The primary and secondary valencies of cobalt respectively in $$\mathrm{[Co(NH_3)_5Cl]Cl_2}$$ are :

'A' and 'B' formed in the following set of reactions are :

Decreasing order of the hydrogen bonding in following forms of water is correctly represented by

A. Liquid water

B. Ice

C. Impure water

Choose the correct answer from the options given below :

Assertion A : Hydrolysis of an alkyl chloride is a slow reaction but in the presence of NaI, the rate of the hydrolysis increases.

Reason R : I$$^{-}$$ is a good nucleophile as well as a good leaving group.

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

An ammoniacal metal salt solution gives a brilliant red precipitate on addition of dimethylglyoxime. The metal ion is :

In the following given reaction, 'A' is

'R' formed in the following sequence of reactions is :

The magnetic moment of a transition metal compound has been calculated to be 3.87 B.M. The metal ion is

Compound (X) undergoes following sequence of reactions to give the Lactone (Y).

In the depression of freezing point experiment

A. Vapour pressure of the solution is less than that of pure solvent

B. Vapour pressure of the solution is more than that of pure solvent

C. Only solute molecules solidify at the freezing point

D. Only solvent molecules solidify at the freezing point

Choose the most appropriate answer from the options given below :

Order of Covalent bond;

$$\mathrm{A.~KF > KI ; LiF > KF}$$

$$\mathrm{B.~KF < KI ; LiF > KF}$$

$$\mathrm{C.~SnCl_4 > SnCl_2 ; CuCl > NaCl}$$

$$\mathrm{D.~LiF > KF ; CuCl < NaCl}$$

$$\mathrm{E.~KF < KI ; CuCl > NaCl}$$

Choose the correct answer from the options given below :

It is observed that characteristic X-ray spectra of elements show regularity. When frequency to the power "n" i.e. $${v^n}$$ of X-rays emitted is plotted against atomic number "Z", following graph is obtained.

The value of 'n' is :

Increasing order of stability of the resonance structures is :

Choose the correct answer from the options given below :

For independent process at 300 K

The number of non-spontaneous process from the following is __________

When $$\mathrm{Fe_{0.93}O}$$ is heated in presence of oxygen, it converts to $$\mathrm{Fe_2O_3}$$. The number of correct statement/s from the following is ________

A. The equivalent weight of $$\mathrm{Fe_{0.93}O}$$ is $${{\mathrm{Molecular\,weight}} \over {0.79}}$$

B. The number of moles of Fe$$^{2+}$$ and Fe$$^{3+}$$ in 1 mole of $$\mathrm{Fe_{0.93}O}$$ is 0.79 and 0.14 respectively

C. $$\mathrm{Fe_{0.93}O}$$ is metal deficient with lattice comprising of cubic closed packed arrangement of O$$^{2-}$$ ions

D. The % composition of Fe$$^{2+}$$ and Fe$$^{3+}$$ in $$\mathrm{Fe_{0.93}O}$$ is 85% and 15% respectively

5 g of NaOH was dissolved in deionized water to prepare a 450 mL stock solution. What volume (in mL) of this solution would be required to prepare 500 mL of 0.1 M solution? _____________

Given : Molar Mass of Na, O and H is 23, 16 and 1 g mol$$^{-1}$$ respectively

Uracil is a base present in RNA with the following structure. % of N in uracil is ___________

Given:

Molar mass N = 14 g mol$$^{-1}$$

O = 16 g mol$$^{-1}$$

C = 12 g mol$$^{-1}$$

H = 1 g mol$$^{-1}$$

Number of moles of AgCl formed in the following reaction is _____________

The number of correct statement/s from the following is __________

A. Larger the activation energy, smaller is the value of the rate constant.

B. The higher is the activation energy, higher is the value of the temperature coefficient.

C. At lower temperatures, increase in temperature causes more change in the value of k than at higher temperature

D. A plot of $$\mathrm{\ln k}$$ vs $$\frac{1}{T}$$ is a straight line with slope equal to $$-\frac{E_a}{R}$$

The dissociation constant of acetic acid is $$x\times10^{-5}$$. When 25 mL of 0.2 $$\mathrm{M~CH_3COONa}$$ solution is mixed with 25 mL of 0.02 $$\mathrm{M~CH_3COOH}$$ solution, the pH of the resultant solution is found to be equal to 5. The value of $$x$$ is ____________

At 298 K, a 1 litre solution containing 10 mmol of $$\mathrm{C{r_2}O_7^{2 - }}$$ and 100 mmol of $$\mathrm{Cr^{3+}}$$ shows a pH of 3.0.

Given : $$\mathrm{C{r_2}O_7^{2 - } \to C{r^{3 + }}\,;\,E^\circ = 1.330}$$V

and $$\mathrm{{{2.303\,RT} \over F} = 0.059}$$ V

The potential for the half cell reaction is $$x\times10^{-3}$$ V. The value of $$x$$ is __________

The d-electronic configuration of $$\mathrm{[CoCl_4]^{2-}}$$ in tetrahedral crystal field in $${e^mt_2^n}$$. Sum of "m" and "number of unpaired electrons" is ___________

If wavelength of the first line of the Paschen series of hydrogen atom is 720 nm, then the wavelength of the second line of this series is _________ nm. (Nearest integer)

Let $$\mathrm{p,q\in\mathbb{R}}$$ and $${\left( {1 - \sqrt 3 i} \right)^{200}} = {2^{199}}(p + iq),i = \sqrt { - 1} $$ then $$\mathrm{p+q+q^2}$$ and $$\mathrm{p-q+q^2}$$ are roots of the equation.

Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations

$$x + y + z = 1$$

$$2x + \mathrm{N}y + 2z = 2$$

$$3x + 3y + \mathrm{N}z = 3$$

has unique solution is $${k \over 6}$$, then the sum of value of k and all possible values of N is :

The relation $$\mathrm{R = \{ (a,b):\gcd (a,b) = 1,2a \ne b,a,b \in \mathbb{Z}\}}$$ is :

$$\mathop {\lim }\limits_{t \to 0} {\left( {{1^{{1 \over {{{\sin }^2}t}}}} + {2^{{1 \over {{{\sin }^2}t}}}}\, + \,...\, + \,{n^{{1 \over {{{\sin }^2}t}}}}} \right)^{{{\sin }^2}t}}$$ is equal to

$${\tan ^{ - 1}}\left( {{{1 + \sqrt 3 } \over {3 + \sqrt 3 }}} \right) + {\sec ^{ - 1}}\left( {\sqrt {{{8 + 4\sqrt 3 } \over {6 + 3\sqrt 3 }}} } \right)$$ is equal to :

Let $$y = y(x)$$ be the solution of the differential equation $${x^3}dy + (xy - 1)dx = 0,x > 0,y\left( {{1 \over 2}} \right) = 3 - \mathrm{e}$$. Then y (1) is equal to

Let $$\Omega$$ be the sample space and $$\mathrm{A \subseteq \Omega}$$ be an event.

Given below are two statements :

(S1) : If P(A) = 0, then A = $$\phi$$

(S2) : If P(A) = 1, then A = $$\Omega$$

Then :

The area enclosed by the curves $${y^2} + 4x = 4$$ and $$y - 2x = 2$$ is :

The equation $${x^2} - 4x + [x] + 3 = x[x]$$, where $$[x]$$ denotes the greatest integer function, has :

If A and B are two non-zero n $$\times$$ n matrices such that $$\mathrm{A^2+B=A^2B}$$, then :

For three positive integers p, q, r, $${x^{p{q^2}}} = {y^{qr}} = {z^{{p^2}r}}$$ and r = pq + 1 such that 3, 3 log$$_yx$$, 3 log$$_zy$$, 7 log$$_xz$$ are in A.P. with common difference $$\frac{1}{2}$$. Then r-p-q is equal to

Let PQR be a triangle. The points A, B and C are on the sides QR, RP and PQ respectively such that

$${{QA} \over {AR}} = {{RB} \over {BP}} = {{PC} \over {CQ}} = {1 \over 2}$$. Then $${{Area(\Delta PQR)} \over {Area(\Delta ABC)}}$$ is equal to :

Let $$f(x) = \left\{ {\matrix{ {{x^2}\sin \left( {{1 \over x}} \right)} & {,\,x \ne 0} \cr 0 & {,\,x = 0} \cr } } \right.$$

Then at $$x=0$$

Let $$\lambda \in \mathbb{R}$$ and let the equation E be $$|x{|^2} - 2|x| + |\lambda - 3| = 0$$. Then the largest element in the set S = {$$x+\lambda:x$$ is an integer solution of E} is ______

The shortest distance between the lines $${{x - 2} \over 3} = {{y + 1} \over 2} = {{z - 6} \over 2}$$ and $${{x - 6} \over 3} = {{1 - y} \over 2} = {{z + 8} \over 0}$$ is equal to ________

The 4$$^\mathrm{th}$$ term of GP is 500 and its common ratio is $$\frac{1}{m},m\in\mathbb{N}$$. Let $$\mathrm{S_n}$$ denote the sum of the first n terms of this GP. If $$\mathrm{S_6 > S_5 + 1}$$ and $$\mathrm{S_7 < S_6 + \frac{1}{2}}$$, then the number of possible values of m is ___________

Let C be the largest circle centred at (2, 0) and inscribed in the ellipse $${{{x^2}} \over {36}} + {{{y^2}} \over {16}} = 1$$. If (1, $$\alpha$$) lies on C, then 10 $$\alpha^2$$ is equal to ____________

A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses is __________

The value of $$12\int\limits_0^3 {\left| {{x^2} - 3x + 2} \right|dx} $$ is ____________

The value of $${8 \over \pi }\int\limits_0^{{\pi \over 2}} {{{{{(\cos x)}^{2023}}} \over {{{(\sin x)}^{2023}} + {{(\cos x)}^{2023}}}}dx} $$ is ___________

The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is ______________.

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

Assertion A : Photodiodes are preferably operated in reverse bias condition for light intensity measurement.

Reason R : The current in the forward bias is more than the current in the reverse bias for a $$p-n$$ junction diode.

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

As per given figure, a weightless pulley P is attached on a double inclined frictionless surfaces. The tension in the string (massless) will be (if g = 10 m/s$$^2$$)

Given below are two statements :

Statement I : If the Brewster's angle for the light propagating from air to glass is $$\mathrm{\theta_B}$$, then the Brewster's angle for the light propagating from glass to air is $$\frac{\pi}{2}-\theta_B$$

Statement II : The Brewster's angle for the light propagating from glass to air is $${\tan ^{ - 1}}({\mu _\mathrm{g}})$$ where $$\mathrm{\mu_g}$$ is the refractive index of glass.

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

A 100 m long wire having cross-sectional area $$\mathrm{6.25\times10^{-4}~m^2}$$ and Young's modulus is $$\mathrm{10^{10}~Nm^{-2}}$$ is subjected to a load of 250 N, then the elongation in the wire will be :

The weight of a body at the surface of earth is 18 N. The weight of the body at an altitude of 3200 km above the earth's surface is (given, radius of earth $$\mathrm{R_e=6400~km}$$) :

From the photoelectric effect experiment, following observations are made. Identify which of these are correct.

A. The stopping potential depends only on the work function of the metal.

B. The saturation current increases as the intensity of incident light increases.

C. The maximum kinetic energy of a photo electron depends on the intensity of the incident light.

D. Photoelectric effect can be explained using wave theory of light.

Choose the correct answer from the options given below :

Two long straight wires P and Q carrying equal current 10A each were kept parallel to each other at 5 cm distance. Magnitude of magnetic force experienced by 10 cm length of wire P is F$$_1$$. If distance between wires is halved and currents on them are doubled, force F$$_2$$ on 10 cm length of wire P will be:

A circular loop of radius $$r$$ is carrying current I A. The ratio of magnetic field at the center of circular loop and at a distance r from the center of the loop on its axis is :

If two charges q$$_1$$ and q$$_2$$ are separated with distance 'd' and placed in a medium of dielectric constant K. What will be the equivalent distance between charges in air for the same electrostatic force?

A conducting circular loop of radius $$\frac{10}{\sqrt\pi}$$ cm is placed perpendicular to a uniform magnetic field of 0.5 T. The magnetic field is decreased to zero in 0.5 s at a steady rate. The induced emf in the circular loop at 0.25 s is :

1 g of a liquid is converted to vapour at 3 $$\times$$ 10$$^5$$ Pa pressure. If 10% of the heat supplied is used for increasing the volume by 1600 cm$$^3$$ during this phase change, then the increase in internal energy in the process will be :

As shown in the figure, a network of resistors is connected to a battery of 24V with an internal resistance of 3 $$\Omega$$. The currents through the resistors R$$_4$$ and R$$_5$$ are I$$_4$$ and I$$_5$$ respectively. The values of I$$_4$$ and I$$_5$$ are :

A travelling wave is described by the equation

$$y(x,t) = [0.05\sin (8x - 4t)]$$ m

The velocity of the wave is : [all the quantities are in SI unit]

The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto which he can throw the same ball is :

Given below are two statements :

Statement I : The temperature of a gas is $$-73^\circ$$C. When the gas is heated to $$527^\circ$$C, the root mean square speed of the molecules is doubled.

Statement II : The product of pressure and volume of an ideal gas will be equal to translational kinetic energy of the molecules.

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

Match List I with List II

Choose the correct answer from the options given below :

Given below are two statements :

Statement I : An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable.

Statement II : Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed.

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

In $$\overrightarrow E $$ and $$\overrightarrow K $$ represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by :

($$\omega$$ - angular frequency) :

A hollow cylindrical conductor has length of 3.14 m, while its inner and outer diameters are 4 mm and 8 mm respectively. The resistance of the conductor is $$n\times10^{-3}\Omega$$. If the resistivity of the material is $$\mathrm{2.4\times10^{-8}\Omega m}$$. The value of $$n$$ is ___________.

A block of a mass 2 kg is attached with two identical springs of spring constant 20 N/m each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is $$\frac{\pi}{\sqrt x}$$ in SI unit. The value of $$x$$ is ____________.

Vectors $$a\widehat i + b\widehat j + \widehat k$$ and $$2\widehat i - 3\widehat j + 4\widehat k$$ are perpendicular to each other when $$3a + 2b = 7$$, the ratio of $$a$$ to $$b$$ is $${x \over 2}$$. The value of $$x$$ is ____________.

A hole is drilled in a metal sheet. At $$\mathrm{27^\circ C}$$, the diameter of hole is 5 cm. When the sheet is heated to $$\mathrm{177^\circ C}$$, the change in the diameter of hole is $$\mathrm{d\times10^{-3}}$$ cm. The value of d will be __________ if coefficient of linear expansion of the metal is $$1.6\times10^{-5}/^\circ$$C.

Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm then its radius of gyration about PQ will be $$\sqrt x$$ cm. The value of $$x$$ is ________.

As shown in the figure, a combination of a thin plano concave lens and a thin plano convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is 30 cm and refraction index of the material for both the lenses is 1.75. Both the lenses are placed at distance of 40 cm from each other. Due to the combination, the image of the object is formed at distance $$x=$$ _________ cm, from concave lens.

A stream of a positively charged particles having $${q \over m} = 2 \times {10^{11}}{C \over {kg}}$$ and velocity $${\overrightarrow v _0} = 3 \times {10^7}\widehat i\,m/s$$ is deflected by an electric field $$1.8\widehat j$$ kV/m. The electric field exists in a region of 10 cm along $$x$$ direction. Due to the electric field, the deflection of the charge particles in the $$y$$ direction is _________ mm.

A spherical body of mass 2 kg starting from rest acquires a kinetic energy of 10000 J at the end of $$\mathrm{5^{th}}$$ second. The force acted on the body is ________ N.