Observation of “Rhumann’s purple” is a confirmatory test for the presence of :

The “N” which does not contribute to the basicity for the compound is :

The correct statement about the synthesis of erythritol (C(CH2OH)4) used in the preparation of PETN is :

Fluorination of an aromatic ring is easily accomplished by treating a diazonium salt with HBF4. Which of the following c

Which one of the following reagents is not suitable for the elimination reaction ?

Consider the reaction sequence below : X is:

Bromination of cyclohexene under conditions given below yields :

Sodium extract is heated with concentrated HNO3 before testing for halogens because :

The transition metal ions responsible for color in ruby and emerald are, respectively :

Which of the following is an example of homoleptic complex?

Identify the correct statement :

Oxidation of succinate ion produces ethylene and carbon dioxide gases. On passing 0.2 Faraday electricity through an aqu

The following statements concern elements in the periodic table. Which of the following is true ?

A solid XY kept in an evacuated sealed container undergoes decomposition to form a mixture of gases X and Y at temperatu

The rate law for the reaction below is given by the expression k [A] [B] A + B $$ \to $$ Product If the concentration of

If 100 mole of H2O2 decompose at 1 bar and 300 K, the work done (kJ) by one mole of O2(g) as it expands against 1 bar pr

An aqueous solution of a salt MX2 at certain temperature has a van’t Hoff factor of 2. The degree of dissociation for th

The bond angle H - X - H is the greatest in the compound :

Aqueous solution of which salt will not contain ions with the electronic configuration 1s22s22p63s23p6 ?

The volume of 0.1N dibasic acid sufficient to neutralize 1 g of a base that furnishes 0.04 mole of OH− in aqueous soluti

Let a1, a2, a3, . . . . . . . , an, . . . . . be in A.P. If a3 + a7 + a11 + a15 = 72, then the sum of its first 17 te

If    $${{{}^{n + 2}C{}_6} \over {{}^{n - 2}{P_2}}}$$ = 11, then n satisfies the equation :

If the coefficients of x−2 and x−4 in the expansion of $${\left( {{x^{{1 \over 3}}} + {1 \over {2{x^{{1 \over 3}}}}}} \r

If    A = $$\left[ {\matrix{ { - 4} & { - 1} \cr 3 & 1 \cr } } \right]$$, then the determ

Let A be a 3 $$ \times $$ 3 matrix such that A2 $$-$$ 5A + 7I = 0 Statement - I :   A$$-$$1 = $${1 \over 7}$$

If x is a solution of the equation, $$\sqrt {2x + 1} $$ $$ - \sqrt {2x - 1} = 1,$$ $$\,\,\left( {x \ge {1 \over 2}} \ri

Let P = {$$\theta $$ : sin$$\theta $$ $$-$$ cos$$\theta $$ = $$\sqrt 2 \,\cos \theta $$} and Q = {$$\theta $$ : sin$$\t

The sum $$\sum\limits_{r = 1}^{10} {\left( {{r^2} + 1} \right) \times \left( {r!} \right)} $$ is equal to :

For x $$ \in $$ R, x $$ \ne $$ 0, if y(x) is a differentiable function such that x $$\int\limits_1^x y $$ (t) dt = (x +

If   A > 0, B > 0   and    A + B = $${\pi \over 6}$$, then the minimum value of t

The mean of 5 observations is 5 and their variance is 124. If three of the observations are 1, 2 and 6 ; then the mean d

Let ABC be a triangle whose circumcentre is at P. If the position vectors of A, B, C and P are $$\overrightarrow a ,\ove

ABC is a triangle in a plane with vertices A(2, 3, 5), B(−1, 3, 2) and C($$\lambda $$, 5, $$\mu $$). If the median thr

The solution of the differential equation $${{dy} \over {dx}}\, + \,{y \over 2}\,\sec x = {{\tan x} \over {2y}},\,\,$$

A hyperbola whose transverse axis is along the major axis of the conic, $${{{x^2}} \over 3} + {{{y^2}} \over 4} = 4$$ an

A straight line through origin O meets the lines 3y = 10 − 4x and 8x + 6y + 5 = 0 at points A and B respectively. Then O

A ray of light is incident along a line which meets another line, 7x − y + 1 = 0, at the point (0, 1). The ray is then r

The value of the integral $$\int\limits_4^{10} {{{\left[ {{x^2}} \right]dx} \over {\left[ {{x^2} - 28x + 196} \right] +

The integral $$\int {{{dx} \over {\left( {1 + \sqrt x } \right)\sqrt {x - {x^2}} }}} $$ is equal to : (where C is a con

Let f(x) = sin4x + cos4 x. Then f is an increasing function in the interval :

Let a, b $$ \in $$ R, (a $$ \ne $$ 0). If the function f defined as $$f\left( x \right) = \left\{ {\matrix{ {{{2{x^2}

$$\mathop {\lim }\limits_{x \to 0} \,{{{{\left( {1 - \cos 2x} \right)}^2}} \over {2x\,\tan x\, - x\tan 2x}}$$ is :

Consider an electromagnetic wave propagating in vacuum. Choose the correct statement :

A bottle has an opening of radius a and length b. A cork of length b and radius (a + $$\Delta $$a) where ($$\Delta $$a &

In the figure shown ABC is a uniform wire. If centre of mass of wire lies vertically below point A, then $${{BC} \over {

Velocity-time graph for a body of mass 10 kg is shown in figure. Work-done on the body in first two seconds of the motio

To determine refractive index of glass slab using a travelling microscope, minimum number of readings required are :

A thin 1 m long rod has a radius of 5 mm. A force of 50 $$\pi $$kN is applied at one end to determine its Young’s modulu

A particle of mass m is acted upon by a force F given by the empirical law F =$${R \over {{t^2}}}\,v\left( t \right).$$

A neutron moving with a speed ‘v’ makes a head on collision with a stationary hydrogen atom in ground state. The minimum

Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30 cm. The wav

A photoelectric surface is illuminated successively by monochromatic light of wavelengths $$\lambda $$ and $${\lambda \

Which of the following shows the correct relationship between the pressure ‘P’ and density $$\rho $$ of an ideal gas at

A conducting metal circular-wire-loop of radius r is placed perpendicular to a magnetic field which varies with time as

The resistance of an electrical toaster has a temperature dependence given by R(T) = R0 [1 + $$\alpha $$(T − T0)] in its

In an engine the piston undergoes vertical simple harmonic motion with amplitude 7 cm. A washer rests on top of the pist

Within a spherical charge distribution of charge density $$\rho $$(r), N equipotential surfaces of potential V0, V0 + $$

An astronaut of mass m is working on a satellite orbiting the earth at a distance h from the earth’s surface. The radius

A particle of mass M is moving in a circle of fixed radius R in such a way that its centripetal acceleration at time t i

Concrete mixture is made by mixing cement, stone and sand in a rotating cylindrical drum. If the drum rotates too fast,

A, B, C and D are four different physical quantities having different dimensions. None of them is dimensionless. But w

A galvanometer has a 50 division scale. Battery has no internal resistance. It is found that there is deflection of 40 d

To get an output of 1 from the circuit shown in figure the input must be :

A hemispherical glass body of radius 10 cm and refractive index 1.5 is silvered on its curved surface. A small air bubbl

Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed ‘v’ in a uniform magnetic field

Figure shows a network of capacitors where the numbers indicates capacitances in micro Farad. The value of capacitance