The correct order of increasing intermolecular hydrogen bond strength is

The correct order of increasing ionic radii is

[Given : Atomic no. Eu, 63; Sm, 62; Tm, 69; Tb, 65; Yb, 70; Dy, 66]

Options:

Arrange the following coordination compounds in the increasing order of magnetic moments. (Atomic numbers : Mn = 25; Fe = 26)

A. [FeF₆]^3$-$

B. [Fe(CN)₆]^3$-$

C. [MnCl₆]^3$-$ (high spin)

D. [Mn(CN)₆]^3$-$

Choose the correct answer from the options given below :

Options:

A solution containing 2.5 $\times$ 10^$-$3 kg of a solute dissolved in 75 $\times$ 10^$-$3 kg of water boils at 373.535 K. The molar mass of the solute is ____________ g mol^$-$1. [nearest integer] (Given : K_b(H₂O) = 0.52 K kg mol^$-$1 and boiling point of water = 373.15 K)

If m and n respectively are the number of local maximum and local minimum points of the function $f(x) = \int\limits_0^{{x^2}} {{{{t^2} - 5t + 4} \over {2 + {e^t}}}dt}$, then the ordered pair (m, n) is equal to

If the solution curve of the differential equation

$(({\tan ^{ - 1}}y) - x)dy = (1 + {y^2})dx$ passes through the point (1, 0), then the abscissa of the point on the curve whose ordinate is tan(1), is

The mean and variance of the data 4, 5, 6, 6, 7, 8, x, y, where x < y, are 6 and ${9 \over 4}$ respectively. Then ${x^4} + {y^2}$ is equal to :

If $y(x) = {\left( {{x^x}} \right)^x},\,x > 0$, then ${{{d^2}x} \over {d{y^2}}} + 20$ at x = 1 is equal to ____________.

If the area of the region $\left\{ {(x,y):{x^{{2 \over 3}}} + {y^{{2 \over 3}}} \le 1,\,x + y \ge 0,\,y \ge 0} \right\}$ is A, then ${{256A} \over \pi }$ is equal to __________.

The distance of the Sun from earth is 1.5 $\times$ 10¹¹ m and its angular diameter is (2000) s when observed from the earth. The diameter of the Sun will be :

When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is :

Decarboxylation of all six possible forms of diaminobenzoic acids C₆H₃(NH₂)₂COOH yields three products A, B and C. Three acids give a product 'A', two acids gives a product 'B' and one acid give a product 'C'. The melting point of product 'C' is

Match List I with List II.

Choose the correct answer from the options given below :

Options:

Consider the following set of quantum numbers.

The number of correct sets of quantum numbers is __________.

When 5 moles of He gas expand isothermally and reversibly at 300 K from 10 litre to 20 litre, the magnitude of the maximum work obtained is __________ J. [nearest integer] (Given : R = 8.3 J K^$-$1 mol^$-$1 and log 2 = 0.3010)

For the reaction taking place in the cell :

Pt (s)| H₂ (g)|H⁺(aq) || Ag⁺(aq) |Ag (s)

E$_{cell}^o$ = + 0.5332 V.

The value of $\Delta$_fG$^\circ$ is ______________ kJ mol^$-$1. (in nearest integer)

0.25 g of an organic compound containing chlorine gave 0.40 g of silver chloride in Carius estimation. The percentage of chlorine present in the compound is ___________. [in nearest integer]

(Given : Molar mass of Ag is 108 g mol^$-$1 and that of Cl is 35.5 g mol^$-$1)

The number of points of intersection of

$|z - (4 + 3i)| = 2$ and $|z| + |z - 4| = 6$, z $\in$ C, is :

The set of values of k, for which the circle $C:4{x^2} + 4{y^2} - 12x + 8y + k = 0$ lies inside the fourth quadrant and the point $\left( {1, - {1 \over 3}} \right)$ lies on or inside the circle C, is :

The value of $\cot \left( {\sum\limits_{n = 1}^{50} {{{\tan }^{ - 1}}\left( {{1 \over {1 + n + {n^2}}}} \right)} } \right)$ is :

$\alpha = \sin 36^\circ$ is a root of which of the following equation?

Let A be a matrix of order 2 $\times$ 2, whose entries are from the set {0, 1, 2, 3, 4, 5}. If the sum of all the entries of A is a prime number p, 2 < p < 8, then the number of such matrices A is ___________.

Let [t] denote the greatest integer $\le$ t and {t} denote the fractional part of t. The integral value of $\alpha$ for which the left hand limit of the function

$f(x) = [1 + x] + {{{\alpha ^{2[x] + {\{x\}}}} + [x] - 1} \over {2[x] + \{ x\} }}$ at x = 0 is equal to $\alpha - {4 \over 3}$, is _____________.

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

Assertion A : Fluorine forms one oxoacid.

Reason R : Fluorine has smallest size amongst all halogens and is highly electronegative.

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

What will be the major product of following sequence of reactions?

Match List-I with List-II.

	List-I		List-II
(A)		I.	$B{r_2}$ in $C{S_2}$
(B)		II.	$N{a_2}C{r_2}{O_7}/{H_2}S{O_4}$
(C)		III.	$Zn$
(D)		IV.	$CHC{l_3}/NaOH$

Choose the correct answer from the options given below :

Given below are two statements.

Statement I : Maltose has two $\alpha$-D-glucose units linked at C₁ and C₄ and is a reducing sugar.

Statement II : Maltose has two monosaccharides : $\alpha$-D-glucose and $\beta$-D-glucose linked at C₁ and C₆ and it is a non-reducing sugar.

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

116 g of a substance upon dissociation reaction, yields 7.5 g of hydrogen, 60 g of oxygen and 48.5 g of carbon. Given that the atomic masses of H, O and C are 1, 16 and 12, respectively. The data agrees with how many formulae of the following?

A. CH₃COOH, B. HCHO, C. CH₃OOCH₃, D. CH₃CHO

It has been found that for a chemical reaction with rise in temperature by 9 K the rate constant gets doubled. Assuming a reaction to be occurring at 300 K, the value of activation energy is found to be ____________ kJ mol^$-$1. [nearest integer]

(Given ln10 = 2.3, R = 8.3 J K^$-$1 mol^$-$1, log 2 = 0.30)

If a₁, a₂, a₃ ...... and b₁, b₂, b₃ ....... are A.P., and a₁ = 2, a₁₀ = 3, a₁b₁ = 1 = a₁₀b₁₀, then a₄ b₄ is equal to -

Let f be a differentiable function in $\left( {0,{\pi \over 2}} \right)$. If $\int\limits_{\cos x}^1 {{t^2}\,f(t)dt = {{\sin }^3}x + \cos x}$, then ${1 \over {\sqrt 3 }}f'\left( {{1 \over {\sqrt 3 }}} \right)$ is equal to

If the equation of the parabola, whose vertex is at (5, 4) and the directrix is $3x + y - 29 = 0$, is ${x^2} + a{y^2} + bxy + cx + dy + k = 0$, then $a + b + c + d + k$ is equal to :

Let $\overrightarrow a$ and $\overrightarrow b$ be the vectors along the diagonals of a parallelogram having area $2\sqrt 2$. Let the angle between $\overrightarrow a$ and $\overrightarrow b$ be acute, $|\overrightarrow a | = 1$, and $|\overrightarrow a \,.\,\overrightarrow b | = |\overrightarrow a \times \overrightarrow b |$. If $\overrightarrow c = 2\sqrt 2 \left( {\overrightarrow a \times \overrightarrow b } \right) - 2\overrightarrow b$, then an angle between $\overrightarrow b$ and $\overrightarrow c$ is :

Let $\alpha$, $\beta$ be the roots of the equation ${x^2} - 4\lambda x + 5 = 0$ and $\alpha$, $\gamma$ be the roots of the equation ${x^2} - \left( {3\sqrt 2 + 2\sqrt 3 } \right)x + 7 + 3\lambda \sqrt 3 = 0$, $\lambda$ > 0. If $\beta + \gamma = 3\sqrt 2$, then ${(\alpha + 2\beta + \gamma )^2}$ is equal to __________.

Let $y = y(x)$ be the solution of the differential equation $(1 - {x^2})dy = \left( {xy + ({x^3} + 2)\sqrt {1 - {x^2}} } \right)dx, - 1 < x < 1$, and $y(0) = 0$. If $\int_{{{ - 1} \over 2}}^{{1 \over 2}} {\sqrt {1 - {x^2}} y(x)dx = k}$, then k^$-$1 is equal to _____________.

Let S = {E₁, E₂, ........., E₈} be a sample space of a random experiment such that $P({E_n}) = {n \over {36}}$ for every n = 1, 2, ........, 8. Then the number of elements in the set $\left\{ {A \subseteq S:P(A) \ge {4 \over 5}} \right\}$ is ___________.

The SI unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be :

Identify the incorrect statement for PCl₅ from the following.

In 3d series, the metal having the highest M²⁺/M standard electrode potential is :

Which of the following is most stable?

Product 'A' of following sequence of reactions is

pH value of 0.001 M NaOH solution is ____________.

The integral $\int\limits_0^1 {{1 \over {{7^{\left[ {{1 \over x}} \right]}}}}dx}$, where [ . ] denotes the greatest integer function, is equal to

The shortest distance between the lines

${{x - 3} \over 2} = {{y - 2} \over 3} = {{z - 1} \over { - 1}}$ and ${{x + 3} \over 2} = {{y - 6} \over 1} = {{z - 5} \over 3}$, is :

If a point A(x, y) lies in the region bounded by the y-axis, straight lines 2y + x = 6 and 5x $-$ 6y = 30, then the probability that y < 1 is :

Let S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Define f : S $\to$ S as

f(n) = \left\{ {\matrix{ {2n} & , & {if\,n = 1,2,3,4,5} \cr {2n - 11} & , & {if\,n = 6,7,8,9,10} \cr } } \right..

Let g : S $\to$ S be a function such that fog(n) = \left\{ {\matrix{ {n + 1} & , & {if\,n\,\,is\,odd} \cr {n - 1} & , & {if\,n\,\,is\,even} \cr } } \right..

Then $g(10)g(1) + g(2) + g(3) + g(4) + g(5))$ is equal to _____________.

One end of a massless spring of spring constant k and natural length l₀ is fixed while the other end is connected to a small object of mass m lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity $\omega$ about an axis passing through fixed end, then the elongation of the spring will be :

Four spheres each of mass m from a square of side d (as shown in figure). A fifth sphere of mass M is situated at the centre of square. The total gravitational potential energy of the system is :

A stone tide to a spring of length L is whirled in a vertical circle with the other end of the spring at the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is $\sqrt {x({u^2} - gL)}$. The value of x is -

According to kinetic theory of gases,

A. The motion of the gas molecules freezes at 0$^\circ$C.

B. The mean free path of gas molecules decreases if the density of molecules is increased.

C. The mean free path of gas molecules increases if temperature is increased keeping pressure constant.

D. Average kinetic energy per molecule per degree of freedom is ${3 \over 2}{k_B}T$ (for monoatomic gases).

Choose the most appropriate answer from the options given below :

A convex lens has power P. It is cut into two halves along its principal axis. Further one piece (out of the two halves) is cut into two halves perpendicular to the principal axis (as shown in figures). Choose the incorrect option for the reported pieces.

A mass of 10 kg is suspended vertically by a rope of length 5 m from the roof. A force of 30 N is applied at the middle point of rope in horizontal direction. The angle made by upper half of the rope with vertical is $\theta$ = tan^$-$1 (x $\times$ 10^$-$1). The value of x is ____________.

(Given, g = 10 m/s²)

Three identical charged balls each of charge 2 C are suspended from a common point P by silk threads of 2 m each (as shown in figure). They form an equilateral triangle of side 1m.

The ratio of net force on a charged ball to the force between any two charged balls will be :

Given below are two statements :

Statement I : In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit (E₁) to higher energy orbit (E₂), is given as hf = E₁ $-$ E₂

Statement II : The jumping of electron from higher energy orbit (E₂) to lower energy orbit (E₁) is associated with frequency of radiation given as f = (E₂ $-$ E₁)/h

This condition is Bohr's frequency condition.

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

A rolling wheel of 12 kg is on an inclined plane at position P and connected to a mass of 3 kg through a string of fixed length and pulley as shown in figure. Consider PR as friction free surface. The velocity of centre of mass of the wheel when it reaches at the bottom Q of the inclined plane PQ will be ${1 \over 2}\sqrt {xgh}$ m/s. The value of x is ___________.

The current density in a cylindrical wire of radius r = 4.0 mm is 1.0 $\times$ 10⁶ A/m². The current through the outer portion of the wire between radial distances ${r \over 2}$ and r is x$\pi$ A; where x is __________.

For a perfect gas, two pressures P₁ and P₂ are shown in figure. The graph shows :

The equation of a particle executing simple harmonic motion is given by $x = \sin \pi \left( {t + {1 \over 3}} \right)m$. At t = 1s, the speed of particle will be

(Given : $\pi$ = 3.14)

A lead bullet penetrates into a solid object and melts. Assuming that 40% of its kinetic energy is used to heat it, the initial speed of bullet is :

(Given : initial temperature of the bullet = 127$^\circ$C, Melting point of the bullet = 327$^\circ$C, Latent heat of fusion of lead = 2.5 $\times$ 10⁴ J kg^$-$1, Specific heat capacity of lead = 125 J/kg K)

Two long parallel conductors S₁ and S₂ are separated by a distance 10 cm and carrying currents of 4A and 2A respectively. The conductors are placed along x-axis in X-Y plane. There is a point P located between the conductors (as shown in figure).

A charge particle of 3$\pi$ coulomb is passing through the point P with velocity $\overrightarrow v = (2\widehat i + 3\widehat j)$ m/s; where $\widehat i$ and $\widehat j$ represents unit vector along x & y axis respectively.

The force acting on the charge particle is $4\pi \times {10^{ - 5}}( - x\widehat i + 2\widehat j)$ N. The value of x is :

If L, C and R are the self inductance, capacitance and resistance respectively, which of the following does not have the dimension of time?

A diatomic gas ($\gamma$ = 1.4) does 400J of work when it is expanded isobarically. The heat given to the gas in the process is __________ J.

In the given circuit 'a' is an arbitrary constant. The value of m for which the equivalent circuit resistance is minimum, will be $\sqrt {{x \over 2}}$. The value of x is __________.

A deuteron and a proton moving with equal kinetic energy enter into a uniform magnetic field at right angle to the field. If r_d and r_p are the radii of their circular paths respectively, then the ratio ${{{r_d}} \over {{r_p}}}$ will be $\sqrt{x}$ : 1 where x is __________.

A metallic rod of length 20 cm is placed in North-South direction and is moved at a constant speed of 20 m/s towards East. The horizontal component of the Earth's magnetic field at that place is 4 $\times$ 10^$-$3 T and the angle of dip is 45$^\circ$. The emf induced in the rod is ___________ mV.

The cut-off voltage of the diodes (shown in figure) in forward bias is 0.6 V. The current through the resister of 40 $\Omega$ is __________ mA.

If a charge q is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be :

Given below are two statements :

Statement I : A time varying electric field is a source of changing magnetic field and vice-versa. Thus a disturbance in electric or magnetic field creates EM waves.

Statement II : In a material medium, the EM wave travels with speed $v = {1 \over {\sqrt {{\mu _0}{ \in _0}} }}$. In the light of the above statements, choose the correct answer from the options given below.

If a wave gets refracted into a denser medium, then which of the following is true?

A particle executes simple harmonic motion. Its amplitude is 8 cm and time period is 6 s. The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is ___________ s.

A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is connected with a wire of length b, as shown in the figure. The capacitance of the arrangement is ${x \over {15}}{{{ \in _0}A} \over b}$. The value of x is ____________.