Two statements are given below.

Statement I : Nitrogen has more ionisation enthalpy and electronegativity than beryllium.

Statement II : $\mathrm{CrO}_3, \mathrm{~B}_2 \mathrm{O}_3$ are acidic oxide.

Correct answer is

At 290 K , a vessel (I) contains equal moles of three liquids $(A, B, C)$. The boiling points of $A, B$ and $C$ are $350 \mathrm{~K}, 373 \mathrm{~K}$ and 308 K respectively. Vessel (I) is heated to 300 K and vapours were collected into vessel (II). Identify the correct statements. (Assume vessel (I) contains liquids and vapours and vessel (II)contains only vapours)

(I) Vessel - I is rich in liquid $B$

(II) Vessel - II is rich in vapour of $C$

(III) The vapour pressures of $A, B, C$ in vessel (I) at 290 K follows the order $C>A>B$

Observe the following reaction.

$$ A B \mathrm{O}_3(\mathrm{~s}) \xrightarrow{1000 \mathrm{~K}} A \mathrm{O}(\mathrm{~s})+B \mathrm{O}_2(\mathrm{~g}) $$

$\Delta_r H$ for this reaction is $x \mathrm{~kJ} \mathrm{~mol}^{-1}$. What is its $\Delta_r U$ (in $\mathrm{kJ} \mathrm{mol}^{-1}$ ) at the same temperature?

$$ \left(R=8.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right) $$

At $300 \mathrm{~K}, \Delta_r G^{\Theta}$ for the reaction $A_2(g) \rightleftharpoons B_2(g)$ is $-11.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The Equilibrium constant at 300 K is approximately ( $R=8314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ )

Identify the correct statements from the following.

I. Reaction of hydrogen with fluorine occurs even in dark.

II. Manufacture of ammonia by Haber process is an endothermic reaction.

III. HF is electron rich hydride.

In which of the following reactions, hydrogen is oned the products?

I. $\mathrm{NaBH}_4+\mathrm{I}_2 \longrightarrow$

II. $\mathrm{BF}_3+\mathrm{NaH} \xrightarrow{450 \mathrm{~K}}$

III. $\mathrm{BF}_3+\mathrm{LiAlH}_4 \longrightarrow$

IV. $\mathrm{B}_2 \mathrm{H}_6+\mathrm{NH}_3 \xrightarrow{\text { heat }}$

Two statements are given below.

Statement I : $\mathrm{SnF}_4, \mathrm{PbF}_4$ are ionic in nature.

Statement II : GeCl ${ }_2$ is more stable than $\mathrm{GeCl}_4$

The correct answer is

Match the pollutant is List I with its maximum permissible limit in drinking water given in List II

What are $X$ and $Y$ respectively in the following reaction sequence?

At $300 \mathrm{~K}, 6 \mathrm{~g}$ of urea was dissolved in 500 mL of water. What is the osmotic pressure (in atm) of resultant solution?

$$ \begin{aligned} & \left(R=0.082 \mathrm{~L}^{\operatorname{atm~K}}{ }^{-1} \mathrm{~mol}^{-1}\right) \\ & (\mathrm{C}=12 ; \mathrm{N}=14 ; \mathrm{O}=16 ; \mathrm{H}=1) \end{aligned} $$

Consider the cell reaction at 300 K .

$$ A(s)+B^{2+}(a q) \rightleftharpoons A^{2+}(a q)+B(s) $$

Its $E^{\ominus}$ is 1.0 V . The $\Delta_r H^{\ominus}$ of the reaction is $-163 \mathrm{kJmol}^{-1}$.

What is $\Delta_r s^{\ominus}$ (in $\mathrm{JK}^{-1}$ ) of the reaction?

$$ \left(F=96500 \mathrm{C} \mathrm{~mol}^{-1}\right) $$

' $A$ ' is a protecting colloid. The following data is obtained for preventing the coagulation of 10 mL of gold sol to which 1 mL of $10 \% \mathrm{NaCl}$ is added. What is the gold number of ' $A$ '?

Two statements are given below.

Statement I : The reaction $\mathrm{Cr}_2 \mathrm{O}_3+2 \mathrm{Al} \longrightarrow \mathrm{Al}_2 \mathrm{O}_3+2 \mathrm{Cr}$ $\left(\Delta G^{\ominus}=-421 \mathrm{~kJ}\right)$ is thermodynamically feasible.

Statement II : The above reaction occurs at room temperature.

The correct answer is

Consider the following reactions

$Y$ can not be obtained from which of the following reaction?

Assertion (A) : Carboxylic acids are more acidic than phenols

Reason (R) : Resonance structures of carboxylate ion are equivalent, while resonance structures of phenoxide ion are not equivalent.

In the reaction sequence $Y$ is

$$ \mathrm{CH}_3 \mathrm{CO}_2 \mathrm{H} \xrightarrow[(2) \Delta]{(1) \mathrm{NH}_3} P \xrightarrow{\mathrm{Br} / \mathrm{NaOH}} Y $$

Define the function, $f, g$ and $h$ from $R$ to $R$ such that $f(x)=x^2-1, g(x)=\sqrt{x^2+1}$ and $h(x)= \begin{cases}0, \text { if } & x \leq 0 \\ x, \text { if } & x \geq 0\end{cases}$ consider the following statements

(i) fog is invertible

(ii) $h$ is an identify function

(iii) $f \circ g$ is not invertible

(iv) $(h \circ f \circ g) x=x^2$

Then, which one of the following is true ?

If $\alpha, \beta$ and $\gamma(\alpha<\beta<\gamma)$ are the values of $x$ such that $\left[\begin{array}{ccc}x-2 & 0 & 1 \\ 1 & x+3 & 2 \\ 2 & 0 & 2 x-1\end{array}\right]$ is a singular matrix, then $2 \alpha+3 \beta+4 \gamma$ is equal to

If $P(x, y)$ represents the complex number $z=x+iy$ in the argand plane and $\arg \left(\frac{z-3 i}{z+4}\right)=\frac{\pi}{2}$, then the equation of the locus of $P$ is

The set of all real values ' $a$ ' for which $-1<\frac{2 x^2+a x+2}{x^2+x+1}<3$ holds for all real values of $x$ is

The quotient, when $3 x^5-4 x^4+5 x^3-3 x^2+6 x-8$ is divided by $x^2+x-3$ is

If $\alpha_1, \alpha_2, \alpha_3, \alpha_4$ and $\alpha_5$ are the roots of $x^5-5 x^4+9 x^3-9 x^2+5 x-1=0$, then $\frac{1}{\alpha_1^2}+\frac{1}{\alpha_2^2}+\frac{1}{\alpha_3^2}+\frac{1}{\alpha_4^2}+\frac{1}{\alpha_5^2}$ is equal to

There were two women participating with some men in a chess tournament. Each participant played two games with the other. The number of games that the men played between themselves is 66 more than that of the men played with the women. Then, the total number of participants in the tournament is

If there are 6 alike fruits, 7 alike vegetables and 8 alike biscuits, then the number of ways of selecting any number of things out of them such that at least one from each category is selected, is

If the coefficients of $r$ th, $(r+1)$ th and $(r+2)$ th terms in the expansion of $(1+x)^n$ are in the ratio of $4: 15: 42$, then $n-r$ is equal to

If the coefficients of $(2 r+6)$ th and $(r-1)$ th terms in the expansion of $(1+x)^{21}$ are equal, then the value of $r$ is equal to

$$ \text { If } \frac{13 x+43}{2 x^2+17 x+30}=\frac{A}{2 x+5}+\frac{B}{x+6} \text {, then } A+B \text { is equal to } $$

The values of $x$ in $(-\pi, \pi)$, which satisfy the equation $8^{1+\cos ^2 x+\cos ^4 x+\ldots \ldots}=4^3$ are

If $\sinh x=\frac{\sqrt{21}}{2}$, then $\cosh 2 x+\sinh 2 x$ is equal to

In $a \triangle A B C$ if $r: R: r_2=1: 3: 7$, then $\sin (A+C)+\sin B$ is equal to

In $\triangle A B C,\left(r_1+r_2\right) \operatorname{cosec}^2 \frac{C}{2}$ is equal to

If the vectors $a \hat{\mathbf{i}}+\mathbf{j}+3 \hat{\mathbf{k}}, 4 \hat{\mathbf{i}}+5 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $4 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}$ are coplanar, then $a$ is equal to

The values of $x$ for which the angle between the vectors $x^2 \hat{\mathbf{i}}+2 x \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+x \hat{\mathbf{k}}$ is obtuse lie in the interval

If $\hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $2 \hat{\mathbf{i}}+\hat{\mathbf{j}}$ are the vertices of a tetrahedron, then its volume is

Based on the following statements, choose the correct option.

Statement I The variance of the first $n$ even natural numbers is $\frac{n^2-1}{4}$.

Statement II The difference between the variance of the first 20 even natural numbers and their arithmetic mean is 112 .

$E_1$ and $E_2$ are two independent events of a random experiment such that $P\left(E_1\right)=\frac{1}{2}$ and $P\left(E_1 \cup E_2\right)=\frac{2}{3}$. Then, match the items of List I with the items of List II.

$$ \begin{array}{lll} \hline & \text { List I } & \text { List II } \\ \hline \text { (A) } & P\left(E_2\right) & \text { (i) }1/2 \\ \hline \text { (B) } & P\left(E_1 / E_2\right) & \text { (ii) } 5 / 6 \\ \hline \text { (C) } & P\left(E_2 / E_1\right) & \text { (iii) } 1 / 3 \\ \hline \text { (D) } & P\left(E_1 \cup E_2\right) & \text { (iv) } 1 / 6 \\ \hline & & \text { (v) } 2 / 3 \\ \hline \end{array} $$

A bag contains 4 red and 5 black balls. Another bag contains 3 red and 6 black balls. If one ball is drawn from first bag and two balls from the second bag at random. The probability that out of the three, two are black and one is red, is

If a random variable $X$ has the following probability distribution, then its variance is nearly

$$ \begin{array}{clllllll} \hline X=x & -3 & -2 & -1 & 0 & 1 & 2 & 3 \\ \hline P(X=x) & 0.05 & 0.1 & 2 K & 0 & 0.3 & K & 0.1 \\ \hline \end{array} $$

If a line $L$ makes angles $\frac{\pi}{3}$ and $\frac{\pi}{4}$ with $Y$-axis and $Z$-axis respectively, then the angle between $L$ and another line having direction ratio $1,1,1$ is

$$\mathop {\lim }\limits_{x \to \infty } \frac{[2 x-3]}{x} \text { is equal to } $$

If a real valued function $f(x)=\left\{\begin{array}{cl}\frac{2 x^2+(k+2) x+9}{3 x^2-7 x-6}, & \text { for } x \neq 3 \\ 1, & \text { for } x=3\end{array}\right.$ is continuous at $x=3$ and $l$ is a finite value, then $l-k$ is equal to

If $f(x)=5 \cos ^3 x-3 \sin ^2 x$ and $g(x)=4 \sin ^3 x+\cos ^2 x$, then the derivative of $f(x)$ with respect to $g(x)$ is

The semi-vertical angle of a right circular cone is $45^{\circ} \%$ If the radius of the base of the cone is measured as 14 cm with an error of $\left(\frac{\sqrt{2}-1}{11}\right) \mathrm{cm}$, then the approximate error in measuring its total surface area is (in sq cm)

If a man of height 1.8 mt , is walking away from the foot of a light pole of height 6 mt , with a speed of 7 km per hour on a straight horizontal road opposite to the pole, then the rate of change of the length of his shadow is (in kmph )

If the curves $2 x^2+k y^2=30$ and $3 y^2=28 x$ cut each other orthogonally, then $k$ is equal to

If $\int \log \left(6 \sin ^2 x+17 \sin x+12\right) \cos x d x=f(x)+c$, then $f\left(\frac{\pi}{2}\right)$ is equal to

$$ \mathop {\lim }\limits_{x \to \infty }\left[\left(1+\frac{1}{n^3}\right)^{\frac{1}{n^3}}\left(1+\frac{8}{n^3}\right)^{\frac{4}{n^3}}\left(1+\frac{27}{n^3}\right)^{\frac{9}{n^3}} \ldots . .(2)^{\frac{1}{n}}\right] \text { is equaln } $$

The general solution of the differential equation $\left(x y+y^2\right) d x-\left(x^2-2 x y\right) d y=0$ is

In the equation $\left(p+\frac{a}{V^2}\right)(V-b)=R T$, where $p$ is pressure, $V$ is volume, $T$ is temperature, $R$ is universal gas constant, $a$ and $b$ are constants. The dimensions of $a$ are

A particle starts from rest and moves in a straight line. It travels a distance $2 L$ with uniform acceleration and then moves with a constant velocity a further distance of $L$. Finally, it comes to rest after moving a distance of $3 L$ under uniform retardation. Then, the ratio of average speed to the maximum speed $\left(\frac{v}{v_m}\right)$ of the particle is

A body of 2 kg mass slides down with an acceleration of $4 \mathrm{~ms}^{-2}$ on an inclined plane having slope of $30^{\circ}$. The external force required to take the same body up the plane with same acceleration will be (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A body of mass 30 kg moving with a velocity $20 \mathrm{~ms}^{-1}$ undergoes one-dimensional elastic collision with another ball of same mass moving in the opposite direction with a velocity of $30 \mathrm{~ms}^{-1}$. After collision the velocity of first and second bodies respectively are

Two blocks of equal masses are tied with a light string passing over a massless pulley (assuming frictionless surfaces ) acceleration of centre of mass of the two blocks is $\left(g=10 \mathrm{~ms}^{-2}\right)$

The displacement of a particle of mass 2 g executing simple harmonic motion is $x=8 \cos \left(50 t+\frac{\pi}{12}\right) \mathrm{m}$, where $t$ is time in second. The maximum kinetic energy of the particle is

A wire of length 100 cm and area of cross-section $2 \mathrm{~mm}^2$ is stretched by two forces of each 440 N applied at the ends of the wire in opposite directions along the length of the wire. If the elongation of the wire is 2 mm , the Young's modulus of the material of the wire is

Water of mass $m$ at $30^{\circ} \mathrm{C}$ is mixed with with 5 g of ice at $-20^{\circ} \mathrm{C}$. If the resultant temperature of the mixture is $6^{\circ} \mathrm{C}$, then the value of $m$ is (specific heat capacity of ice $=0.5 \mathrm{cal} \mathrm{g}^{-10} \mathrm{C}^{-1}$, specific heat capacity of water $=1$ calg ${ }^{-1}{ }^{\circ} \mathrm{C}^{-1}$ and latent heat of fusion of ice $=80 \mathrm{cal} \mathrm{g}^{-1}$ )

The total internal energy of 2 moles of a monoatomic gas at a temperature $27^{\circ} \mathrm{C}$ is $U$. The total internal energy of 3 moles of a diatomic gas at a temperature $127^{\circ} \mathrm{C}$ is

The fundamental frequency of an open pipe is 100 hz If the bottom end of the pipe is closed and $1 / 3$ rd of the pipe is filled with water, then the fundamental frequency of the pipe is

When a convex lens is immersed in a liquid of refractive index equal to $80 \%$ of the refractive index of the material of the lens. The focal length of the lens increases by $100 \%$. The refractive index of the liquid is

The magnitude of an electric field which can just suspend a deuteron of mass $3.2 \times 10^{-27} \mathrm{~kg}$ freely in ari is

A metallic wire loop of side $(l) 0.1 \mathrm{~m}$ and resistance of $1 \Omega$ is moved with a constant velocity in a uniform magnetic field of $2 \mathrm{Wm}^{-2}$ as shown in the figure. The magnetic field is perpendicular to the plane of the loop. The loop is connected to a network of resistors. The velocity of loop, so as to have a steady current of 1 mA in loop is

In the circuit shown in the figure, neglecting the source resistance, the voltmeter and ammeter readings respectively are

Light of wavelength $4000\mathop {\rm{A}}\limits^{\rm{o}}$ is incident on a sodium surface for which the threshold wavelength of photoelectrons is $5420 \mathop {\rm{A}}\limits^{\rm{o}}$. The work function of sodium is

The principle quantum number $n$ corresponding to the exited state of $\mathrm{He}^{+}$ion. If on transition to the ground state two photons in succession with wavelength $1026 \mathop {\rm{A}}\limits^{\rm{o}}$ and $304 \mathop {\rm{A}}\limits^{\rm{o}}$ are emitted $\left(R=1.097 \times 10^{-7} \mathrm{~m}^{-1}\right)$

$$ \text { Truth table for the given circuit is } $$

If $R_C$ and $R_B$ are respectively the resistances of in collector and base sides of the circuit and $\beta$ is the current amplification factor, then the voltage gain of a transistor amplifier in common emitter configuration is