– 1 – Head Office: 5/5, Amer Complex, Opp. PNB, M.P. Nagar, Zone-II, Bhopal (M.P.) Ph. 0755-4074100 Web: www.heritageiita.com MM : 240 J EE (Ad vance d ) 2 014 Tim e : 3 Hr. Topics covered : Chemistry : Hydrogen, s-Block Elements, Some p-Block Elements (B, C), Organic Chemistry-(Some Basic Principles and Techniques) Mathematics : Probability (part-1) based on Permutation and Combination, Sequence and Series, Exponential and Logarithmic Series, Straight lines, Circle. Physics : Rigid Body Rotation, Gravitation, Properties of Bulk MatterInstructions : (i ) The que st ion p aper cons ists of 3 p art s ( Chemistry , Mathematics and Physics). Each part has 6 sections. (ii) Section I contains 6 multiple choice questions which have only one correct answer. Each question carries +3 marks each for correct answer and–1 mar k for each wrong answer. (iii) Se ction II contains 4 multiple choice questions which have one or more answers are correct. Each question carries +4 marks each for correct answer. There are no negative marks in this section. (iv) Section IIIcontains 2 questions. Each question contains STATEMENT-1 (Assertion) and STATEMENT-2 (Reason). (A) St atement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1 (B) Statement-1 is True, Sta tement-2 is T rue; Sta tement-2 is NOTa correct explanation for Statement-1 ( C) Statement-1 is True, S tatement-2 is False ( D) Statement-1 is False, Statement-2 is True Each question carries +3 marks each for correct answer and –1 mar k for each wrong answer. ( v) Se ction IV: This section contains one paragraph. Based upon this paragraph, 3 multiple choice questions have to be answered. Each question has only one correct answer and carries +4 marks for correct answer and –1 mark for wrong answer. (vi) Section V contains 2 quest ions. For each question, one choice of col umn-I matches with one or more than one choice of column-II. For each question, you will be awarded 2 marks for each ro w in which you have darkened the bubble(s) corresponding to the correct answer. Thus, each question in this section carries a maximum of8 marks. There are no negative marks in this section. (vii) Se ction VI : This section contains 3 questions. The answers to each of the questions is a single digit integer, ranging from 0 to 9 without being given any option. Each question has only one correct answer and carries +4 marks for correct answer. There are no negative marks in this section. (vi ii) Rough w ork must not be done on the ans wer sheet and do not use w hite-fluid or any other rubbing material on Answer Sheet. H A Code-A3
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(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True
SECTION-IV
Paragraph Type
This section contain 1 paragraph. Based upon this paragraph 3 multiple choice questions have to be answered. Each
question has 4 choices (A), (B), (C) and (D) for i ts answer, out of which ONLY ONE is correct.
Paragraph for Question Nos. 13 to 15
Lithium ion has very high charge density therefore it gives mainly its oxide. Sodium ion has low charge density, it gives
mainly peroxide K, Rb and Cs ions give superoxide with O2 gas.
22
1 OO2 22
2 2O O 2O
13. O –2 ion is maximum polarised by
(A) Li+ (B) Na+
(C) Rb+ (D) K+
14. In hydrolysis, the alkali oxides, peroxides and superoxides act as
(A) Bronsted acid (B) Bronsted base
(C) Lewis acid (D) Lewis base
15. Which compound will liberate O2 gas with cold H2O?
(A) Na2O
2(B) KO
2
(C) Na2O (D) Cs
2O
2
SECTION-V
Matrix-Match Type
This section contains 2 questions. Each question contains statements given in two columns which have to be matched.
The statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled p, q, r, s and
t. Any given statement in Column I can have correct matching with One OR More statement(s) in Column II. The
appropriate bubbles corresponding to the answers to these questions have to be darkened as illustrated in the following
example. If the correct matches are A-p, s and t; B-q and r; C-p and q; and D-s and t; then the correct darkening of bubbles will look like the following.
28. Let L1 be a straight line passing through the origin and L
2 be the straight line x + y = 4. If the intercepts made
by the circle x2 + y2 – 4x – 6y – 3 = 0 on L1 and L
2 are equal and if m
1, m
2 be slopes of possible equation
of L1 then
(A) 1 224
7m m (B) 1 2
12
7m m
(C) 1 217
7m m (D) 1 2
11
7m m
29. If x + y = 15, x, y > 0 then
(A) Maximum value of xy2 is 500 (B) Maximum value of xy2 is (7.5)3
(C) Maximum value of x2y3 is 62 93 (D) Maximum value of x2y3 is 510
30. The point (1, 4) is inside the circle S whose equation is of the form x2 + y2 – 6x – 10y + k = 0. Then possible
values of k if the circle neither touches the axes nor cuts them is/are
(A) 27 (B) 26
(C) 28 (D) 30
SECTION - III
Reasoning Type
The section contains 2 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out
of which ONLY ONE is correct.
31. STATEMENT-1 : Tangent to the circle x2 + y2 = 25 at (3, 4) is parallel to the line 3x + 4y – 11 = 0.
and
STATEMENT-2 : If two lines are parallel then their slopes are equal.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True
32. Consider the circle x2 + y2 = 100.
STATEMENT-1 : From (10, 10), two mutually perpendicular tangents can be drawn to given circle.and
STATEMENT-2 : The locus of the point from which two mutually perpendicular tangents can be drawn to given
circle is x2 + y2 = 200.
(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C) Statement-1 is True, Statement-2 is False
(D) Statement-1 is False, Statement-2 is True
SECTION-IV
Paragraph Type
This section contain 1 paragraph. Based upon this paragraph, 3 multiple choice questions have to be answered. Eachquestion has 4 choices (A), (B), (C) and (D) for i ts answer, out of which ONLY ONE is correct.
Paragraph for Question Nos. 33 to 35
Consider all possible arrangements of letters of word ‘ORANGE’ and a word is selected at random.
33. The probability that in selected word, vowels are in alphabetical order, is
34. The probability that first and last letter of selected word are vowels, is
(A)1
5(B)
2
5
(C)1
10(D)
1
3
35. The probability that first letter of selected word is vowel and last letter of selected word is consonant, is
(A) 15
(B) 215
(C)1
15(D)
3
10
SECTION-V
Matrix-Match Type
This section contains 2 questions. Each question contains statements given in two columns which have to be matched.The statements in Column I are labelled A, B, C and D, while the statements in Column II are labelled p, q, r, sand t. Any given statement in Column I can have correct matching with One OR More statement(s) in Column II. Theappropriate bubbles corresponding to the answers to these questions have to be darkened as illustrated in the followingexample. If the correct matches are A-p, s and t; B-q and r; C-p and q; and D-s and t; then the correct darkening of
bubbles will look like the following.
A
B
C
D
p
p
p
p
q
q
q
q
r
r
r
r
s
s
s
s
p q r s
t
t
t
t
t
36. Match the following
Column I Column II
(A) Equation of the base of an equilateral triangle (p) 1 sq-unit
is x + y = 2 and vertex opposite to it is
(2, – 1). Then area of triangle is
(B) Area of triangle formed by joining the origin (q) 2 sq-unit
to the point of intersection of the line
5 2 3 5x y and circle x2 + y2 = 10 is
greater than or equal to
(C) Area of triangle formed by the line (r) 5 sq-unit
xy + 2x + 2y + 4 = 0 and x + y + 2 = 0 is
less than or equal to
(D) Area of triangle formed by 2x2 – 5xy + 3y2 = 0 (s)1
(A) Let a, b, c be positive real numbers different (p) Are in A.P.
from 1. If loga200, 2log
b10, 2log
c5 + log
c4
are in H.P., then a, b, c
(B) Let a, b, c be different positive real numbers (q) Are in G.P.
such that a > b > c. If 2log(a – c),
log(a2 – c2), log(a2 + 2b2 + c2) are in A.P.,
then a, b, c
(C) If a, b, c are in A.P. and a2, b2, c2 are in (r) Are in H.P.
H.P., then a3
, b3
, c3
(D) If a, b, c are in A.P., b, c, d are in G.P., (s) Are in A.G.P.
c, d, e are in H.P., then a, c, e
(t) Satisfy 3b = 2a + c
SECTION-VI
Integer Answer Type
This section contains 3 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. The
appropriate bubbles below the respective question numbers in the ORS have to be darkened. For example, if the correctanswers to question numbers X, Y and Z (say) are 6, 0 and 9, respectively, then the correct darkening of bubbles will
look like the following :
0
X
Y
Z 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
38. A third order diagonal matrix is formed using the digits 1, 2, 3, 4, 5, 6 without repetition (along principal
diagonal). The probability that the sum of the diagonal elements of a matrix thus formed is 9, is p then1
p
([] represents greatest integer function) is _______.
39. A straight line with negative slope and passing through (2, 2) cuts x-axis at P and y-axis at Q then absolute
minimum value of OP + OQ is _______.
40. C1 : x2 + y2 = r 2, C
2 : x2 + y2 – 4x – 4y – 1 = 0. The largest integral value of r for which C
47. A disc of radius r rolls on a horizontal ground with linear acceleration a and angular acceleration
Q
P
R
ar
r
(A) Acceleration of point P is 22 2a R r (B) Acceleration of point P is a + r
(C) Acceleration of point Q is 2 22a r R (D) Acceleration at point Q is a + R + 2r
48. A cubical block of density (c) is floating on a liquid of density
l.
l
PB
= Pressure at the bottom of vessel
l = length of the cubical block inside liquid
FB
= Force of buoyancy on cubical block
Fn
= Net force by the liquid on the block
If the container is made to move with some acceleration in upward direction
(A) PB increases (B) PB remains same
(C) l increases (D) l remains same and FB increases
49. Two wires of same mass A and B are made of same material. Diameter of wire B is twice of diameter of wire
A then
(A) Strain in both the wires is same
(B) Strain in wire A is 4 times strain in B
(C) Extension of wire A is 16 times extension of B
(D) Both the wires will have same extension
50. Choose the incorrect statement(s) from the following
(A) Total energy and total angular momentum of solar system is constant(B) A rocket must necessarily have escape velocity from the very beginning of its motion to escape from earth
(C) A satellite can be in a stable orbit in a plane not passing through the earths center
(D) Velocity of escape for a particle resting on earth is equal to velocity of escape for a particle orbiting around
earth
SECTION - III
Reasoning Type
This section contains 2 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, outof which ONLY ONE is correct.