The element having greatest difference between its first and second ionization energies, is:

The increasing order of reactivity of the following compounds towards aromatic electrophilic substitution reaction is:

Consider the van der Waals constants, a and b, for the following gases,

Which gas is expected to have the highest critical temperature?

The given plots represents the variation of the concentration of a reactant R with time for two different reactions (i) and (ii). The respective orders of the reactions are:

Among the following, the set of parameters that represents path functions, is:

(1) q + w

(2) q

(3) w

(4) H – TS 

The ore that contains the metal in the form of fluoride is:

Excessive release of CO₂ into the atmosphere results in:

Aniline dissolved in dilute HCl is reacted with sodium nitrate at 0°C. This solution was added dropwise to a solution containing equimolar mixture of aniline and phenol in dil. HCl. The structure of the major product is:

Among the following, the molecule expected to be stabilized by anion formation is:

C₂, O₂, NO, F₂

The correct order of the oxidation states of nitrogen in NO, N₂O, NO₂ and N₂O₃ is:

Liquid 'M' and liquid 'N' form an ideal solution. The vapour pressures of pure liquids 'M' and 'N' are 450 and 700 mmHg, respectively, at the same temperature. Then correct statement is:

(x_M = Mole fraction of ‘M’ in solution;

x_N = Mole fraction of ‘N’ in solution;

y_M = Mole fraction of ‘M’ in vapour phase;

y_N = Mole fraction of ‘N’ in vapour phase)

The osmotic pressure of a dilute solution of an ionic compound XY in water is four times that of a solution of 0.01 M BaCl₂ in water. Assuming complete dissociation of the given ionic compounds in water, the concentration of XY (in mol L^-1) in solution is:

The number of water molecule(s) not coordinated to copper ion directly in CuSO₄.5H₂O is:

The standard Gibbs energy for the given cell reaction in kJ mol^-1 at 298 K is:

Zn(s) + Cu ²⁺ (aq) →Zn²⁺ (aq) + Cu(s)

E° = 2V at 298 K

(Faraday’s constant, F = 96000 C mol-1)

The major product of the following reaction is:

For any given series of spectral lines of atomic hydrogen, let $\mathrm{\Delta }\overline{v}={\overline{v}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\overline{v}}_{\mathrm{m}\mathrm{i}\mathrm{n}}$ be the difference in maximum and minimum frequencies in cm^-1. The ratio $\frac{\mathrm{\Delta }{\overline{v}}_{Lyman}}{\mathrm{\Delta }{\overline{v}}_{Balmer}}$ is:

The organic compound that gives following qualitative analysis is:

C₆₀, an allotrope of carbon contains:

The major product of the following reaction is:

The one that will show optical activity is:

(en = ethane-1,2-diamine)

The correct IUPAC name of the following compound is:

Match the catalysts (Column I) with products (Column II).

Which of the following statements is not true about sucrose?

Magnesium powder burns in air to give:

The major product of the following reaction is:

The major product of the following reaction is:

$\mathrm{C}{\mathrm{H}}_3\mathrm{C}\equiv \mathrm{C}\mathrm{H}\underset{(ii)DI}{\overset{(i)DCl(1equiv.)}{\to }}$

The major product of the following reaction is:

$\mathrm{C}{\mathrm{H}}_3\mathrm{C}\mathrm{H}=\mathrm{C}\mathrm{H}\mathrm{C}{\mathrm{O}}_2\mathrm{C}{\mathrm{H}}_3\stackrel{{\text{LiAlH}}_4}{\to }$

The degenerate orbitals of [Cr(H₂O)₆]³⁺ are:

The aerosol is a kind of colloid in which:

For a reaction, N₂ (g) + 3H₂ (g) → 2NH₃ (g); identify dihydrogen (H₂) as a limiting reagent in the following reaction mixtures.

Slope of a line passing throughP(2, 3) and intersecting the linex + y = 7at a distance of 4 units from P, is:

If the standard deviation of the numbers -1, 0, 1, k is $\sqrt{5}$ where k > 0, then k is equal to:

If f(x) is a non-zero polynomial of degree four, having local extreme points at x = -1, 0, 1; then the set

S = {x ∈ R : f(x) = f(0)} contains exactly:

The integral ∫sec^2⁄3 x cosec^4⁄3 x dx is equal to:

(Here C is a constant of integration)

Four persons can hit a target correctly with probabilities $\frac{1}{2},\frac{1}{3},\frac{1}{4}\mathrm{a}\mathrm{n}\mathrm{d}\frac{1}{8}$ respectively. If all hit at the target independently, then the probability that the target would be hit, is:

If the line, $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{4}$ meets the plane, $x+2y+3z=15$ at a point P, then the distance of P from the origin is: 

If the tangent to the curve, y = x³ + ax – b at the point (1, -5) is perpendicular to the line,

 - x + y + 4 = 0, then which one of the following points lies on the curve?

The value of ${\int }_0^{\pi /2}\frac{\mathrm{s}\mathrm{i}{\mathrm{n}}^{3}x}{\mathrm{s}\mathrm{i}\mathrm{n}x+\mathrm{c}\mathrm{o}\mathrm{s}x}\mathrm{d}\mathrm{x}$ is:

The value of cos² 10° – cos 10° cos 50°+ cos² 50° is:

If the line $y=mx+7\sqrt{3}$ is normal to the hyperbola $\frac{x^2}{24}-\frac{y^2}{18}=1,$ then a value of m is:

The solution of the differential equation $x\frac{\mathrm{d}y}{\mathrm{d}x}+2y=x^2$ (x ≠ 0) with y(1) = 1, is:

For any two statements p and q, the negation of the expressionp∨(~p ∧ q)  is:

All the points in the set $\mathrm{S}=\left\{\frac{\alpha +i}{\alpha -i}:\alpha \in \mathrm{R}\right\}\left(i=\sqrt{-1}\right)$ lie on a:

If the fourth term in the Binomial expansion of ${\left(\frac{2}{x}+x^{\mathrm{l}\mathrm{o}{\mathrm{g}}_{8}x}\right)}^6$ (x > 0) is 20 × 8⁷, then a value of x is:

If the function $f$ defined on $\left(\frac{\pi }{6},\frac{\pi }{3}\right)$ by

$f\left(x\right)=\{\begin{array}{cc}\frac{\sqrt{2}\mathrm{c}\mathrm{o}\mathrm{s}x-1}{\mathrm{c}\mathrm{o}\mathrm{t}x-1},& x\ne \frac{\pi }{4}\\ \mathrm{k},& x=\frac{\pi }{4}\end{array}$ is continuous, then k is equal to:

If the functionf : R - {1,-1} →Adefined by $f\left(x\right)=\frac{x^2}{1-x^2},$ is surjective, then A is equal to: 

A plane passing through the points(0, -1, 0) and (0, 0, 1) and making an angle $\frac{\pi }{4}$ with the planey – z + 5 = 0, also passes through the point: 

Let the sum of the firstterms of a non-constant A.P., a₁, a₂, a₃,……… be $50n+\frac{n\left(n-7\right)}{2}A$, where A is a constant. If d is the common difference of this A.P., then the ordered pair (d, a₅₀)is equal to:

Let S = {θ ϵ [-2π, 2π] : 2 cos² θ + 3 sin θ = 0} Then the sum of the elements of S is:

Let p, q ∈ R. If $2-\sqrt{3}$ is a root of the quadratic equation,x² + px + q = 0, then: 

Let f(x) = 15 – |x – 10|; x ∈ R. Then the set of all values of x, at which the function, g(x) = f(f(x)) is not differentiable, is:

Let S be the set of all values offor which the tangent to the curvey = f(x) = x³ – x² – 2x at (x, y) is parallel to the line segment joining the points (1, f(1)) and (-1, f(-1)), then S is equal to:

If a tangent to the circle x² + y² = 1 intersects the coordinate axes at distinct points P and Q, then the locus of the mid-point of PQ is:

Let $\overrightarrow{\alpha }=3\hat{i}+\hat{j}\mathrm{a}\mathrm{n}\mathrm{d}\overrightarrow{{\beta }_{}}=2\hat{i}-\hat{j}+3\hat{k}.$If $\overrightarrow{{\beta }_{}}={\overrightarrow{\beta }}_1-{\overrightarrow{\beta }}_2,\mathrm{w}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{e}\overrightarrow{\beta }$ is parallel to $\overrightarrow{\alpha }\mathrm{a}\mathrm{n}\mathrm{d}{\overrightarrow{\beta }}_2$ is perpendicular to $\overrightarrow{\alpha },\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{n}{\overrightarrow{\beta }}_1\times {\overrightarrow{\beta }}_2$ is equal to: 

The area (in sq. units) of the region A = {(x, y): x² ≤ y ≤ x +2} is:

If $\left[\begin{array}{cc}1& 1\\ 0& 1\end{array}\right]\cdot \left[\begin{array}{cc}1& 2\\ 0& 1\end{array}\right]\cdot \left[\begin{array}{cc}1& 3\\ 0& 1\end{array}\right]\dots \dots \dots \left[\begin{array}{cc}1& \mathrm{n}-1\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}1& 78\\ 0& 1\end{array}\right],$then the inverse of $\left[\begin{array}{cc}1& \mathrm{n}\\ 0& 1\end{array}\right]$ is:

Let $\sum _{k=1}^{10}f\left(a+k\right)=16\left(2^{10}-1\right),$ where the function $f$ satisfies f(x + y) = f(x)f(y) for all natural numbers x, y and f(1) = 2. Then the natural number 'a' is: 

A committee of 11 members is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with at least 3 females, then:

Let $\alpha \mathrm{a}\mathrm{n}\mathrm{d}\beta$ be the roots of the equationx² + x +1 = 0. Then for y ≠ 0 in R,

$\left|\begin{array}{ccc}y+1& \alpha & \beta \\ \alpha & y+\beta & 1\\ \beta & 1& y+\alpha \end{array}\right|$ is equal to: 

If one end of a focal chord of the parabola, y² = 16x is at (1, 4), then the length of this focal chord is: