The K_sp for bismuth sulphide (Bi₂S₃) is 1.08 $\times$ 10^$-$73. The solubility of Bi₂S₃ in mol L^$-$1 at 298 K is :

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

Assertion A : The amphoteric nature of water is explained by using Lewis acid/base concept.

Reason R : Water acts as an acid with NH₃ and as a base with H₂S.

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

Amongst the following, the major product of the given chemical reaction is

Which of the following conditions or reaction sequence will NOT give acetophenone as the major product?

Amongst BeF₂, BF₃, H₂O, NH₃, CCl₄ and HCl, the number of molecules with non-zero net dipole moment is ____________.

A solution of Fe₂(SO₄)₃ is electrolyzed for 'x' min with a current of 1.5 A to deposit 0.3482 g of Fe. The value of x is ___________. [nearest integer]

Given : 1 F = 96500 C mol^$-$1

Atomic mass of Fe = 56 g mol^$-$1

Amongst FeCl₃.3H₂O, K₃[Fe(CN)₆] and [Co(NH₃)₆]Cl₃, the spin-only magnetic moment value of the inner-orbital complex that absorbs light at shortest wavelength is ____________ B.M. [nearest integer]

How many of the given compounds will give a positive Biuret test ____________ ?

Glycine, Glycylalanine, Tripeptide, Biuret

The correct order of electron gain enthalpies of Cl, F, Te and Po is

Which of the following ketone will NOT give enamine on treatment with secondary amines? [where t-Bu is $-$C(CH₃)₃]

A protein 'A' contains 0.30% of glycine (molecular weight 75). The minimum molar mass of the protein 'A' is __________ $\times$ 10³ g mol^$-$1 [nearest integer]

Let $A = \{ x \in R:|x + 1| < 2\}$ and $B = \{ x \in R:|x - 1| \ge 2\}$. Then which one of the following statements is NOT true?

Let a, b $\in$ R be such that the equation $a{x^2} - 2bx + 15 = 0$ has a repeated root $\alpha$. If $\alpha$ and $\beta$ are the roots of the equation ${x^2} - 2bx + 21 = 0$, then ${\alpha ^2} + {\beta ^2}$ is equal to :

Let z₁ and z₂ be two complex numbers such that ${\overline z _1} = i{\overline z _2}$ and $\arg \left( {{{{z_1}} \over {{{\overline z }_2}}}} \right) = \pi$. Then :

The minimum energy that must be possessed by photons in order to produce the photoelectric effect with platinum metal is :

[Given : The threshold frequency of platinum is 1.3 $\times$ 10¹⁵ s^$-$1 and h = 6.6 $\times$ 10^$-$34 J s.]

The correct order of reduction potentials of the following pairs is

A. Cl₂/Cl^$-$

B. I²/I^$-$

C. Ag⁺/Ag

D. Na⁺/Na

E. Li⁺/Li

Choose the correct answer from the options given below.

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

Assertion A : A mixture contains benzoic acid and napthalene. The pure benzoic acid can be separated out by the use of benzene.

Reason R : Benzoic acid is soluble in hot water.

In the light of the above statements, choose the most appropriate answer from the options given below.

The major product formed in the following reaction, is

At 345 K, the half life for the decomposition of a sample of a gaseous compound initially at 55.5 kPa was 340 s. When the pressure was 27.8 kPa, the half life was found to be 170 s. The order of the reaction is ____________. [integer answer]

At 25$^\circ$C and 1 atm pressure, the enthalpy of combustion of benzene (I) and acetylene (g) are $-$ 3268 kJ mol^$-$1 and $-$1300 kJ mol^$-$1, respectively. The change in enthalpy for the reaction 3 C₂H₂(g) $\to$ C₆H₆ (I), is :

Solute A associates in water. When 0.7 g of solute A is dissolved in 42.0 g of water, it depresses the freezing point by 0.2$^\circ$C. The percentage association of solute A in water, is :

[Given : Molar mass of A = 93 g mol^$-$1. Molal depression constant of water is 1.86 K kg mol^$-$1.]

The metal ion (in gaseous state) with lowest spin-only magnetic moment value is :

During halogen test, sodium fusion extract is boiled with concentrated HNO₃ to

In the given reaction

'A' can be

The neutralization occurs when 10 mL of 0.1M acid 'A' is allowed to react with 30 mL of 0.05 M base M(OH)₂. The basicity of the acid 'A' is __________.

[M is a metal]

The value of 2sin (12$^\circ$) $-$ sin (72$^\circ$) is :

$\mathop {\lim }\limits_{x \to {\pi \over 2}} \left( {{{\tan }^2}x\left( {{{(2{{\sin }^2}x + 3\sin x + 4)}^{{1 \over 2}}} - {{({{\sin }^2}x + 6\sin x + 2)}^{{1 \over 2}}}} \right)} \right)$ is equal to

The value of ${\tan ^{ - 1}}\left( {{{\cos \left( {{{15\pi } \over 4}} \right) - 1} \over {\sin \left( {{\pi \over 4}} \right)}}} \right)$ is equal to :

Let $f(x) = \left[ {2{x^2} + 1} \right]$ and g(x) = \left\{ {\matrix{ {2x - 3,} & {x < 0} \cr {2x + 3,} & {x \ge 0} \cr } } \right.\(, where [t] is the greatest integer \)\le\( t. Then, in the open interval (\)-1, 1), the number of points where fog is discontinuous is equal to ______________.

If the sum of the co-efficient of all the positive even powers of x in the binomial expansion of ${\left( {2{x^3} + {3 \over x}} \right)^{10}}$ is ${5^{10}} - \beta \,.\,{3^9}$, then $\beta$ is equal to ____________.

If the mean deviation about the mean of the numbers 1, 2, 3, .........., n, where n is odd, is ${{5(n + 1)} \over n}$, then n is equal to ______________.

Let $f(x) = |(x - 1)({x^2} - 2x - 3)| + x - 3,\,x \in R$. If m and M are respectively the number of points of local minimum and local maximum of f in the interval (0, 4), then m + M is equal to ____________.

The interference pattern is obtained with two coherent light sources of intensity ratio 4 : 1. And the ratio ${{{I_{\max }} + {I_{\min }}} \over {{I_{\max }} - {I_{\min }}}}$ is ${5 \over x}$. Then, the value of x will be equal to :

A light whose electric field vectors are completely removed by using a good polaroid, allowed to incident on the surface of the prism at Brewster's angle. Choose the most suitable option for the phenomenon related to the prism.

Identify the logic operation performed by the given circuit:

A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark n is ${1 \over n}$. If the die is thrown thrice, then the probability, that the sum of the numbers obtained is 48, is :

The total number of three-digit numbers, with one digit repeated exactly two times, is ______________.

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

Assertion A : Two identical balls A and B thrown with same velocity 'u' at two different angles with horizontal attained the same range R. IF A and B reached the maximum height h₁ and h₂ respectively, then $R = 4\sqrt {{h_1}{h_2}}$

Reason R : Product of said heights.

${h_1}{h_2} = \left( {{{{u^2}{{\sin }^2}\theta } \over {2g}}} \right)\,.\,\left( {{{{u^2}{{\cos }^2}\theta } \over {2g}}} \right)$

Choose the correct answer :

A long solenoid carrying a current produces a magnetic field B along its axis. If the current is doubled and the number of turns per cm is halved, the new value of magnetic field will be equal to

The electromagnetic waves travel in a medium at a speed of 2.0 $\times$ 10⁸ m/s. The relative permeability of the medium is 1.0. The relative permittivity of the medium will be :

The system of equations

$- kx + 3y - 14z = 25$

$- 15x + 4y - kz = 3$

$- 4x + y + 3z = 4$

is consistent for all k in the set

The area of the region enclosed between the parabolas y² = 2x $-$ 1 and y² = 4x $-$ 3 is

The coefficient of x¹⁰¹ in the expression ${(5 + x)^{500}} + x{(5 + x)^{499}} + {x^2}{(5 + x)^{498}} + \,\,.....\,\, + \,\,{x^{500}}$, x > 0, is

If ${b_n} = \int_0^{{\pi \over 2}} {{{{{\cos }^2}nx} \over {\sin x}}dx,\,n \in N}$, then

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

$2{x^2}{{dy} \over {dx}} - 2xy + 3{y^2} = 0$ such that $y(e) = {e \over 3}$, then y(1) is equal to :

The line y = x + 1 meets the ellipse ${{{x^2}} \over 4} + {{{y^2}} \over 2} = 1$ at two points P and Q. If r is the radius of the circle with PQ as diameter then (3r)² is equal to :

Let $\overrightarrow b = \widehat i + \widehat j + \lambda \widehat k$, $\lambda$ $\in$ R. If $\overrightarrow a$ is a vector such that $\overrightarrow a \times \overrightarrow b = 13\widehat i - \widehat j - 4\widehat k$ and $\overrightarrow a \,.\,\overrightarrow b + 21 = 0$, then $\left( {\overrightarrow b - \overrightarrow a } \right).\,\left( {\widehat k - \widehat j} \right) + \left( {\overrightarrow b + \overrightarrow a } \right).\,\left( {\widehat i - \widehat k} \right)$ is equal to _____________.

Let l₁ be the line in xy-plane with x and y intercepts ${1 \over 8}$ and ${1 \over {4\sqrt 2 }}$ respectively, and l₂ be the line in zx-plane with x and z intercepts $- {1 \over 8}$ and $- {1 \over {6\sqrt 3 }}$ respectively. If d is the shortest distance between the line l₁ and l₂, then d^$-$2 is equal to _______________.

A solid metallic cube having total surface area 24 m² is uniformly heated. If its temperature is increased by 10$^\circ$C, calculate the increase in volume of the cube. (Given $\alpha$ = 5.0 $\times$ 10^$-$4 $^\circ$C^$-$1).

A copper block of mass 5.0 kg is heated to a temperature of 500$^\circ$C and is placed on a large ice block. What is the maximum amount of ice that can melt? [Specific heat of copper : 0.39 J g^$-$1 $^\circ$C^$-$1 and latent heat of fusion of water : 335 J g^$-$1]

Two metallic plates form a parallel plate capacitor. The distance between the plates is 'd'. A metal sheet of thickness ${d \over 2}$ and of area equal to area of each plate is introduced between the plates. What will be the ratio of the new capacitance to the original capacitance of the capacitor?

Two cells of same emf but different internal resistances r₁ and r₂ are connected in series with a resistance R. The value of resistance R, for which the potential difference across second cell is zero, is :

A proton, a neutron, an electron and an $\alpha$ particle have same energy. If $\lambda$_p, $\lambda$_n, $\lambda$_e and $\lambda$_a are the de Broglie's wavelengths of proton, neutron, electron and $\alpha$ particle respectively, then choose the correct relation from the following :

Water is being filled at the rate of 1 cm³ / sec in a right circular conical vessel (vertex downwards) of height 35 cm and diameter 14 cm. When the height of the water level is 10 cm, the rate (in cm² / sec) at which the wet conical surface area of the vessel increases is

Let $$A = \left( {\matrix{ 2 & { - 2} \cr 1 & { - 1} \cr } } \right)\( and \)B = \left( {\matrix{ { - 1} & 2 \cr { - 1} & 2 \cr } } \right)\(. Then the number of elements in the set {(n, m) : n, m \)\in$$ {1, 2, .........., 10} and nAⁿ + mB^m = I} is ____________.

The value of b > 3 for which $12\int\limits_3^b {{1 \over {({x^2} - 1)({x^2} - 4)}}dx = {{\log }_e}\left( {{{49} \over {40}}} \right)}$, is equal to ___________.

Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by ${X_P}(t) = \alpha t + \beta {t^2}$ and ${X_Q}(t) = ft - {t^2}$. At what time, both the buses have same velocity?

A disc with a flat small bottom beaker placed on it at a distance R from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $\omega$. The coefficient of static friction between the bottom of the beaker and the surface of the disc is $\mu$. The beaker will revolve with the disc if :

The ratio of specific heats $\left( {{{{C_P}} \over {{C_V}}}} \right)$ in terms of degree of freedom (f) is given by :

For a particle in uniform circular motion, the acceleration $\overrightarrow a$ at any point P(R, $\theta$) on the circular path of radius R is (when $\theta$ is measured from the positive x-axis and v is uniform speed) :

Given below are two statements :

Statement I : Susceptibilities of paramagnetic and ferromagnetic substances increase with decrease in temperature.

Statement II : Diamagnetism is a result of orbital motions of electrons developing magnetic moments opposite to the applied magnetic field.

Choose the correct answer from the options given below :

A sinusoidal voltage V(t) = 210 sin 3000 t volt is applied to a series LCR circuit in which L = 10 mH, C = 25 $\mu$F and R = 100 $\Omega$. The phase difference ($\Phi$) between the applied voltage and resultant current will be :

If n represents the actual number of deflections in a converted galvanometer of resistance G and shunt resistance S. Then the total current I when its figure of merit is K will be:

For $z = {a^2}{x^3}{y^{{1 \over 2}}}$, where 'a' is a constant. If percentage error in measurement of 'x' and 'y' are 4% and 12% respectively, then the percentage error for 'z' will be _______________%.

A curved in a level road has a radius 75 m. The maximum speed of a car turning this curved road can be 30 m/s without skidding. If radius of curved road is changed to 48 m and the coefficient of friction between the tyres and the road remains same, then maximum allowed speed would be ___________ m/s.

Moment of Inertia (M.I.) of four bodies having same mass 'M' and radius '2R' are as follows:

I₁ = M.I. of solid sphere about its diameter

I₂ = M.I. of solid cylinder about its axis

I₃ = M.I. of solid circular disc about its diameter

I₄ = M.I. of thin circular ring about its diameter

If 2(I₂ + I₃) + I₄ = x . I₁, then the value of x will be __________.

A block of mass 200 g is kept stationary on a smooth inclined plane by applying a minimum horizontal force F = $\sqrt{x}$N as shown in figure.

The value of x = _____________.

When a gas filled in a closed vessel is heated by raising the temperature by 1$^\circ$C, its pressure increases by 0.4%. The initial temperature of the gas is ___________ K.

The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be ____________ %.

In a series LCR circuit, the inductance, capacitance and resistance are L = 100 mH, C = 100 $\mu$F and R = 10 $\Omega$ respectively. They are connected to an AC source of voltage 220 V and frequency of 50 Hz. The approximate value of current in the circuit will be ___________ A.

27 identical drops are charged at 22V each. They combine to form a bigger drop. The potential of the bigger drop will be _____________ V.

Two satellites S₁ and S₂ are revolving in circular orbits around a planet with radius R₁ = 3200 km and R₂ = 800 km respectively. The ratio of speed of satellite S₁ to be speed of satellite S₂ in their respective orbits would be ${1 \over x}$ where x = ___________.