Element "E" belongs to the period 4 and group 16 of the periodic table. The valence shell electron configuration of the element, which is just above "E" in the group is

Nitrogen gas is obtained by thermal decomposition of :

Which one of the lanthanoids given below is the most stable in divalent form?

Given below are two statements :

Statement I : [Ni(CN)₄]^2$-$ is square planar and diamagnetic complex, with dsp² hybridization for Ni but [Ni(CO)₄] is tetrahedral, paramagnetic and with sp³-hybridication for Ni.

Statement II : [NiCl₄]^2$-$ and [Ni(CO)₄] both have same d-electron configuration have same geometry and are paramagnetic.

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

Which one of the following techniques is not used to spot components of a mixture separated on thin layer chromatographic plate?

Which of the following structure are aromatic in nature?

The major product (P) in the reaction

is

The correct structure of product 'A' formed in the following reaction.

is

Which one of the following compounds is inactive towards S_N1 reaction?

Identify the major product formed in the following sequence of reactions:

A primary aliphatic amine on reaction with nitrous acid in cold (273 K) and there after raising temperature of reaction mixture to room temperature (298 K), gives a/an

Stability of $\alpha$-Helix structure of proteins depends upon

The formula of the purple colour formed in Laissaigne's test for sulphur using sodium nitroprusside is :

A 2.0 g sample containing MnO₂ is treated with HCl liberating Cl₂. The Cl₂ gas is passed into a solution of KI and 60.0 mL of 0.1 M Na₂S₂O₃ is required to titrate the liberated iodine. The percentage of MnO₂ in the sample is _____________. (Nearest integer)

[Atomic masses (in u) Mn = 55; Cl = 35.5; O = 16, I = 127, Na = 23, K = 39, S = 32]

If the work function of a metal is 6.63 $\times$ 10^$-$19J, the maximum wavelength of the photon required to remove a photoelectron from the metal is ____________ nm. (Nearest integer)

[Given : h = 6.63 $\times$ 10^$-$34 J s, and c = 3 $\times$ 10⁸ m s^$-$1]

The hybridization of P exhibited in PF₅ is sp^xd^y. The value of y is __________.

4.0 L of an ideal gas is allowed to expand isothermally into vacuum until the total volume is 2.0 L. The amount of heat absorbed in this expansion is ____________ L atm.

The vapour pressures of two volatile liquids A and B at 25$^\circ$C are 50 Torr and 100 Torr, respectively. If the liquid mixture contains 0.3 mole fraction of A, then the mole fraction of liquid B in the vapour phase is ${x \over {17}}$. The value of x is ______________.

The solubility product of a sparingly soluble salt A₂X₃ is 1.1 $\times$ 10^$-$23. If specific conductance of the solution is 3 $\times$ 10^$-$5 S m^$-$1, the limiting molar conductivity of the solution is $x \,\times$ 10^$-$3 S m² mol^$-$1. The value of x is ___________.

The quantity of electricity in Faraday needed to reduce 1 mol of Cr₂O$_7^{2 - }$ to Cr³⁺ is ____________.

For a first order reaction A $\to$ B, the rate constant, k = 5.5 $\times$ 10^$-$14 s^$-$1. The time required for 67% completion of reaction is x $\times$ 10^$-$1 times the half life of reaction. The value of x is _____________ (Nearest integer)

(Given : log 3 = 0.4771)

Number of complexes which will exhibit synergic bonding amongst, $[Cr{(CO)_6}]$, $[Mn{(CO)_5}]$ and $[M{n_2}{(CO)_{10}}]$ is ___________.

In the estimation of bromine, 0.5 g of an organic compound gave 0.40 g of silver bromide. The percentage of bromine in the given compound is _________ % (nearest integer)

(Relative atomic masses of Ag and Br are 108u and 80u, respectively).

Let a function f : N $\to$ N be defined by

f(n) = \left[ {\matrix{ {2n,} & {n = 2,4,6,8,......} \cr {n - 1,} & {n = 3,7,11,15,......} \cr {{{n + 1} \over 2},} & {n = 1,5,9,13,......} \cr } } \right.

then, f is

If the system of linear equations

$2x + 3y - z = - 2$

$x + y + z = 4$

$x - y + |\lambda |z = 4\lambda - 4$

where, $\lambda$ $\in$ R, has no solution, then

The total number of 5-digit numbers, formed by using the digits 1, 2, 3, 5, 6, 7 without repetition, which are multiple of 6, is :

Let A₁, A₂, A₃, ....... be an increasing geometric progression of positive real numbers. If A₁A₃A₅A₇ = ${1 \over {1296}}$ and A₂ + A₄ = ${7 \over {36}}$, then the value of A₆ + A₈ + A₁₀ is equal to

Let [t] denote the greatest integer less than or equal to t. Then, the value of the integral $\int\limits_0^1 {[ - 8{x^2} + 6x - 1]dx}$ is equal to :

Let f : R $\to$ R be defined as

f(x) = \left[ {\matrix{ {[{e^x}],} & {x < 0} \cr {a{e^x} + [x - 1],} & {0 \le x < 1} \cr {b + [\sin (\pi x)],} & {1 \le x < 2} \cr {[{e^{ - x}}] - c,} & {x \ge 2} \cr } } \right.

where a, b, c $\in$ R and [t] denotes greatest integer less than or equal to t. Then, which of the following statements is true?

The area of the region S = {(x, y) : y² $\le$ 8x, y $\ge$ $\sqrt2$x, x $\ge$ 1} is

Let the solution curve $y = y(x)$ of the differential equation

$\left[ {{x \over {\sqrt {{x^2} - {y^2}} }} + {e^{{y \over x}}}} \right]x{{dy} \over {dx}} = x + \left[ {{x \over {\sqrt {{x^2} - {y^2}} }} + {e^{{y \over x}}}} \right]y$

pass through the points (1, 0) and (2$\alpha$, $\alpha$), $\alpha$ > 0. Then $\alpha$ is equal to

Let y = y(x) be the solution of the differential equation $x(1 - {x^2}){{dy} \over {dx}} + (3{x^2}y - y - 4{x^3}) = 0$, $x > 1$, with $y(2) = - 2$. Then y(3) is equal to :

The number of real solutions of

${x^7} + 5{x^3} + 3x + 1 = 0$ is equal to ____________.

The probability, that in a randomly selected 3-digit number at least two digits are odd, is :

Let R₁ and R₂ be relations on the set {1, 2, ......., 50} such that

R₁ = {(p, pⁿ) : p is a prime and n $\ge$ 0 is an integer} and

R₂ = {(p, pⁿ) : p is a prime and n = 0 or 1}.

Then, the number of elements in R₁ $-$ R₂ is _______________.

The number of real solutions of the equation ${e^{4x}} + 4{e^{3x}} - 58{e^{2x}} + 4{e^x} + 1 = 0$ is ___________.

The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was misread as 5. Then, the correct variance is equal to _____________.

If $\overrightarrow a = 2\widehat i + \widehat j + 3\widehat k$, $\overrightarrow b = 3\widehat i + 3\widehat j + \widehat k$ and $\overrightarrow c = {c_1}\widehat i + {c_2}\widehat j + {c_3}\widehat k$ are coplanar vectors and $\overrightarrow a \,.\,\overrightarrow c = 5$, $\overrightarrow b \bot \overrightarrow c$, then $122({c_1} + {c_2} + {c_3})$ is equal to ___________.

A ray of light passing through the point P(2, 3) reflects on the x-axis at point A and the reflected ray passes through the point Q(5, 4). Let R be the point that divides the line segment AQ internally into the ratio 2 : 1. Let the co-ordinates of the foot of the perpendicular M from R on the bisector of the angle PAQ be ($\alpha$, $\beta$). Then, the value of 7$\alpha$ + 3$\beta$ is equal to ____________.

Let A = {1, a₁, a₂ ....... a₁₈, 77} be a set of integers with 1 < a₁ < a₂ < ....... < a₁₈ < 77.

Let the set A + A = {x + y : x, y $\in$ A} contain exactly 39 elements. Then, the value of a₁ + a₂ + ...... + a₁₈ is equal to _____________.

The number of positive integers k such that the constant term in the binomial expansion of ${\left( {2{x^3} + {3 \over {{x^k}}}} \right)^{12}}$, x $\ne$ 0 is 2⁸ . l, where l is an odd integer, is ______________.

The number of elements in the set {z = a + ib $\in$ C : a, b $\in$ Z and 1 < | z $-$ 3 + 2i | < 4} is __________.

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

Assertion A : Product of Pressure (P) and time (t) has the same dimension as that of coefficient of viscosity.

Reason R : Coefficient of viscosity = ${{Force} \over {Velocity\,gradient}}$

Choose the correct answer from the options given below :

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a = k²rt², where k is a constant. The power delivered to the particle by the force acting on it is given as

Motion of a particle in x-y plane is described by a set of following equations $x = 4\sin \left( {{\pi \over 2} - \omega t} \right)\,m$ and $y = 4\sin (\omega t)\,m$. The path of the particle will be :

Match List-I with List-II

Choose the correct answer from the options given below :

Two planets A and B of equal mass are having their period of revolutions T_A and T_B such that T_A = 2T_B. These planets are revolving in the circular orbits of radii r_A and r_B respectively. Which out of the following would be the correct relationship of their orbits?

A water drop of diameter 2 cm is broken into 64 equal droplets. The surface tension of water is 0.075 N/m. In this process the gain in surface energy will be :

Given below are two statements :

Statement I : When $\mu$ amount of an ideal gas undergoes adiabatic change from state (P₁, V₁, T₁) to state (P₂, V₂, T₂), then work done is $W = {{\mu R({T_2} - {T_1})} \over {1 - \gamma }}$, where $\gamma = {{{C_p}} \over {{C_v}}}$ and R = universal gas constant.

Statement II : In the above case, when work is done on the gas, the temperature of the gas would rise.

Choose the correct answer from the options given below :

Given below are two statements :

Statement I : A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive.

Statement II : An electric dipole is placed in a non-uniform electric field. The net electric force on the dipole will not be zero.

Choose the correct answer from the options given below :

The three charges q/2, q and q/2 are placed at the corners A, B and C of a square of side 'a' as shown in figure. The magnitude of electric field (E) at the corner D of the square, is :

An infinitely long hollow conducting cylinder with radius R carries a uniform current along its surface.

Choose the correct representation of magnetic field (B) as a function of radial distance (r) from the axis of cylinder.

A radar sends an electromagnetic signal of electric field (E₀) = 2.25 V/m and magnetic field (B₀) = 1.5 $\times$ 10^$-$8 T which strikes a target on line of sight at a distance of 3 km in a medium. After that, a part of signal (echo) reflects back towards the radar with same velocity and by same path. If the signal was transmitted at time t = 0 from radar, then after how much time echo will reach to the radar?

The refracting angle of a prism is A and refractive index of the material of the prism is cot (A/2). Then the angle of minimum deviation will be -

The aperture of the objective is 24.4 cm. The resolving power of this telescope, if a light of wavelength 2440 $\mathop A\limits^o$ is used to see th object will be :

The de Broglie wavelengths for an electron and a photon are $\lambda$_e and $\lambda$_p respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two ?

The Q-value of a nuclear reaction and kinetic energy of the projectile particle, K_p are related as :

For using a multimeter to identify diode from electrical components, choose the correct statement out of the following about the diode :

The velocity of sound in a gas, in which two wavelengths 4.08 m and 4.16 m produce 40 beats in 12s, will be :

A pendulum is suspended by a string of length 250 cm. The mass of the bob of the pendulum is 200 g. The bob is pulled aside until the string is at 60$^\circ$ with vertical as shown in the figure. After releasing the bob, the maximum velocity attained by the bob will be ____________ ms^$-$1. (if g = 10 m/s²)

A meter bridge setup is shown in the figure. It is used to determine an unknown resistance R using a given resistor of 15 $\Omega$. The galvanometer (G) shows null deflection when tapping key is at 43 cm mark from end A. If the end correction for end A is 2 cm, then the determined value of R will be ____________ $\Omega$.

Current measured by the ammeter (A) in the reported circuit when no current flows through 10 $\Omega$ resistance, will be ________________ A.

An AC source is connected to an inductance of 100 mH, a capacitance of 100 $\mu$F and a resistance of 120 $\Omega$ as shown in figure. The time in which the resistance having a thermal capacity 2 J/$^\circ$C will get heated by 16$^\circ$C is _____________ s.

The position vector of 1 kg object is $\overrightarrow r = \left( {3\widehat i - \widehat j} \right)m$ and its velocity $\overrightarrow v = \left( {3\widehat j + \widehat k} \right)m{s^{ - 1}}$. The magnitude of its angular momentum is $\sqrt x$ Nm where x is ___________.

A man of 60 kg is running on the road and suddenly jumps into a stationary trolly car of mass 120 kg. Then, the trolly car starts moving with velocity 2 ms^$-$1. The velocity of the running man was ___________ ms^$-$1, when he jumps into the car.

A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2 Mg force. In this situation, tension in the string is ${x \over 5}$ Mg for x = ______________. Neglect mass of the string and friction of the block (bigger mass) with ice slab.

(Given g = acceleration due to gravity)

The total internal energy of two mole monoatomic ideal gas at temperature T = 300 K will be _____________ J. (Given R = 8.31 J/mol.K)

A singly ionized magnesium atom (A = 24) ion is accelerated to kinetic energy 5 keV, and is projected perpendicularly into a magnetic field B of the magnitude 0.5 T. The radius of path formed will be _____________ cm.

A telegraph line of length 100 km has a capacity of 0.01 $\mu$F/km and it carries an alternating current at 0.5 kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is _____________ mH. (if $\pi$ = $\sqrt{10}$)