left( {{x^2} - 2x} \right)\left( {{x^2} - 2} \right){e^{2x}}$$ satisfies $$y(0) = 0$$, then the value of y(2) is _______________.

The locus of the mid point of the line segment joining the point (4, 3) and the points on the ellipse $${x^2} + 2{y^2} = 4$$ is an ellipse with eccentricity :

Let $$\overrightarrow a = \widehat i + \widehat j + 2\widehat k$$, $$\overrightarrow b = 2\widehat i - 3\widehat j + \widehat k$$ and $$\overrightarrow c = \widehat i - \widehat j + \widehat k$$ be three given vectors. Let $$\overrightarrow v $$ be a vector in the plane of $$\overrightarrow a $$ and $$\overrightarrow b $$ whose projection on $$\overrightarrow c $$ is $${2 \over {\sqrt 3 }}$$. If $$\overrightarrow v \,.\,\widehat j = 7$$, then $$\overrightarrow v \,.\,\left( {\widehat i + \widehat k} \right)$$ is equal to :

The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observation was taken such that the sum of correct and incorrect observations is 70. If the correct mean is 16, then the correct variance is equal to :

$$16\sin (20^\circ )\sin (40^\circ )\sin (80^\circ )$$ is equal to :

If the inverse trigonometric functions take principal values then

$${\cos ^{ - 1}}\left( {{3 \over {10}}\cos \left( {{{\tan }^{ - 1}}\left( {{4 \over 3}} \right)} \right) + {2 \over 5}\sin \left( {{{\tan }^{ - 1}}\left( {{4 \over 3}} \right)} \right)} \right)$$ is equal to :

Let f : R $$\to$$ R satisfy $$f(x + y) = {2^x}f(y) + {4^y}f(x)$$, $$\forall$$x, y $$\in$$ R. If f(2) = 3, then $$14.\,{{f'(4)} \over {f'(2)}}$$ is equal to ____________.

Let p and q be two real numbers such that p + q = 3 and p⁴ + q⁴ = 369. Then $${\left( {{1 \over p} + {1 \over q}} \right)^{ - 2}}$$ is equal to _________.

If $${z^2} + z + 1 = 0$$, $$z \in C$$, then

$$\left| {\sum\limits_{n = 1}^{15} {{{\left( {{z^n} + {{( - 1)}^n}{1 \over {{z^n}}}} \right)}^2}} } \right|$$ is equal to _________.

Let $$X = \left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr 0 & 0 & 0 \cr } } \right],\,Y = \alpha I + \beta X + \gamma {X^2}$$ and $$Z = {\alpha ^2}I - \alpha \beta X + ({\beta ^2} - \alpha \gamma ){X^2}$$, $$\alpha$$, $$\beta$$, $$\gamma$$ $$\in$$ R. If $${Y^{ - 1}} = \left[ {\matrix{ {{1 \over 5}} & {{{ - 2} \over 5}} & {{1 \over 5}} \cr 0 & {{1 \over 5}} & {{{ - 2} \over 5}} \cr 0 & 0 & {{1 \over 5}} \cr } } \right]$$, then ($$\alpha$$ $$-$$ $$\beta$$ + $$\gamma$$)² is equal to ____________.

The total number of 3-digit numbers, whose greatest common divisor with 36 is 2, is ___________.

If a₁ (> 0), a₂, a₃, a₄, a₅ are in a G.P., a₂ + a₄ = 2a₃ + 1 and 3a₂ + a₃ = 2a₄, then a₂ + a₄ + 2a₅ is equal to ___________.

The integral $${{24} \over \pi }\int_0^{\sqrt 2 } {{{(2 - {x^2})dx} \over {(2 + {x^2})\sqrt {4 + {x^4}} }}} $$ is equal to ____________.

If the probability that a randomly chosen 6-digit number formed by using digits 1 and 8 only is a multiple of 21 is p, then 96 p is equal to _______________.

The dimension of mutual inductance is :

In the arrangement shown in figure a₁, a₂, a₃ and a₄ are the accelerations of masses m₁, m₂, m₃ and m₄ respectively. Which of the following relation is true for this arrangement?

Arrange the four graphs in descending order of total work done; where W₁, W₂, W₃ and W₄ are the work done corresponding to figure a, b, c and d respectively.

A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the ball to its total kinetic energy is

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : If we move from poles to equator, the direction of acceleration due to gravity of earth always points towards the center of earth without any variation in its magnitude.

Reason R : At equator, the direction of acceleration due to the gravity is towards the center of earth.

In the light of above statements, choose the correct answer from the options given below:

If p is the density and $$\eta$$ is coefficient of viscosity of fluid which flows with a speed v in the pipe of diameter d, the correct formula for Reynolds number R_e is :

A flask contains argon and oxygen in the ratio of 3 : 2 in mass and the mixture is kept at 27$$^\circ$$C. The ratio of their average kinetic energy per molecule respectively will be :

The charge on capacitor of capacitance 15$$\mu$$F in the figure given below is :

A parallel plate capacitor with plate area A and plate separation d = 2 m has a capacitance of 4 $$\mu$$F. The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant K = 3 (as shown in figure) will be :

Sixty four conducting drops each of radius 0.02 m and each carrying a charge of 5 $$\mu$$C are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be :

The equivalent resistance between points A and B in the given network is :

A bar magnet having a magnetic moment of 2.0 $$\times$$ 10⁵ JT^$$-$$1, is placed along the direction of uniform magnetic field of magnitude B = 14 $$\times$$ 10^$$-$$5 T. The work done in rotating the magnet slowly through 60$$^\circ$$ from the direction of field is :

Two coils of self inductance L₁ and L₂ are connected in series combination having mutual inductance of the coils as M. The equivalent self inductance of the combination will be :

A metallic conductor of length 1 m rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity 5 rad s^$$-$$1. If the horizontal component of earth's magnetic field is 0.2 $$\times$$ 10^$$-$$4 T, then emf induced between the two ends of the conductor is :

Which is the correct ascending order of wavelengths?

For a specific wavelength 670 nm of light coming from a galaxy moving with velocity v, the observed wavelength is 670.7 nm. The value of v is :

A metal surface is illuminated by a radiation of wavelength 4500 $$\mathop A\limits^o $$. The ejected photo-electron enters a constant magnetic field of 2 mT making an angle of 90$$^\circ$$ with the magnetic field. If it starts revolving in a circular path of radius 2 mm, the work function of the metal is approximately :

A ball is projected vertically upward with an initial velocity of 50 ms^$$-$$1 at t = 0s. At t = 2s, another ball is projected vertically upward with same velocity. At t = __________ s, second ball will meet the first ball (g = 10 ms^$$-$$2).

A batsman hits back a ball of mass 0.4 kg straight in the direction of the bowler without changing its initial speed of 15 ms^$$-$$1. The impulse imparted to the ball is ___________ Ns.

A system to 10 balls each of mass 2 kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the 7^th and 8^th ball is __________ N when 6^th ball just leaves the table.

A geyser heats water flowing at a rate of 2.0 kg per minute from 30$$^\circ$$C to 70$$^\circ$$C. If geyser operates on a gas burner, the rate of combustion of fuel will be ___________ g min^$$-$$1.

[Heat of combustion = 8 $$\times$$ 10³ Jg^$$-$$1, Specific heat of water = 4.2 Jg^$$-$$1 $$^\circ$$C^$$-$$1]

A set of 20 tuning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is _________ Hz.

Two 10 cm long, straight wires, each carrying a current of 5A are kept parallel to each other. If each wire experienced a force of 10^$$-$$5 N, then separation between the wires is ____________ cm.

A small bulb is placed at the bottom of a tank containing water to a depth of $$\sqrt7$$ m. The refractive index of water is $${4 \over 3}$$. The area of the surface of water through which light from the bulb can emerge out is x$$\pi$$ m². The value of x is __________.

A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in 1 cm on main scale and 50 Vernier scale divisions are equal to 49 main scale divisions, then least count of the travelling microscope is __________ $$\times$$ 10^$$-$$6 m.

The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength 6630 $$\mathop A\limits^o $$ is 0.42 V. If the threshold frequency is x $$\times$$ 10¹³ /s, where x is _________ (nearest integer).

(Given, speed light = 3 $$\times$$ 10⁸ m/s, Planck's constant = 6.63 $$\times$$ 10^$$-$$34 Js)