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

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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

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 prod

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 formatio

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

The osmotic pressure exerted by a solution prepared by dissolving 2.0 g of protein of molar mass 60 kg mol$$-$$1 in 200

40% of HI undergoes decomposition to H2 and I2 at 300 K. $$\Delta$$G$$^\Theta $$ for this decomposition reaction at one

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 $$\

Catalyst A reduces the activation energy for a reaction by 10 kJ mol$$-$$1 at 300 K. The ratio of rate constants, $${{{}

Reaction of [Co(H2O)6]2+ with excess ammonia and in the presence of oxygen results into a diamagnetic product. Number of

The moles of methane required to produce 81 g of water after complete combustion is _____________ $$\times$$ 10$$-$$2 mo

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}

If the system of equations $$\alpha$$x + y + z = 5, x + 2y + 3z = 4, x + 3y + 5z = $$\beta$$ has infinitely many solutio

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

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 con

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}} \rig

If $$y = y(x)$$ is the solution of the differential equation $$x{{dy} \over {dx}} + 2y = x\,{e^x}$$, $$y(1) = 0$$ then t

If the solution of the differential equation $${{dy} \over {dx}} + {e^x}\left( {{x^2} - 2} \right)y = \left( {{x^2} - 2x

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} =

Let $$\overrightarrow a = \widehat i + \widehat j + 2\widehat k$$, $$\overrightarrow b = 2\widehat i - 3\widehat j + \

The mean and standard deviation of 50 observations are 15 and 2 respectively. It was found that one incorrect observatio

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

If the inverse trigonometric functions take principal values then $${\cos ^{ - 1}}\left( {{3 \over {10}}\cos \left( {{{\

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.\,{{

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

If $${z^2} + z + 1 = 0$$, $$z \in C$$, then $$\left| {\sum\limits_{n = 1}^{15} {{{\left( {{z^n} + {{( - 1)}^n}{1 \over {

Let $$X = \left[ {\matrix{ 0 & 1 & 0 \cr 0 & 0 & 1 \cr 0 & 0 & 0 \cr } } \right],\,Y = \alpha I + \beta

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

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, t

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. Whi

Arrange the four graphs in descending order of total work done; where W1, W2, W3 and W4 are the work done corresponding

A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of ro

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

If p is the density and $$\eta$$ is coefficient of viscosity of fluid which flows with a speed v in the pipe of diameter

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 t

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 capac

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

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

Two coils of self inductance L1 and L2 are connected in series combination having mutual inductance of the coils as M. T

A metallic conductor of length 1 m rotates in a vertical plane parallel to east-west direction about one of its end with

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

A metal surface is illuminated by a radiation of wavelength 4500 $$\mathop A\limits^o $$. The ejected photo-electron ent

A ball is projected vertically upward with an initial velocity of 50 ms$$-$$1 at t = 0s. At t = 2s, another ball is proj

A batsman hits back a ball of mass 0.4 kg straight in the direction of the bowler without changing its initial speed of

A system to 10 balls each of mass 2 kg are connected via massless and unstretchable string. The system is allowed to sli

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

A set of 20 tuning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats with respect to t

Two 10 cm long, straight wires, each carrying a current of 5A are kept parallel to each other. If each wire experienced

A small bulb is placed at the bottom of a tank containing water to a depth of $$\sqrt7$$ m. The refractive index of wate

A travelling microscope is used to determine the refractive index of a glass slab. If 40 divisions are there in 1 cm on

The stopping potential for photoelectrons emitted from a surface illuminated by light of wavelength 6630 $$\mathop A\lim