The compound which will have the lowest rate towards nucleophilic aromatic substitution on treatment with OH$^-$ is

Which of the following conformations will be the most stable?

A litre of buffer solution contains 0.1 mole of each of NH$_3$ and NH$_4$Cl. On the addition of 0.02 mole of HCl by dissolving gaseous HCl, the pH of the solution is found to be _____________ $\times$ 10$^{-3}$ (Nearest integer)

[Given : $\mathrm{pK_b(NH_3)=4.745}$

$\mathrm{\log2=0.301}$

$\mathrm{\log3=0.477}$

$\mathrm{T=298~K]}$

The osmotic pressure of solutions of PVC in cyclohexanone at 300 K are plotted on the graph.

The molar mass of PVC is ____________ g mol$^{-1}$ (Nearest integer)

(Given : R = 0.083 L atm K$^{-1}$ mol$^{-1}$)

An athlete is given 100 g of glucose (C$_6$H$_{12}$O$_6$) for energy. This is equivalent to 1800kJ of energy. The 50% of this energy gained is utilized by the athlete for sports activities at the event. In order to avoid storage of energy, the weight of extra water he would need to perspire is ____________ g (Nearest integer)

Assume that there is no other way of consuming stored energy.

Given : The enthalpy of evaporation of water is 45 kJ mol$^{-1}$

Molar mass of C, H & O are 12, 1 and 16 g mol$^{-1}$.

The minimum value of the function $f(x) = \int\limits_0^2 {{e^{|x - t|}}dt}$ is :

Let $y(x) = (1 + x)(1 + {x^2})(1 + {x^4})(1 + {x^8})(1 + {x^{16}})$. Then $y' - y''$ at $x = - 1$ is equal to

Let S$_1$ and S$_2$ be respectively the sets of all $a \in \mathbb{R} - \{ 0\}$ for which the system of linear equations

$ax + 2ay - 3az = 1$

$(2a + 1)x + (2a + 3)y + (a + 1)z = 2$

$(3a + 5)x + (a + 5)y + (a + 2)z = 3$

has unique solution and infinitely many solutions. Then

Let $y = y(x)$ be the solution curve of the differential equation ${{dy} \over {dx}} = {y \over x}\left( {1 + x{y^2}(1 + {{\log }_e}x)} \right),x > 0,y(1) = 3$. Then ${{{y^2}(x)} \over 9}$ is equal to :

The constant term in the expansion of ${\left( {2x + {1 \over {{x^7}}} + 3{x^2}} \right)^5}$ is ___________.

Let S = {1, 2, 3, 5, 7, 10, 11}. The number of non-empty subsets of S that have the sum of all elements a multiple of 3, is _____________.

Let $x$ and $y$ be distinct integers where $1 \le x \le 25$ and $1 \le y \le 25$. Then, the number of ways of choosing $x$ and $y$, such that $x+y$ is divisible by 5, is ____________.

A parallel plate capacitor has plate area 40 cm$^2$ and plates separation 2 mm. The space between the plates is filled with a dielectric medium of a thickness 1 mm and dielectric constant 5. The capacitance of the system is :

The correct sequence of reagents for the preparation of Q and R is :

Match items of Row I with those of Row II.

Row I :

Row II :

(i) $\alpha$-$\mathrm{D}$-$(-)$-$\mathrm{Fructofuranose}$

(ii) $\beta$-D-$(-)$-Fructofuranose

(iii) $\alpha$-D-$(-)$ Glucopyranose

(iv) $\beta$-D-$(-)$-Glucopyranose

Correct match is

Identify the product formed (A and E)

'25 volume' hydrogen peroxide means

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

Assertion A : Acetal / Ketal is stable in basic medium.

Reason R : The high leaving tendency of alkoxide ion gives the stability to acetal/ketal in basic medium.

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

Match the List-I with List-II :

Correct match is -

The density of a monobasic strong acid (Molar mass 24.2 g/mol) is 1.21 kg/L. The volume of its solution required for the complete neutralization of 25 mL of 0.24 M NaOH is __________ $\times$ 10$^{-2}$ mL (Nearest integer)

In sulphur estimation, 0.471 g of an organic compound gave 1.4439 g of barium sulphate. The percentage of sulphur in the compound is ____________ (Nearest Integer)

(Given : Atomic mass Ba: 137 u, S: 32 u, O: 16 u)

For the first order reaction A $\to$ B, the half life is 30 min. The time taken for 75% completion of the reaction is _________ min. (Nearest integer)

Given : log 2 = 0.3010

log 3 = 0.4771

log 5 = 0.6989

The mean and variance of the marks obtained by the students in a test are 10 and 4 respectively. Later, the marks of one of the students is increased from 8 to 12. If the new mean of the marks is 10.2, then their new variance is equal to :

Let M be the maximum value of the product of two positive integers when their sum is 66. Let the sample space $S = \left\{ {x \in \mathbb{Z}:x(66 - x) \ge {5 \over 9}M} \right\}$ and the event $\mathrm{A = \{ x \in S:x\,is\,a\,multiple\,of\,3\}}$. Then P(A) is equal to :

Let $f(x) = \int {{{2x} \over {({x^2} + 1)({x^2} + 3)}}dx}$. If $f(3) = {1 \over 2}({\log _e}5 - {\log _e}6)$, then $f(4)$ is equal to

Consider the lines $L_1$ and $L_2$ given by

${L_1}:{{x - 1} \over 2} = {{y - 3} \over 1} = {{z - 2} \over 2}$

${L_2}:{{x - 2} \over 1} = {{y - 2} \over 2} = {{z - 3} \over 3}$.

A line $L_3$ having direction ratios 1, $-$1, $-$2, intersects $L_1$ and $L_2$ at the points $P$ and $Q$ respectively. Then the length of line segment $PQ$ is

The points of intersection of the line $ax + by = 0,(a \ne b)$ and the circle ${x^2} + {y^2} - 2x = 0$ are $A(\alpha ,0)$ and $B(1,\beta )$. The image of the circle with AB as a diameter in the line $x + y + 2 = 0$ is :

Let $\mathrm{z_1=2+3i}$ and $\mathrm{z_2=3+4i}$. The set $\mathrm{S = \left\{ {z \in \mathbb{C}:{{\left| {z - {z_1}} \right|}^2} - {{\left| {z - {z_2}} \right|}^2} = {{\left| {{z_1} - {z_2}} \right|}^2}} \right\}}$ represents a

Let $\mathrm{A_1,A_2,A_3}$ be the three A.P. with the same common difference d and having their first terms as $\mathrm{A,A+1,A+2}$, respectively. Let a, b, c be the $\mathrm{7^{th},9^{th},17^{th}}$ terms of $\mathrm{A_1,A_2,A_3}$, respective such that \left| {\matrix{ a & 7 & 1 \cr {2b} & {17} & 1 \cr c & {17} & 1 \cr } } \right| + 70 = 0.

If $a=29$, then the sum of first 20 terms of an AP whose first term is $c-a-b$ and common difference is $\frac{d}{12}$, is equal to ___________.

The root mean square velocity of molecules of gas is

Inert gases have positive electron gain enthalpy. Its correct order is :

Match List I with List II

Choose the correct answer from the options given below :

The number of paramagnetic species from the following is _____________.

$\mathrm{{[Ni{(CN)_4}]^{2 - }},[Ni{(CO)_4}],{[NiC{l_4}]^{2 - }}}$

$\mathrm{{[Fe{(CN)_6}]^{4 - }},{[Cu{(N{H_3})_4}]^{2 + }}}$

$\mathrm{{[Fe{(CN)_6}]^{3 - }}\,and\,{[Fe{({H_2}O)_6}]^{2 + }}}$

The total number of lone pairs of electrons on oxygen atoms of ozone is __________.

The vector $\overrightarrow a = - \widehat i + 2\widehat j + \widehat k$ is rotated through a right angle, passing through the y-axis in its way and the resulting vector is $\overrightarrow b$. Then the projection of $3\overrightarrow a + \sqrt 2 \overrightarrow b$ on $\overrightarrow c = 5\widehat i + 4\widehat j + 3\widehat k$ is :

Let $x=2$ be a local minima of the function $f(x)=2x^4-18x^2+8x+12,x\in(-4,4)$. If M is local maximum value of the function $f$ in ($-4,4)$, then M =

The value of $\mathop {\lim }\limits_{n \to \infty } {{1 + 2 - 3 + 4 + 5 - 6\, + \,.....\, + \,(3n - 2) + (3n - 1) - 3n} \over {\sqrt {2{n^4} + 4n + 3} - \sqrt {{n^4} + 5n + 4} }}$ is :

In the cumene to phenol preparation in presence of air, the intermediate is

The radius of the $\mathrm{2^{nd}}$ orbit of $\mathrm{Li^{2+}}$ is $x$. The expected radius of the $\mathrm{3^{rd}}$ orbit of $\mathrm{Be^{3+}}$ is

The correct order in aqueous medium of basic strength in case of methyl substituted amines is :

Consider the cell

$\mathrm{Pt(s)|{H_2}(g)\,(1\,atm)|{H^ + }\,(aq,[{H^ + }] = 1)||F{e^{3 + }}(aq),F{e^{2 + }}(aq)|Pt(s)}$

Given $\mathrm{E_{F{e^{3 + }}/F{e^{2 + }}}^o = 0.771\,V}$ and $\mathrm{E_{{H^ + }/1/2\,{H_2}}^o = 0\,V,\,T = 298\,K}$

If the potential of the cell is 0.712 V, the ratio of concentration of Fe$^{2+}$ to Fe$^{3+}$ is _____________ (Nearest integer)

How many of the following metal ions have similar value of spin only magnetic moment in gaseous state? ______________

(Given : Atomic number V, 23; Cr, 24; Fe, 26; Ni, 28)

V$^{3+}$, Cr$^{3+}$, Fe$^{2+}$, Ni$^{3+}$

The distance of the point P(4, 6, $-$2) from the line passing through the point ($-$3, 2, 3) and parallel to a line with direction ratios 3, 3, $-$1 is equal to :

Let $f:(0,1)\to\mathbb{R}$ be a function defined $f(x) = {1 \over {1 - {e^{ - x}}}}$, and $g(x) = \left( {f( - x) - f(x)} \right)$. Consider two statements

(I) g is an increasing function in (0, 1)

(II) g is one-one in (0, 1)

Then,

For some a, b, c $\in\mathbb{N}$, let $f(x) = ax - 3$ and $\mathrm{g(x)=x^b+c,x\in\mathbb{R}}$. If ${(fog)^{ - 1}}(x) = {\left( {{{x - 7} \over 2}} \right)^{1/3}}$, then $(fog)(ac) + (gof)(b)$ is equal to ____________.

Let $S = \left\{ {\alpha :{{\log }_2}({9^{2\alpha - 4}} + 13) - {{\log }_2}\left( {{5 \over 2}.\,{3^{2\alpha - 4}} + 1} \right) = 2} \right\}$. Then the maximum value of $\beta$ for which the equation ${x^2} - 2{\left( {\sum\limits_{\alpha \in s} \alpha } \right)^2}x + \sum\limits_{\alpha \in s} {{{(\alpha + 1)}^2}\beta = 0}$ has real roots, is ____________.

If the area enclosed by the parabolas $\mathrm{P_1:2y=5x^2}$ and $\mathrm{P_2:x^2-y+6=0}$ is equal to the area enclosed by $\mathrm{P_1}$ and $\mathrm{y=\alpha x,\alpha > 0}$, then $\alpha^3$ is equal to ____________.

If the sum of all the solutions of ${\tan ^{ - 1}}\left( {{{2x} \over {1 - {x^2}}}} \right) + {\cot ^{ - 1}}\left( {{{1 - {x^2}} \over {2x}}} \right) = {\pi \over 3}, - 1 < x < 1,x \ne 0$, is $\alpha - {4 \over {\sqrt 3 }}$, then $\alpha$ is equal to _____________.

Match List I with List II

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 : Photodiodes are used in forward bias usually for measuring the light intensity.

Reason R : For a p-n junction diode, at applied voltage V the current in the forward bias is more than the current in the reverse bias for $\mathrm{|{V_z}| > \pm v \ge |{v_0}|}$ where $\mathrm{v_0}$ is the threshold voltage and $\mathrm{V_z}$ is the breakdown voltage.

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

A uniform metallic wire carries a current 2 A, when 3.4 V battery is connected across it. The mass of uniform metallic wire is 8.92 $\times$ 10$^{-3}$ kg, density is 8.92 $\times$ 10$^{3}$ kg/m$^3$ and resistivity is 1.7 $\times$ 10$^{-8}~\Omega$-$\mathrm{m}$. The length of wire is :

As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of 45$^\circ$ with the load axis. The length of wire is 62.8 cm and its diameter is 4 mm. The Young's modulus is found to be $x\times10^4$ Nm$^{-2}$. The value of $x$ is ___________.

An LCR series circuit of capacitance 62.5 nF and resistance of 50 $\Omega$, is connected to an A.C. source of frequency 2.0 kHz. For maximum value of amplitude of current in circuit, the value of inductance is __________ mH.

(Take $\pi^2=10$)

A uniform electric field of 10 N/C is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy 0.5 eV. The length of each plate is 10 cm. The angle ($\theta$) of deviation of the path of electron as it comes out of the field is ___________ (in degree).

A solenoid of 1200 turns is wound uniformly in a single layer on a glass tube 2 m long and 0.2 m in diameter. The magnetic intensity at the center of the solenoid when a current of 2 A flows through it is :

An object of mass 8 kg is hanging from one end of a uniform rod CD of mass 2 kg and length 1 m pivoted at its end C on a vertical wall as shown in figure. It is supported by a cable AB such that the system is in equilibrium. The tension in the cable is (Take g = 10 m/s$^2$)

Match List I with List II

	List I (Current configuration)		List II (Magnitude of Magnetic Field at point O)
A.		I.	${B_0} = {{{\mu _0}I} \over {4\pi r}}[\pi + 2]$
B.		II.	${B_0} = {{{\mu _0}} \over {4 }}{I \over r}$
C.		III.	${B_0} = {{{\mu _0}I} \over {2\pi r}}[\pi - 1]$
D.		IV.	${B_0} = {{{\mu _0}I} \over {4\pi r}}[\pi + 1]$

Choose the correct answer from the options given below :

In Young's double slits experiment, the position of 5$\mathrm{^{th}}$ bright fringe from the central maximum is 5 cm. The distance between slits and screen is 1 m and wavelength of used monochromatic light is 600 nm. The separation between the slits is :

Assume that the earth is a solid sphere of uniform density and a tunnel is dug along its diameter throughout the earth. It is found that when a particle is released in this tunnel, it executes a simple harmonic motion. The mass of the particle is 100 g. The time period of the motion of the particle will be (approximately)

(Take g = 10 m s$^{-2}$ , radius of earth = 6400 km)

Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV, has a de-Broglie wavelength of $\lambda_0$. IF the voltage is increased to 40 kV, then the de-Broglie wavelength associated with the electron beam would be :

An electromagnetic wave is transporting energy in the negative $z$ direction. At a certain point and certain time the direction of electric field of the wave is along positive $y$ direction. What will be the direction of the magnetic field of the wave at that point and instant?

$\mathrm{I_{CM}}$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. $\mathrm{I_{AB}}$ is it's moment of inertia about an axis AB perpendicular to plane and parallel to axis CM at a distance $\frac{2}{3}$R from center. Where R is the radius of the disc. The ratio of $\mathrm{I_{AB}}$ and $\mathrm{I_{CM}}$ is $x:9$. The value of $x$ is _____________.

A ray of light is incident from air on a glass plate having thickness $\sqrt3$ cm and refractive index $\sqrt2$. The angle of incidence of a ray is equal to the critical angle for glass-air interface. The lateral displacement of the ray when it passes through the plate is ____________ $\times$ 10$^{-2}$ cm. (given $\sin 15^\circ = 0.26$)

The wavelength of the radiation emitted is $\lambda_0$ when an electron jumps from the second excited state to the first excited state of hydrogen atom. If the electron jumps from the third excited state to the second orbit of the hydrogen atom, the wavelength of the radiation emitted will $\frac{20}{x}\lambda_0$. The value of $x$ is _____________.

In the given circuit, the equivalent resistance between the terminal A and B is __________ $\Omega$.

T is the time period of simple pendulum on the earth's surface. Its time period becomes $x$ T when taken to a height R (equal to earth's radius) above the earth's surface. Then, the value of $x$ will be :

A car travels a distance of '$x$' with speed $v_1$ and then same distance '$x$' with speed $v_2$ in the same direction. The average speed of the car is :

In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes $x$ times its initial resonant frequency $\omega_0$. The value of $x$ is :

A car is moving with a constant speed of 20 m/s in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take g = 10 m/s$^2$)

If $\overrightarrow P = 3\widehat i + \sqrt 3 \widehat j + 2\widehat k$ and $\overrightarrow Q = 4\widehat i + \sqrt 3 \widehat j + 2.5\widehat k$ then, the unit vector in the direction of $\overrightarrow P \times \overrightarrow Q$ is ${1 \over x}\left( {\sqrt 3 \widehat i + \widehat j - 2\sqrt 3 \widehat k} \right)$. The value of $x$ is _________.

An object of mass 'm' initially at rest on a smooth horizontal plane starts moving under the action of force F = 2N. In the process of its linear motion, the angle $\theta$ (as shown in figure) between the direction of force and horizontal varies as $\theta=\mathrm{k}x$, where k is a constant and $x$ is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be $E = {n \over k}\sin \theta$. The value of n is ___________.

The distance between two consecutive points with phase difference of 60$^\circ$ in a wave of frequency 500 Hz is 6.0 m. The velocity with which wave is travelling is __________ km/s