This practice test consists of AIEEE 2008 questions to help you practice for actual AIEEE main examination.

AIEEE 2008 Question Paper

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Question

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°. 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°. Then the height of the pole is

Possible Answers

Selected	Possible Answer
	$\frac {7 \sqrt{3}}{2}. \frac {1}{\sqrt{3+1}}m$
	$\frac {7 \sqrt{3}}{2}.(\sqrt {3}-1)m$
	$\frac {7 \sqrt{3}}{2}. \frac {1}{\sqrt{3-1}}m$
	$\frac {7 \sqrt{3}}{2}. (\sqrt {3}+1)m$

Question

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

Possible Answers

Selected	Possible Answer
	$\frac{2}{3}$
	$\frac{1}{3}$
	$\frac{1}{2}$
	$\frac{1}{6}$

Question

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

Possible Answers

Selected	Possible Answer
	1
	0
	$\frac {2}{5}$
	$\frac {3}{5}$

Question

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

Possible Answers

Selected	Possible Answer
	$\frac{4}{3}$
	$\frac{8}{3}$
	$\frac{2}{3}$
	$\frac{5}{3}$

Question

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

Possible Answers

Selected	Possible Answer
	(2, 0)
	(0, 2)
	(1, 0)
	(0, 1)

Question

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

Possible Answers

Selected	Possible Answer
	(-3,-4)
	(3,-4)
	(-3,4)
	(3,4)

Question

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

Possible Answers

Selected	Possible Answer
	$g(y) = \frac {y+3}{4}$
	$g (y) = 4 + \frac {y+3}{4}$
	$g (y) = \frac {y-3}{4}$
	$g (y)= \frac {3y+4}{3}$

Question

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

Possible Answers

Selected	Possible Answer
	$\frac{-1}{i+1}$
	$\frac{-1}{i-1}$
	$\frac{1}{i+1}$
	$\frac{1}{i-1}$

Question

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

Possible Answers

Selected	Possible Answer
	T is an equivalence relation on R but S is not
	both S and T are equivalence relations on R
	S is an equivalence relation on R but T is not
	neither S nor T is an equivalence relation on R

Question

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

Possible Answers

Selected	Possible Answer
	2
	-4
	-2
	1

Question

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

Possible Answers

Selected	Possible Answer
	y = x ln x + x
	$y = xe^{(x-1)}$
	y = ln x + x
	y = x ln x +

Question

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?

Possible Answers

Selected	Possible Answer
	a = 3, b = 4
	a = 0, b = 7
	a = 5, b = 2
	a = 1, b = 6

Question

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 α and β?

Possible Answers

Selected	Possible Answer
	α = 1, β = 1
	α = 2, β = 2
	α = 1, β = 2
	α = 2, β = 1

Question

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

Possible Answers

Selected	Possible Answer
	$\pi$
	$\frac {\pi}{2}$
	0
	$\frac {\pi}{4}$

Question

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

Possible Answers

Selected	Possible Answer
	a = 2, b = 8
	a = 4, b = 6
	a = 6, b = 4
	a = 8, b = 2

Question

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

Possible Answers

Selected	Possible Answer
	-5
	2
	5
	-2

Question

Directions: Below mentions Five questions are Assertion−Reason type questions. Each of these questions contains two statements : Statement − 1 (Assertion) and Statement−2 (Reason). Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice.

Statement − 1: For every natural number $n \underline > 2 , \frac {1}{\sqrt {1}}+ \frac{1} {\sqrt{2}}+...+ \frac {1}{\sqrt{n}}>\sqrt{n}$

Statement −2: For every natural number $n \underline > 2 , \sqrt{n(n+1)}<n+1$

Possible Answers

Selected	Possible Answer
	Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1
	Statement −1 is false, Statement −2 is true
	Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.
	Statement − 1 is true, Statement − 2 is false.

Question

Let A be a 2 × 2 matrix with real entries. Let I be the 2 × 2 identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that A^2 = 1

Statement −1: If A ≠ I and A ≠ − I, then det A = − 1.

Statement −2: If A ≠ I and A ≠ − I, then tr (A) ≠ 0.

Possible Answers

Selected	Possible Answer
	Statement −1 is false, Statement −2 is true
	Statement − 1 is true, Statement − 2 is false.
	Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1
	Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.

Question

Statement −1: $\overset{n} {\underset{r=0}{\sum}}(r+1) ^nC_r=(n+2)2^{n-1}$
Statement −2: $\overset{n} {\underset{r=0}{\sum}}(r+1) ^nC_rx^r = (1+x)^n +nx (1+x)^{n-1}$

Possible Answers

Selected	Possible Answer
	Statement −1 is false, Statement −2 is true
	Statement − 1 is true, Statement − 2 is false.
	Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.
	Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1

Question

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 $\sim (p \leftrightarrow \sim )$

Possible Answers

Selected	Possible Answer
	Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.
	Statement − 1 is true, Statement − 2 is false.
	Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1
	Statement −1 is false, Statement −2 is true

Question

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.

Possible Answers

Selected	Possible Answer
	Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1.
	Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1
	Statement − 1 is true, Statement − 2 is false.
	Statement −1 is false, Statement −2 is true

Question

Let $f(x)= \Big \{ \overset{(x-1)\sin \Big ( \frac{1}{x-1} \Big ) }{\underset{0}{}} \qquad \overset{if x \not = 1} {\underset{if x=1} {}} \Big \}$ Then which one of the following is ture?

Possible Answers

Selected	Possible Answer
	f is neither differentiable at x = 0 nor at x = 1
	f is differentiable at x = 0 and at x = 1
	f is differentiable at x = 1 but not at x = 0
	f is differentiable at x = 0 but not at x = 1

Question

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

Possible Answers

Selected	Possible Answer
	-4
	-12
	12
	4

Question

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

Possible Answers

Selected	Possible Answer
	The cubic has minima at both $\sqrt {\frac {p}{3}}$ and $-\sqrt {\frac {p}{3}}$
	The cubic has maxima at both $\sqrt {\frac {p}{3}}$ and $-\sqrt {\frac {p}{3}}$
	The cubic has minima at $\sqrt {\frac {p}{3}}$ and maxima at $-\sqrt {\frac {p}{3}}$
	The cubic has minima at $-\sqrt {\frac {p}{3}}$ and maxima at $\sqrt {\frac {p}{3}}$

Question

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

Possible Answers

Selected	Possible Answer
	1
	5
	7
	3

Question

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

Possible Answers

Selected	Possible Answer
	$p \rightarrow (p \rightarrow q)$
	$p \rightarrow (p \leftrightarrow q)$
	$p \rightarrow (p \lor q)$
	$p \rightarrow (p \land q)$

Question

The value of $\cot \Bigg ( \cos ec^{-1} \cfrac {5}{3}+ \tan^{-1} \cfrac {2}{3} \Bigg )$ is

Possible Answers

Selected	Possible Answer
	$\frac {5}{17}$
	$\frac {3}{17}$
	$\frac{6}{17}$
	$\frac {4}{17}$

Question

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

Possible Answers

Selected	Possible Answer

Question

Let l $= \overset{1}{\underset{0}{\int}} \cfrac {\sin x }{\sqrt{x}} dx$ and $J = \overset{1}{\underset{0}{\int}} \cfrac {\cos x }{\sqrt{x}} dx$ Then which one of the following is true?

Possible Answers

Selected	Possible Answer
	$l < \frac {2}{3}$ and j < 2
	$l>\frac {2}{3}$ and j < 2
	$l < \frac {2}{3}$ and j > 2
	$l>\frac {2}{3}$ and j > 2

Question

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

Possible Answers

Selected	Possible Answer
	$\frac{5}{3}$
	$\frac{2}{3}$
	$\frac{1}{3}$
	$\frac{4}{3}$

Question

The value of $\sqrt{2} \int \cfrac {\sin x dx }{sin \Big ( x - \cfrac {\pi}{4} \Big ) }$ is

Possible Answers

Selected	Possible Answer
	$x - log \Big \| \cos \Big ( x - \frac{\pi}{4} \Big ) \Big \| + c$
	$x - log \Big \| \sin \Big ( x - \frac{\pi}{4} \Big ) \Big \| + c$
	$x + log \Big \| \cos \Big ( x - \frac{\pi}{4} \Big ) \Big \| + c$
	$x + log \Big \| \cos \Big ( x - \frac{\pi}{4} \Big ) \Big \| + c$

Question

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

Possible Answers

Selected	Possible Answer
	$8 \cdot ^ 6C_4 \cdot ^7C_4$
	$6 \cdot 7 \cdot ^8C_4$
	$6 \cdot 8 \cdot ^7C_4$
	$7 \cdot ^6C_4 \cdot ^8C_4$

Question

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

Possible Answers

Selected	Possible Answer
	0
	-1
	2
	1

Question

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

Possible Answers

Selected	Possible Answer
	if detA = $\pm$ , then $A^{-1}$ need not exist
	if detA = $\pm$ , then $A^{-1}$ exists but all its entries are not necessarily integers
	if detA = $\pm$ , then $A^{-1}$ exists and all its entries are integers
	If detA $\not = \pm 1$ , then $A^{-1}$ exists and all its entries are non-integers

Question

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

Possible Answers

Selected	Possible Answer
	3
	1
	2
	4

Question

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

Possible Answers

Selected	Possible Answer
	mixture of o− and p−bromoanilines
	mixture of o− and p−bromotoluenes
	mixture of o− and m−bromotoluenes
	mixture of o− and p−dibromobenzenes

Question

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,

Possible Answers

Selected	Possible Answer
	4 and 2
	6 and 3
	4 and 3
	6 and 2

Question

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

Possible Answers

Selected	Possible Answer
	p-nitrophenol
	2,4,6-trinitrobenzene
	nitrobenzene
	o-nitrophenol

Question

In the following sequence of reactions, the alkene affords the compound ‘B’

$CH_3CH= CHCH_3 \overset{O_3}{\longrightarrow}A\overset{H_2O}{\underset{Zn}{\longrightarrow}} B$

The Compound B is

Possible Answers

Selected	Possible Answer

Question

In which of the following octahedral complexes of Co (at. no. 27), will the magnitude of $\Delta_0$ be the highest?

Possible Answers

Selected	Possible Answer
	$[ Co(CN)_6]^{3-}$
	$[Co(H_2O)_6]^{3+}$
	$[Co(NH_3)_6]^{3+}$
	$[Co(C_2O_40_3]^{3-}$

Question

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 ration of 1:9 If the degree of dissociation of X and Z be equal then the ratio of total pressure at these equilibria is

Possible Answers

Selected	Possible Answer
	1 : 36
	1 : 1
	1 : 9
	1 : 3

Question

Oxidising power of chlorine in aqueous solution can be determined by the parameters indicated below:

$\frac {1}{2} Cl_2(g) \xrightarrow{\frac {1}{2} \Delta _{diss} H^{\theta} }Cl_(g) \xrightarrow {\Delta _{eg} H^{\theta}} Cl^{-} (g) \xrightarrow {\Delta _{hyd} H^{\theta}} Cl^{-} (aq)$

The energy invloved in the conversion of $\frac{1}{2} Cl_2 (g)$ to $Cl^{-} (g)$

(using the data.
$\Delta _{diss} H^{\theta}_{Cl_2} = 240 kJmol^{-1} , \Delta _{eq} H^{\theta}_{Cl} = -349 kJmol^{-1} , \Delta_{hyd} H _{Cl}^{\theta} = -381 kJLmol^{-1}$ ) Will be

Possible Answers

Selected	Possible Answer
	$-610 \quad kJmol^{-1}$
	$-850 \quad kJmol ^{-1}$
	$+120 \quad kJmol^{-1}$
	$+152 \quad kJmol^{-1}$

Question

Bakelite is obtained from phenol by reacting with

Possible Answers

Selected	Possible Answer

Question

For the following three reactions a, b and c, equilibrium constants are given:

A $CO(g)+H_2 O(g) \rightleftharpoons CO_2 (g) + H_2 (g); \quad \quad K_1$

B $CH_4(g)+H_2 O(g) \rightleftharpoons CO_2 (g) + 3H_2 (g); \quad \quad K_2$

C $CO_4(g)+2H_2 O(g) \rightleftharpoons CO_2 (g) + 4H_2 (g); \quad \quad K_3$
Which of the following relations is correct ?

Possible Answers

Selected	Possible Answer

	$K_1 \sqrt{K_2} = K_3$

Question

α-D-()~~glucose and β-D~~()-glucose are

Possible Answers

Selected	Possible Answer
	enantiomers
	epimers
	conformers
	anomers

Question

The absolute configuration of

Possible Answers

Selected	Possible Answer
	R, S
	R, R
	S, S
	S, R

Question

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

Possible Answers

Selected	Possible Answer
	1000 K
	750 K
	500 K
	1250 K

Question

Four species aare 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?

Possible Answers

Selected	Possible Answer
	iv < ii < iii < I
	ii < iii < i < iv
	iii < i < iv < ii
	i < iii < ii < iv

Question

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

Possible Answers

Selected	Possible Answer
	$C^{2-}_2,O^{-}_2, CO,NO$
	$NO^{+},C^{2-}_2 , CN^{-} ,N_2$
	$N_2 , O^{-}_{2} ,NO^{+} ,CO$
	$CN^{-}, N_2 , O^{2-}_{2}, C^{2-}_{2}$

Question

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

Possible Answers

Selected	Possible Answer
	$O^{-}_2$ and $CN^{-}$
	$CN^{-}$ and $CN^{+}$
	$CN^{-}$ and $NO^{+}$
	$NO^{+}$ and $CN^{+}$

Question

The ionization enthalpy of hydrogen atom is $1.312 * 10^6 Jmol^{-1}$ . The energy required to excite the electron in the atom from n = 1 to n = 2 is

Possible Answers

Selected	Possible Answer
	$6.56 * 10^5 Jmol^{-1}$
	$9.84 * 10^5 Jmol^{-1}$
	$8.51 * 10^5 Jmol^{-1}$
	$7.56 * 10^5 Jmol^{-1}$

Question

Which one of the following is the correct statement?

Possible Answers

Selected	Possible Answer
	Chlorides of both beryllium and aluminium have bridged chloride structures in solid phase

	Boric acid is a protonic acid
	Beryllium exhibits coordination number of six

Question

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

Possible Answers

Selected	Possible Answer
	−0.26 V
	−0.339 V
	0.26 V
	0.399 V

Question

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

Possible Answers

Selected	Possible Answer
	furnishes $H^{+}$ ions in addition to those from oxalic acid
	oxidises oxalic acid to carbon dioxide and water
	reduces permanganate to $Mn^{2+}$
	gets oxidised by oxalic acid to chlorine

Question

The vapour pressure of water at $20^{\circ} C$ is 17.5 mm Hg. If 18 g of glucose $(C_6 H_{12} O_6)$ is added to 178.2 g of water at $20^{\circ}C$ , the vapour pressure of the resulting solution will be

Possible Answers

Selected	Possible Answer
	15.750 mm Hg
	16.500 mm Hg
	17.325 mm Hg
	17.675 mm Hg

Question

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

Possible Answers

Selected	Possible Answer

Question

In context with the industrial preparation of hydrogen from water gas (CO + H_2) , which of the following

is the correct statement?

Possible Answers

Selected	Possible Answer
	is removed through occlusion with Pd
	CO is oxidised to with steam in the presence of a catalyst followed by absorption of in alkali
	CO and are fractionally separated using differences in their densities
	CO is removed by absorption in aqueous solution

Question

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

Possible Answers

Selected	Possible Answer

Question

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

Possible Answers

Selected	Possible Answer
	D < A < C < B
	A < C < B < D
	B < D < A < C
	C < B < D < A

Question

The hydrocarbon which can react with sodium in liquid ammonia is

Possible Answers

Selected	Possible Answer

	$CH_3CH_2CH_2C \equiv CCH_2CH_2CH_3$
	$CH_3CH_2C \equiv CCH_2CH_3$
	$CH_3CH_2C \equiv CH$

Question

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

Possible Answers

Selected	Possible Answer

	$CH_3 \equiv C-CH_3$

Question

The correct decreasing order of priority for the functional groups of organic compounds in the IUPAC system of nomenclature is

Possible Answers

Selected	Possible Answer

Question

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

Possible Answers

Selected	Possible Answer
	7.01
	9.22
	9.58
	4.79

Question

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

Possible Answers

Selected	Possible Answer

Question

Identify the wrong statements in the following:

Possible Answers

Selected	Possible Answer
	Acid rains is mostly because of oxides of nitrogen and sulphur
	Chlorofluorocarbons are responsible for ozone layer depletion
	Greenhouse effect is responsible for global warming
	Ozone layer does not permit infrared radiation from the sun to reach the earth

Question

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

Possible Answers

Selected	Possible Answer
	lesser energy difference between 5f and 6d than between 4f and 5d orbitals
	4f orbitals more diffused than the 5f orbitals
	more energy difference between 5f and 6d than between 4f and 5d orbitals
	more reactive nature of the actinoids than the lanthanoids

Question

Which of the following factors is of no significance for roasting sulphide ores to the oxides and not subjecting the sulphide ores to carbon reduction directly?

Possible Answers

Selected	Possible Answer
	is more volatile than
	is thermodynamically more stable than CS2
	Metal sulphides are less stable than the corresponding oxides
	Metal sulphides are thermodynamically more stable than

Question

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)

Possible Answers

Selected	Possible Answer
	34 mol percent
	48 mol percent
	52 mol percent
	50 mol percent

Question

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

Possible Answers

Selected	Possible Answer
	$- \cfrac{d[A]}{dt} = \quad \cfrac {d[B]}{dt}$
	$- \cfrac{d[A]}{dt} = \cfrac {1}{2} \quad \cfrac {d[B]}{dt}$
	$- \cfrac{d[A]}{dt} = \cfrac {1}{4} \quad \cfrac {d[B]}{dt}$
	$- \cfrac{d[A]}{dt} = 4 \cfrac {d[B]}{dt}$

Question

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

Possible Answers

Selected	Possible Answer

Question

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

Possible Answers

Selected	Possible Answer
	$1.1 kms^{-1}$
	$110 kms^{-1}$
	$0.11 kms^{-1}$
	$11 kms^{-1}$

Question

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

Possible Answers

Selected	Possible Answer
	$\sqrt {\cfrac{Vg \rho_1}{k}}$
	$\cfrac {Vg( \rho_1 - \rho_2)}{k}$

	$\cfrac {Vg \rho_1}{k}$

Question

Below three questions are based on the following paragraph

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 $d = 1 \overset{\circ}{A}$ and $i = 30^{\circ}$ , V should be about $(h = 6.6 * 10^{-34} Js, m_e = 9.1 * 10^{-31} kg,e =1.6 *10^{-19} C)$

Possible Answers

Selected	Possible Answer
	2000 V
	50 V
	500 V
	1000 V

Question

If a strong diffraction peak is observed when electrons are incident at an angle ‘i’ from the normal to the crystal planes with distance ‘d’ between them (see figure), de Broglie wavelength $\lambda_{dB}$ of electrons can be calculated by the relationship (n is an integer)

Possible Answers

Selected	Possible Answer
	$d \cos i = n \lambda_{dB}$
	$2d \cos i = n \lambda_{dB}$
	$2d \sin i = n \lambda_{dB}$
	$d \sin i = n \lambda_{dB}$

Question

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)?

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Selected	Possible Answer

Question

Shown in the figure below is a meter-bridge set up with null deflection in the galvanometer.

The value of the unknown resistor R is

Possible Answers

Selected	Possible Answer
	$55 \Omega$
	$220 \Omega$
	$13.75 \Omega$
	$110 \Omega$

Question

While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of 18 cm during winter. Repeating the same experiment during summer, she measures the column length to be x cm for the second resonance. Then

Possible Answers

Selected	Possible Answer
	x > 54
	18 > x
	36 > x > 18
	54 > x > 36

Question

The dimension of magnetic field in M, L, T and C (Coulomb) is given as

Possible Answers

Selected	Possible Answer
	$MT^{-2}C^{-1}$
	$MT^2C^{-2}$
	$MLT^{-1}C^{-1}$
	$MT^{-1}C^{-1}$

Question

Consider a uniform square plate of side ‘a’ and mass ‘m’. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

Possible Answers

Selected	Possible Answer
	$\frac {2}{3} ma^2$
	$\frac {1}{12} ma^2$
	$\frac {5}{6} ma^2$
	$\frac {7}{12} ma^2$

Question

A body of mass m = 3.513 kg is moving along the x-axis with a speed of $5.00 ms^{-1}$ . The magnitude of its momentum is recorded as

Possible Answers

Selected	Possible Answer
	$17.56 \quad kg \quad ms^{-1}$
	$17.565 \quad kg \quad ms^{-1}$
	$17.57 \quad kg \quad ms^{-1}$
	$17.6 \quad kg \quad ms^{-1}$

Question

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Possible Answers

Selected	Possible Answer

	20,000 J – 50,000 J
	200 J – 500 J
	2,000 J – 5,000 J

Question

A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between its plates is ‘d’. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant k_1 = 3 and thickness $\frac {d}{3}$ while the other one has dielectric constant k_2 = 6 and thickness $\frac {2d}{3}$ . Capacitance of the capacitor is now

Possible Answers

Selected	Possible Answer
	40.5 pF
	20.25 pF
	1.8 pF
	45 pF

Question

A thin rod of length ‘L’ is lying along the x-axis with its ends at X = 0 and X = L. Its linear density (mass/length) varies with X as $k \Big ( \frac {X}{L} \Big )^n$ , where where n can be zero or any positive number. If the position $X_{CM}$ of the centre of mass of the rod is plotted against ‘n’, which of the following graphs best approximates the dependence of $X_{CM}$ on n ?

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Selected	Possible Answer

Question

The speed of sound in oxygen (O_2) at a certain temperature is $460 ms^{-1}$ . The speed of sound in helium (He) at the same temperature will be (assumed both gases to be ideal)

Possible Answers

Selected	Possible Answer
	$650 ms^{-1}$
	$500 ms^{-1}$
	None
	$460 ms^{-1}$

Question

This question contains Statement -1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement – I:
Energy is released when heavy nuclei undergo fission or light nuclei undergo fusion. and
Statement – II
For heavy nuclei, binding energy per nucleon increases with increasing Z while for light nuclei it decrease with increasing Z.

Possible Answers

Selected	Possible Answer
	Statement – 1is true, Statement – 2 is true; Statement -2 is not a correct explanation for Statement-1.
	Statement – 1 is true, Statement – 2 is False.
	Statement – 1is false, Statement – 2 is true.
	Statement – 1is true, Statement – 2 is true; Statement -2 is correct explanation for Statement-1.

Question

This question contains Statement -1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.

Statement – I:
For a mass M kept at the centre of a cube of side ‘a’, the flux of gravitational field passing through its sides is $4 \pi GM$
and
Statement – II.
If the direction of a field due to a point source is radial and its dependence on the distance ‘r’ for the source is given as $\frac {1}{r^2}$ , its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface

Possible Answers

Selected	Possible Answer
	Statement – 1is true, Statement – 2 is true; Statement -2 is correct explanation for Statement-1.
	Statement – 1is true, Statement – 2 is true; Statement -2 is not a correct explanation for Statement-1.
	Statement – 1is false, Statement – 2 is true.
	Statement – 1 is true, Statement – 2 is False.

Question

A jar filled with two non mixing liquids 1 and 2 having densities $\rho _1$ and $\rho _2$ respectively. A solid ball, made of a material of density $\rho _3$ , is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for $\rho _1$ , $\rho _2$ and $\rho _3$ ?

Possible Answers

Selected	Possible Answer
	$\rho _1 < \rho _3 < \rho _2$
	$\rho _1 < \rho _3 < \rho _2$
	$\rho _1 < \rho _2 < \rho _3$
	$\rho _3 < \rho _1 < \rho _2$

Question

A working transistor with its three legs marked P, Q and R is tested using a multimeter. No conduction is found between P and Q. By connecting the common (negative) terminal of the multimeter to R and the other (positive) terminal to P or Q, some resistance is seen on the multimeter. Which of the following is true for the transistor?

Possible Answers

Selected	Possible Answer
	It is an npn transistor with R as collector
	It is an npn transistor with R as base
	It is a pnp transistor with R as emitter
	It is a pnp transistor with R as collector

Question

Given below two Question are based on the following paragraph.
Consider a block of conducting material of resistivity ‘ $\rho$ ’ shown in the figure. Current ‘I’ enters at ‘A’ and leaves from ‘D’. We apply superposition principle to find voltage ‘ $\Delta V$ ‘developed between ‘B’ and ‘C’. The calculation is done in the following steps:
(i) Take current ‘I’ entering from ‘A’ and assume it to spread over a hemispherical surface in the block.
(ii) Calculate field E® at distance ‘r’ from A by using Ohm’s law $E= \rho j$ , where j is the current per unit area at ‘r’.
(iii) From the ‘r’ dependence of E(r) , obtain the potential V(r) at r.
(iv) Repeat (i), (ii) and (iii) for current ‘I’ leaving ‘D’ and superpose results for ‘A’ and ‘D’.

$\Delta V$ measured between B and C is

Possible Answers

Selected	Possible Answer
	$\frac {\rho l}{ \rho l}{2 \pi (a-b)}$
	$\frac {\rho l}{ \pi a}- \frac { \rho l}{ \pi (a+b)}$
	$\frac {\rho l}{2 \pi a}- \frac { \rho l}{2 \pi (a+b)}$
	$\frac {\rho l}{ a}- \frac { \rho l}{ (a+b)}$

Question

For current entering at A, the electric field at a distance ‘r’ from A is

Possible Answers

Selected	Possible Answer
	$\frac {\rho l}{r^2}$
	$\frac {\rho l }{4 \pi r^2}$
	$\frac {\rho l}{8 \pi r^2}$
	$\frac {\rho l}{2 \pi r^2}$

Question

A student measures the focal length of convex lens by putting an object pin at a distance ‘u’ from the lens and measuring the distance ‘v’ of the image pin. The graph between ‘u’ and ‘v’ plotted by the student should look like

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Selected	Possible Answer

Question

A block of mass 0.50 kg is moving with a speed of 2.00 m/s on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Possible Answers

Selected	Possible Answer
	1.00 J
	0.67 J
	0.34 J
	0.16 J

Question

Suppose an electron is attracted towards the origin by a force k/r where ‘k’ is a constant and ‘r’ is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the $n^{th}$ orbital of the electron is found to be ‘ r_n ’ and the kinetic energy of the electron to be T_n . Then which of the following is true?

Possible Answers

Selected	Possible Answer
	$T_n \propto 1/n$ , $r_n \propto n^2$
	$T_n \propto 1/n^2$ , $r_n \propto n^2$
	indenpendent of $n,r_n \propto n$
	$T_n \propto 1/n$ , $r_n \propto n$

Question

A wave travelling along the X-axis is described by the equation $y(x,t) = 0.005 \cos (\alpha x- \beta t)$ If the

wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then $\alpha$ and $\beta$ in appropriate units are

Possible Answers

Selected	Possible Answer
	$\alpha = 25.00 \pi , \beta = \pi$
	$\alpha = 12.50 \pi, \beta = \frac {\pi}{2.0}$
	$\alpha = \frac {0.08}{\pi}, \frac {2.0}{\pi}$
	$\alpha = \frac {0.04}{\pi}, \beta = \frac {1.0}{\pi}$

Question

Two coaxial solenoids are made by winding thin insulated wire over a pipe of cross sectional area A = 10 cm^2 and length = 20 cm. If one of the solenoids has 300 turns and the other 400 turns, their mutual inductance is $( \mu _0 = 4 \pi * 10^{-7} Tm A^{-1} )$

Possible Answers

Selected	Possible Answer
	$4.8 \pi * 10^{-4} H$
	$2.4 \pi * 10^{-5} H$
	$2.4 \pi * 10^{-4} H$
	$4.8 \pi * 10^{-5} H$

Question

In the circuit below, A and B represent two inputs and C represents the output.

The circuit represents

Possible Answers

Selected	Possible Answer
	OR gate
	NOR gate
	AND gate
	NAND gate

Question

A body is at rest at x = 0. At t = 0, it starts moving in the positive x-direction with a constant acceleration. At the same instant another body passes through x = 0 moving in the positive xdirection with a constant speed. The position of the first body is given by x_1(t) after time ‘t’ and that of the second body by x_2(t) after the same time interval. Which of the following graphs correctly describes (x_1 - x_2) as a function of time ‘t’?

Possible Answers

Selected	Possible Answer

Question

An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distance are measured by

Possible Answers

Selected	Possible Answer
	A vernier scale provided on the microscope
	A screw gauage provided on the microscope
	A standard laboratory scale
	A meter scale provided on the microscope

Question

A horizontal overhead power line is at a height of 4m from the ground and carries a current of 100 A from east to west. The magnetic field directly below it on the ground is $\mu _0 = 4 \pi * 10^{-7} T m A^{-1})$

Possible Answers

Selected	Possible Answer
	$5 * 10^{-6}$ T southward
	$2.5 * 10^{-7}$ T southward
	$2.5 * 10^{-7}$ nsouthward
	$5 * 10^{-6}$ nouthward

Question

Relative permittivity and permeability of a material are $\epsilon _r$ and $\mu _r$ Which of the following values of these quantities are allowed for a diamagnetic material?

Possible Answers

Selected	Possible Answer
	$\epsilon _r = 1.5, \mu _r =1.5$
	$\epsilon _r = 1.5, \mu _r =0.5$
	$\epsilon _r = 0.5, \mu _r =0.5$
	$\epsilon _r = 0.5, \mu _r =1.5$

Question

Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main scale. The total number of divisions on the circular scale is 50. Further, it is found that the screw gauge has a zero error of − 0.03 mm while measuring the diameter of a thin wire, a student notes the main scale reading of 3 mm and the number of circular scale divisions in line with the main scale as 35. The diameter of the wire is

Possible Answers

Selected	Possible Answer
	3.32 mm
	3.38 mm
	3.73 mm
	3.67 mm

Question

An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume V_1 and contains ideal gas at pressure P_1 and temperature T_1 . The other chamber has volume V_2 and contains ideal gas at pressure P_2 and temperature T_2 . If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be

Possible Answers

Selected	Possible Answer
	$\frac {T_1 T_2 (P_1 V_1 + P_2 V_2 )}{P_1 V_1 T_1 +P_2 V_2 T_2}$
	$\frac {T_1 T_2 (P_1 V_1 + P_2 V_2)}{P_1 V_1 T_2 + P_2 V_2 T_1}$
	$\frac {P_1 V_2 T_2 + P_2 Y_1}{P_1 V_1 + P_2 V_2}$
	$\frac {P_1 V_1 T_1 + P_2 V_2 T_2}{P_1 V_1 + P_2 V_2}$

Question

A capillary tube (A) is dropped in water. Another identical tube (B) is dipped in a soap water solution. Which of the following shows the relative nature of the liquid columns in the two tubes?

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Selected	Possible Answer

Question

A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the following graphs most closely represents the electric field E® produced by the shell in the range $0 \underline < r < \infty$ , where r is distance from the centre of the shell?

Possible Answers

Selected	Possible Answer

Question

A 5V battery with internal resistance $2 \Omega$ and a 2V battery with internal resistance $1 \Omega$ are connected to a $10 \Omega$ resistor as shown in the figure. The current in the $10 \Omega$ resistor is

Possible Answers

Selected	Possible Answer
	to
	to
	to
	to

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	$x - log \Big \| \cos \Big ( x - \frac{\pi}{4} \Big ) \Big \| + c$
	$x - log \Big \| \sin \Big ( x - \frac{\pi}{4} \Big ) \Big \| + c$
	$x + log \Big \| \cos \Big ( x - \frac{\pi}{4} \Big ) \Big \| + c$
	$x + log \Big \| \cos \Big ( x - \frac{\pi}{4} \Big ) \Big \| + c$

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