AIEEE 2008 — 27 Apr Offline Set C-5 (Previous Year Paper)

AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of the point A from a certain point C on the ground is $60^\circ$. He moves away from the pole along the line BC to a point D such that CD = 7 m. From D the angle of elevation of the point A is $45^\circ$. Then the height of the pole is

1. A.$\frac{7\sqrt{3}}{2}\cdot\frac{1}{\sqrt{3}-1}$ m
2. B.$\frac{7\sqrt{3}}{2}(\sqrt{3}+1)$ m✓
3. C.$\frac{7\sqrt{3}}{2}(\sqrt{3}-1)$ m
4. D.$\frac{7\sqrt{3}}{2}\cdot\frac{1}{\sqrt{3}+1}$

Correct answer: B

It is given that the events A and B are such that $P(A) = \frac{1}{4}$, $P(A|B) = \frac{1}{2}$ and $P(B|A) = \frac{2}{3}$. Then P(B) is

1. A.$\frac{1}{6}$
2. B.$\frac{1}{3}$✓
3. C.$\frac{2}{3}$
4. D.$\frac{1}{2}$

Correct answer: B

A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then $P(A\cup B)$ is

1. A.$\frac{3}{5}$
2. B.0
3. C.1✓
4. D.$\frac{2}{5}$

Correct answer: C

A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2. Then the length of the semi-major axis is

1. A.$\frac{8}{3}$✓
2. B.$\frac{2}{3}$
3. C.$\frac{4}{3}$
4. D.$\frac{5}{3}$

Correct answer: A

A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at

1. A.(0, 2)
2. B.(1, 0)✓
3. C.(0, 1)
4. D.(2, 0)

Correct answer: B

The point diametrically opposite to the point P(1, 0) on the circle $x^2 + y^2 + 2x + 4y - 3 = 0$ is

1. A.(3, -4)
2. B.(-3, 4)
3. C.(-3, -4)✓
4. D.(3, 4)

Correct answer: C

Let $f : N \to Y$ be a function defined as $f(x) = 4x + 3$, where $Y = \{y \in N : y = 4x + 3 \text{ for some } x \in N\}$. Show that f is invertible and its inverse is

1. A.$g(y) = \frac{3y+4}{3}$
2. B.$g(y) = 4 + \frac{y+3}{4}$
3. C.$g(y) = \frac{y+3}{4}$
4. D.$g(y) = \frac{y-3}{4}$✓

Correct answer: D

The conjugate of a complex number is $\frac{1}{i-1}$. Then the complex number is

1. A.$\frac{-1}{i-1}$
2. B.$\frac{1}{i+1}$
3. C.$\frac{-1}{i+1}$✓
4. D.$\frac{1}{i-1}$

Correct answer: C

Let R be the real line. Consider the following subsets of the plane $R\times R$. $S = \{(x, y) : y = x + 1 \text{ and } 0 < x < 2\}$, $T = \{(x, y) : x - y \text{ is an integer}\}$. Which one of the following is true?

1. A.neither S nor T is an equivalence relation on R
2. B.both S and T are equivalence relations on R
3. C.S is an equivalence relation on R but T is not
4. D.T is an equivalence relation on R but S is not✓

Correct answer: D

The perpendicular bisector of the line segment joining P(1, 4) and Q(k, 3) has y-intercept -4. Then a possible value of k is

1. A.1
2. B.2
3. C.-2
4. D.-4✓

Correct answer: D

The solution of the differential equation $\frac{dy}{dx} = \frac{x+y}{x}$ satisfying the condition y(1) = 1 is

1. A.$y = \ln x + x$
2. B.$y = x\ln x + x^2$
3. C.$y = xe^{(x-1)}$
4. D.$y = x\ln x + x$✓

Correct answer: D

The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80. Then which one of the following gives possible values of a and b?

1. A.a = 0, b = 7
2. B.a = 5, b = 2
3. C.a = 1, b = 6
4. D.a = 3, b = 4✓

Correct answer: D

The vector $\vec{a} = \alpha\hat{i} + 2\hat{j} + \beta\hat{k}$ lies in the plane of the vectors $\vec{b} = \hat{i} + \hat{j}$ and $\vec{c} = \hat{j} + \hat{k}$ and bisects the angle between $\vec{b}$ and $\vec{c}$. Then which one of the following gives possible values of $\alpha$ and $\beta$?

1. A.$\alpha = 2, \beta = 2$
2. B.$\alpha = 1, \beta = 2$
3. C.$\alpha = 2, \beta = 1$
4. D.$\alpha = 1, \beta = 1$✓

Correct answer: D

The non-zero vectors $\vec{a}$, $\vec{b}$ and $\vec{c}$ are related by $\vec{a} = 8\vec{b}$ and $\vec{c} = -7\vec{b}$. Then the angle between $\vec{a}$ and $\vec{c}$ is

1. A.0
2. B.$\pi/4$
3. C.$\pi/2$
4. D.$\pi$✓

Correct answer: D

The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz-plane at the point $\left(0, \frac{17}{2}, \frac{-13}{2}\right)$. Then

1. A.a = 2, b = 8
2. B.a = 4, b = 6
3. C.a = 6, b = 4✓
4. D.a = 8, b = 2

Correct answer: C

If the straight lines $\frac{x-1}{k} = \frac{y-2}{2} = \frac{z-3}{3}$ and $\frac{x-2}{3} = \frac{y-3}{k} = \frac{z-1}{2}$ intersect at a point, then the integer k is equal to

1. A.-5✓
2. B.5
3. C.2
4. D.-2

Correct answer: A

Statement-1: For every natural number $n \ge 2$, $\frac{1}{\sqrt{1}} + \frac{1}{\sqrt{2}} + \dots + \frac{1}{\sqrt{n}} > \sqrt{n}$. Statement-2: For every natural number $n \ge 2$, $\sqrt{n(n+1)} < n + 1$.

1. A.Statement-1 is false, Statement-2 is true
2. B.Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
3. C.Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1✓
4. D.Statement-1 is true, Statement-2 is false

Correct answer: C

Let A be a $2\times2$ matrix with real entries. Let I be the $2\times2$ identity matrix. Denote by tr(A), the sum of diagonal entries of A. Assume that $A^2 = I$. Statement-1: If $A \ne I$ and $A \ne -I$, then det A = -1. Statement-2: If $A \ne I$ and $A \ne -I$, then $tr(A) \ne 0$.

1. A.Statement-1 is false, Statement-2 is true
2. B.Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
3. C.Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
4. D.Statement-1 is true, Statement-2 is false✓

Correct answer: D

Statement-1: $\sum_{r=0}^{n}(r+1)\,{}^nC_r = (n+2)2^{n-1}$. Statement-2: $\sum_{r=0}^{n}(r+1)\,{}^nC_rx^r = (1+x)^n + nx(1+x)^{n-1}$.

1. A.Statement-1 is false, Statement-2 is true
2. B.Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1✓
3. C.Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
4. D.Statement-1 is true, Statement-2 is false

Correct answer: B

Let p be the statement 'x is an irrational number', q be the statement 'y is a transcendental number', and r be the statement 'x is a rational number iff y is a transcendental number'. Statement-1: r is equivalent to either q or p. Statement-2: r is equivalent to $\sim(p \leftrightarrow \sim q)$.

1. A.Statement-1 is false, Statement-2 is true
2. B.Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
3. C.Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
4. D.Statement-1 is true, Statement-2 is false✓

Correct answer: D

In a shop there are five types of ice-creams available. A child buys six ice-creams. Statement-1: The number of different ways the child can buy the six ice-creams is ${}^{10}C_5$. Statement-2: The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging 6 A's and 4 B's in a row.

1. A.Statement-1 is false, Statement-2 is true✓
2. B.Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
3. C.Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
4. D.Statement-1 is true, Statement-2 is false

Correct answer: A

The first two terms of a geometric progression add up to 12. The sum of the third and the fourth terms is 48. If the terms of the geometric progression are alternately positive and negative, then the first term is

1. A.-4
2. B.-12✓
3. C.12
4. D.4

Correct answer: B

Suppose the cubic $x^3 - px + q$ has three distinct real roots where p > 0 and q > 0. Then which one of the following holds?

1. A.The cubic has minima at $\sqrt{\frac{p}{3}}$ and maxima at $-\sqrt{\frac{p}{3}}$✓
2. B.The cubic has minima at $-\sqrt{\frac{p}{3}}$ and maxima at $\sqrt{\frac{p}{3}}$
3. C.The cubic has minima at both $\sqrt{\frac{p}{3}}$ and $-\sqrt{\frac{p}{3}}$
4. D.The cubic has maxima at both $\sqrt{\frac{p}{3}}$ and $-\sqrt{\frac{p}{3}}$

Correct answer: A

How many real solutions does the equation $x^7 + 14x^5 + 16x^3 + 30x - 560 = 0$ have?

1. A.7
2. B.1✓
3. C.3
4. D.5

Correct answer: B

The statement $p \to (q \to p)$ is equivalent to

1. A.$p \to (p \to q)$
2. B.$p \to (p \vee q)$✓
3. C.$p \to (p \wedge q)$
4. D.$p \to (p \leftrightarrow q)$

Correct answer: B

The value of $\cot\left(\csc^{-1}\frac{5}{3} + \tan^{-1}\frac{2}{3}\right)$ is

1. A.$\frac{6}{17}$✓
2. B.$\frac{3}{17}$
3. C.$\frac{4}{17}$
4. D.$\frac{5}{17}$

Correct answer: A

The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is

1. A.$(x-2)y'^2 = 25 - (y-2)^2$
2. B.$(y-2)y'^2 = 25 - (y-2)^2$
3. C.$(y-2)^2y'^2 = 25 - (y-2)^2$✓
4. D.$(x-2)^2y'^2 = 25 - (y-2)^2$

Correct answer: C

Let $I = \int_0^1\frac{\sin x}{\sqrt{x}}dx$ and $J = \int_0^1\frac{\cos x}{\sqrt{x}}dx$. Then which one of the following is true?

1. A.$I > \frac{2}{3}$ and $J > 2$
2. B.$I < \frac{2}{3}$ and $J < 2$✓
3. C.$I < \frac{2}{3}$ and $J > 2$
4. D.$I > \frac{2}{3}$ and $J < 2$

Correct answer: B

The area of the plane region bounded by the curves $x + 2y^2 = 0$ and $x + 3y^2 = 1$ is equal to

1. A.$\frac{5}{3}$
2. B.$\frac{1}{3}$
3. C.$\frac{2}{3}$
4. D.$\frac{4}{3}$✓

Correct answer: D

The value of $\sqrt{2}\int\frac{\sin x\,dx}{\sin\left(x - \frac{\pi}{4}\right)}$ is

1. A.$x + \log\left|\cos\left(x - \frac{\pi}{4}\right)\right| + c$
2. B.$x - \log\left|\sin\left(x - \frac{\pi}{4}\right)\right| + c$
3. C.$x + \log\left|\sin\left(x - \frac{\pi}{4}\right)\right| + c$✓
4. D.$x - \log\left|\cos\left(x - \frac{\pi}{4}\right)\right| + c$

Correct answer: C

How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

1. A.$8\cdot{}^6C_4\cdot{}^7C_4$
2. B.$6\cdot7\cdot{}^8C_4$
3. C.$6\cdot8\cdot{}^7C_4$
4. D.$7\cdot{}^6C_4\cdot{}^8C_4$✓

Correct answer: D

Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that $x = cy + bz$, $y = az + cx$ and $z = bx + ay$. Then $a^2 + b^2 + c^2 + 2abc$ is equal to

1. A.2
2. B.-1
3. C.0
4. D.1✓

Correct answer: D

Let A be a square matrix all of whose entries are integers. Then which one of the following is true?

1. A.If det A = $\pm1$, then $A^{-1}$ exists but all its entries are not necessarily integers
2. B.If det A $\ne \pm1$, then $A^{-1}$ exists and all its entries are non-integers
3. C.If det A = $\pm1$, then $A^{-1}$ exists and all its entries are integers✓
4. D.If det A = $\pm1$, then $A^{-1}$ need not exist

Correct answer: C

The quadratic equations $x^2 - 6x + a = 0$ and $x^2 - cx + 6 = 0$ have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is

1. A.1
2. B.4
3. C.3
4. D.2✓

Correct answer: D

The organic chloro compound, which shows complete stereochemical inversion during a $S_N2$ reaction, is

1. A.$(C_2H_5)_2CHCl$
2. B.$(CH_3)_3CCl$
3. C.$(CH_3)_2CHCl$
4. D.$CH_3Cl$✓

Correct answer: D

Toluene is nitrated and the resulting product is reduced with tin and hydrochloric acid. The product so obtained is diazotised and then heated with cuprous bromide. The reaction mixture so formed contains

1. A.mixture of o- and p-bromotoluenes✓
2. B.mixture of o- and p-dibromobenzenes
3. C.mixture of o- and p-bromoanilines
4. D.mixture of o- and m-bromotoluenes

Correct answer: A

The coordination number and the oxidation state of the element 'E' in the complex $[E(en)_2(C_2O_4)]NO_2$ (where (en) is ethylene diamine) are, respectively,

1. A.6 and 2
2. B.4 and 2
3. C.4 and 3
4. D.6 and 3✓

Correct answer: D

Identify the wrong statements in the following:

1. A.Chlorofluorocarbons are responsible for ozone layer depletion
2. B.Greenhouse effect is responsible for global warming
3. C.Ozone layer does not permit infrared radiation from the sun to reach the earth✓
4. D.Acid rains is mostly because of oxides of nitrogen and sulphur

Correct answer: C

Phenol, when it first reacts with concentrated sulphuric acid and then with concentrated nitric acid, gives

1. A.2,4,6-trinitrobenzene
2. B.o-nitrophenol✓
3. C.p-nitrophenol
4. D.nitrobenzene

Correct answer: B

In the following sequence of reactions, the alkene affords the compound 'B': $CH_3CH=CHCH_3 \xrightarrow{O_3} A \xrightarrow{H_2O/Zn} B$. The compound B is

1. A.$CH_3CH_2CHO$
2. B.$CH_3COCH_3$
3. C.$CH_3CH_2COCH_3$
4. D.$CH_3CHO$✓

Correct answer: D

Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids, the main reason being

1. A.4f orbitals more diffused than the 5f orbitals
2. B.lesser energy difference between 5f and 6d than between 4f and 5d orbitals✓
3. C.more energy difference between 5f and 6d than between 4f and 5d orbitals
4. D.more reactive nature of the actinoids than the lanthanoids

Correct answer: B

In which of the following octahedral complexes of Co (at. no. 27), will the magnitude of $\Delta_o$ be the highest?

1. A.$[Co(CN)_6]^{3-}$✓
2. B.$[Co(C_2O_4)_3]^{3-}$
3. C.$[Co(H_2O)_6]^{3+}$
4. D.$[Co(NH_3)_6]^{3+}$

Correct answer: A

At $80^\circ$C, the vapour pressure of pure liquid 'A' is 520 mm Hg and that of pure liquid 'B' is 1000 mm Hg. If a mixture solution of 'A' and 'B' boils at $80^\circ$C and 1 atm pressure, the amount of 'A' in the mixture is (1 atm = 760 mm Hg)

1. A.52 mol percent
2. B.34 mol percent
3. C.48 mol percent
4. D.50 mol percent✓

Correct answer: D

For a reaction $\frac{1}{2}A \rightarrow 2B$, rate of disappearance of 'A' is related to the rate of appearance of 'B' by the expression

1. A.$-\frac{d[A]}{dt} = \frac{1}{2}\frac{d[B]}{dt}$
2. B.$-\frac{d[A]}{dt} = \frac{1}{4}\frac{d[B]}{dt}$✓
3. C.$-\frac{d[A]}{dt} = \frac{d[B]}{dt}$
4. D.$-\frac{d[A]}{dt} = 4\frac{d[B]}{dt}$

Correct answer: B

The equilibrium constants $K_{P_1}$ and $K_{P_2}$ for the reactions $X \rightleftharpoons 2Y$ and $Z \rightleftharpoons P + Q$, respectively are in the ratio of 1 : 9. If the degree of dissociation of X and Z be equal then the ratio of total pressure at these equilibria is

1. A.1 : 36✓
2. B.1 : 1
3. C.1 : 3
4. D.1 : 9

Correct answer: A

Oxidising power of chlorine in aqueous solution can be determined by the parameters indicated below: $\frac{1}{2}Cl_2(g) \xrightarrow{\frac{1}{2}\Delta_{diss}H^\circ} Cl(g) \xrightarrow{\Delta_{eg}H^\circ} Cl^-(g) \xrightarrow{\Delta_{hyd}H^\circ} Cl^-(aq)$. The energy involved in the conversion of $\frac{1}{2}Cl_2(g)$ to $Cl^-(aq)$ (using the data, $\Delta_{diss}H^\circ_{Cl_2} = 240$ kJ mol$^{-1}$, $\Delta_{eg}H^\circ_{Cl} = -349$ kJ mol$^{-1}$, $\Delta_{hyd}H^\circ_{Cl^-} = -381$ kJ mol$^{-1}$) will be

1. A.$+152$ kJ mol$^{-1}$
2. B.$-610$ kJ mol$^{-1}$✓
3. C.$-850$ kJ mol$^{-1}$
4. D.$+120$ kJ mol$^{-1}$

Correct answer: B

Bakelite is obtained from phenol by reacting with

1. A.$(CH_2OH)_2$
2. B.$CH_3CHO$
3. C.$CH_3COCH_3$
4. D.HCHO✓

Correct answer: D

For the following three reactions a, b and c, equilibrium constants are given: a. $CO(g) + H_2O(g) \rightleftharpoons CO_2(g) + H_2(g)$; $K_1$ b. $CH_4(g) + H_2O(g) \rightleftharpoons CO(g) + 3H_2(g)$; $K_2$ c. $CH_4(g) + 2H_2O(g) \rightleftharpoons CO_2(g) + 4H_2(g)$; $K_3$. Which of the following relations is correct?

1. A.$K_1\sqrt{K_2} = K_3$
2. B.$K_2K_3 = K_1$
3. C.$K_3 = K_1K_2$✓
4. D.$K_3K_2^3 = K_1^2$

Correct answer: C

The absolute configuration of tartaric acid drawn as $HO_2C-CH(OH)-CH(OH)-CO_2H$ with the C1-OH on a hashed bond and the C2-OH on a wedged bond (see figure) is

1. A.S, S
2. B.R, R✓
3. C.R, S
4. D.S, R

Correct answer: B

The electrophile, $E^\oplus$ attacks the benzene ring to generate the intermediate $\sigma$-complex. Of the following, which $\sigma$-complex is of lowest energy?

1. A.sigma-complex of nitrobenzene with E at the para position
2. B.sigma-complex of benzene (no substituent)✓
3. C.sigma-complex of nitrobenzene with E at the ortho position
4. D.sigma-complex of nitrobenzene with E at the meta position

Correct answer: B

$\alpha$-D-(+)-glucose and $\beta$-D-(+)-glucose are

1. A.conformers
2. B.epimers
3. C.anomers✓
4. D.enantiomers

Correct answer: C

Standard entropy of $X_2$, $Y_2$ and $XY_3$ are 60, 40 and 50 JK$^{-1}$mol$^{-1}$, respectively. For the reaction, $\frac{1}{2}X_2 + \frac{3}{2}Y_2 \rightarrow XY_3$, $\Delta H = -30$ kJ, to be at equilibrium, the temperature will be

1. A.1250 K
2. B.500 K
3. C.750 K✓
4. D.1000 K

Correct answer: C

Four species are listed below: i. $HCO_3^-$ ii. $H_3O^+$ iii. $HSO_4^-$ iv. $HSO_3F$. Which one of the following is the correct sequence of their acid strength?

1. A.iv < ii < iii < i
2. B.ii < iii < i < iv
3. C.i < iii < ii < iv✓
4. D.iii < i < iv < ii

Correct answer: C

Which one of the following constitutes a group of the isoelectronic species?

1. A.$C_2^{2-}$, $O_2^-$, CO, NO
2. B.$NO^+$, $C_2^{2-}$, $CN^-$, $N_2$✓
3. C.$CN^-$, $N_2$, $O_2^{2-}$, $C_2^{2-}$
4. D.$N_2$, $O_2^-$, $NO^+$, CO

Correct answer: B

Which one of the following pairs of species have the same bond order?

1. A.$CN^-$ and $NO^+$✓
2. B.$CN^-$ and $CN^+$
3. C.$O_2^-$ and $CN^-$
4. D.$NO^+$ and $CN^+$

Correct answer: A

The ionization enthalpy of hydrogen atom is $1.312\times10^6$ J mol$^{-1}$. The energy required to excite the electron in the atom from n = 1 to n = 2 is

1. A.$8.51\times10^5$ J mol$^{-1}$
2. B.$6.56\times10^5$ J mol$^{-1}$
3. C.$7.56\times10^5$ J mol$^{-1}$
4. D.$9.84\times10^5$ J mol$^{-1}$✓

Correct answer: D

Which one of the following is the correct statement?

1. A.Boric acid is a protonic acid
2. B.Beryllium exhibits coordination number of six
3. C.Chlorides of both beryllium and aluminium have bridged chloride structures in solid phase✓
4. D.$B_2H_6\cdot2NH_3$ is known as 'inorganic benzene'

Correct answer: C

Given $E^\circ_{Cr^{3+}/Cr} = -0.72$ V, $E^\circ_{Fe^{2+}/Fe} = -0.42$ V. The potential for the cell $Cr|Cr^{3+}(0.1\ M)||Fe^{2+}(0.01\ M)|Fe$ is

1. A.0.26 V✓
2. B.0.399 V
3. C.-0.339 V
4. D.-0.26 V

Correct answer: A

Amount of oxalic acid present in a solution can be determined by its titration with $KMnO_4$ solution in the presence of $H_2SO_4$. The titration gives unsatisfactory result when carried out in the presence of HCl, because HCl

1. A.gets oxidised by oxalic acid to chlorine
2. B.furnishes $H^+$ ions in addition to those from oxalic acid
3. C.reduces permanganate to $Mn^{2+}$✓
4. D.oxidises oxalic acid to carbon dioxide and water

Correct answer: C

The vapour pressure of water at $20^\circ$C is 17.5 mm Hg. If 18 g of glucose $(C_6H_{12}O_6)$ is added to 178.2 g of water at $20^\circ$C, the vapour pressure of the resulting solution will be

1. A.17.675 mm Hg
2. B.15.750 mm Hg
3. C.16.500 mm Hg
4. D.17.325 mm Hg✓

Correct answer: D

Among the following substituted silanes the one which will give rise to cross linked silicone polymer on hydrolysis is

1. A.$R_4Si$
2. B.$RSiCl_3$✓
3. C.$R_2SiCl_2$
4. D.$R_3SiCl$

Correct answer: B

In context with the industrial preparation of hydrogen from water gas $(CO + H_2)$, which of the following is the correct statement?

1. A.CO and $H_2$ are fractionally separated using differences in their densities
2. B.CO is removed by absorption in aqueous $Cu_2Cl_2$ solution
3. C.$H_2$ is removed through occlusion with Pd
4. D.CO is oxidised to $CO_2$ with steam in the presence of a catalyst followed by absorption of $CO_2$ in alkali✓

Correct answer: D

In a compound atoms of element Y from ccp lattice and those of element X occupy $2/3^{rd}$ of tetrahedral voids. The formula of the compound will be

1. A.$X_4Y_3$✓
2. B.$X_2Y_3$
3. C.$X_2Y$
4. D.$X_3Y_4$

Correct answer: A

Gold numbers of protective colloids A, B, C and D are 0.50, 0.01, 0.10 and 0.005, respectively. The correct order of their protective powers is

1. A.D < A < C < B
2. B.C < B < D < A
3. C.A < C < B < D✓
4. D.B < D < A < C

Correct answer: C

The hydrocarbon which can react with sodium in liquid ammonia is

1. A.$CH_3CH_2CH_2C\equiv CCH_2CH_2CH_3$
2. B.$CH_3CH_2C\equiv CH$✓
3. C.$CH_3CH=CHCH_3$
4. D.$CH_3CH_2C\equiv CCH_2CH_3$

Correct answer: B

The treatment of $CH_3MgX$ with $CH_3C\equiv C-H$ produces

1. A.$CH_3-CH=CH_2$
2. B.$CH_3C\equiv C-CH_3$
3. C.$CH_3-CH=CH-CH_3$
4. D.$CH_4$✓

Correct answer: D

The $pK_a$ of a weak acid, HA, is 4.80. The $pK_b$ of a weak base, BOH, is 4.78. The pH of an aqueous solution of the corresponding salt, BA, will be

1. A.9.58
2. B.4.79
3. C.7.01✓
4. D.9.22

Correct answer: C

Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see in figure). Electrons accelerated by potential V are diffracted from a crystal. If d = 1 Å and i = $30^\circ$, V should be about ($h = 6.6\times10^{-34}$ Js, $m_e = 9.1\times10^{-31}$ kg, $e = 1.6\times10^{-19}$ C)

1. A.2000 V
2. B.50 V✓
3. C.500 V
4. D.1000 V

Correct answer: B

Wave property of electrons implies that they will show diffraction effects. Davisson and Germer demonstrated this by diffracting electrons from crystals. The law governing the diffraction from a crystal is obtained by requiring that electron waves reflected from the planes of atoms in a crystal interfere constructively (see in figure). In an experiment, electrons are made to pass through a narrow slit of width 'd' comparable to their de Broglie wavelength. They are detected on a screen at a distance 'D' from the slit (see figure). Which of the following graph can be expected to represent the number of electrons 'N' detected as a function of the detector position 'y' (y = 0 corresponds to the middle of the slit)?

1. A.Graph (1)
2. B.Graph (2)
3. C.Graph (3)
4. D.Graph (4)✓

Correct answer: D

A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 kms$^{-1}$, the escape velocity from the surface of the planet would be

1. A.1.1 kms$^{-1}$
2. B.11 kms$^{-1}$
3. C.110 kms$^{-1}$✓
4. D.0.11 kms$^{-1}$

Correct answer: C

A spherical solid ball of volume V is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_2$ $(\rho_2 < \rho_1)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., $F_{viscous} = -kv^2$ $(k > 0)$. The terminal speed of the ball is

1. A.$\sqrt{\frac{Vg(\rho_1-\rho_2)}{k}}$✓
2. B.$\frac{Vg\rho_1}{k}$
3. C.$\sqrt{\frac{Vg\rho_1}{k}}$
4. D.$\frac{Vg(\rho_1-\rho_2)}{k}$

Correct answer: A