8/12/2019 Aiot Advanced Xi Paper 1 20 Jan 13 Eng http://slidepdf.com/reader/full/aiot-advanced-xi-paper-1-20-jan-13-eng 1/20 Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. Date : 20-01-2013 Duration : 3 Hours Max. Marks : 219 PAPER 1 CODE 0 ALL INDIA OPEN TEST (AIOT) JEE ADVANCE INSTRUCTIONS A. General : 1. This Question Paper contains 63 questions. 2. The question paper CODE is printed on the right hand top corner on this sheet of this booklet. 3. No additional sheets will be provided for rough work. 4. Blank paper, clipboard, log tables, slide rules, calculators, cellular phones, pagers and electronic gadgets in any form are not allowed. 5. The answer sheet, a machine-gradable Objective Response Sheet (ORS), is provided separately. 6. Do not Tamper / mutilate the ORS or this booklet. 7. Do not break the seals of the question-paper booklet before instructed to do so by the invigilators. 8. Write your Name, Roll No. and Sign in the space provide on the back page of this booklet. B. Filling the bottom-half of the ORS : Use only Black ball point pen only for filling the ORS. Do not use Gel / Ink / Felt pen as it might smudge the ORS. 9. Write your Roll no. in the boxes given at the top left corner of your ORS with black ball point pen. Also, darken the corresponding bubbles with Black ball point pen only. Also fill your roll no on the back side of your ORS in the space provided (if the ORS is both side printed). 10. Fill your Paper Code as mentioned on the Test Paper and darken the corresponding bubble with Black ball point pen. 11. If student does not fill his/her roll no. and paper code correctly and properly, then his/her marks will not be displayed and 5 marks will be deducted (paper wise) from the total. 12. Since it is not possible to erase and correct pen filled bubble, you are advised to be extremely careful while darken the bubble corresponding to your answer. 13. Neither try to erase / rub / scratch the option nor make the Cross (X) mark on the option once filled. Do not scribble, smudge, cut, tear, or wrinkle the ORS. Do not put any stray marks or whitener anywhere on the ORS. 14. If there is any discrepancy between the written data and the bubbled data in your ORS, the bubbled data will be taken as final. C. Question paper format and Marking scheme : 15. The question paper consists of 3 parts (Physics,Chemistry & Mathematics). Each part consists of FOUR Sections. 16. For each question in Section –I, you will be awarded 3 marks if you darken the bubble corresponding to the correct answer and zero marks if no bubble is darkened. There is no negative marking for incorrect answer in this section. 17. For each question in Section –II, you will be awarded 4 marks if you darken the bubble corresponding to the correct answer and zero marks if no bubble is darkened. There is no negative marking for incorrect answer in this section. 18. For each question in Section –III, you will be awarded 3 marks if you darken the bubble corresponding to the correct answer and zero marks if no bubble is darkened. There is no negative marking for incorrect answer in this section. 19. For each question in Section –IV, you will be awarded 4 marks if you darken the bubble corresponding to the correct answer and zero marks if no bubble is darkened. In case of bu bbling of incorrect answer, minus one ( –1) markwill be awarded. D O N O T B R E A K T H E S E A L S W I T H O U T B E I N G I N S T R U C T E D T O D O S O B Y T H E I N V I G I L A T O R CLASS-XI | TARGET : JEE (IITs) 2014 | COURSE : ALL INDIA TEST SERIES (VIKALP)
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This section contains 7 questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out ofwhich ONLY ONE is correct.
43. A value of a for which one root of quadratic equation (a2 – 5a + 3) x2 + (2a – 3) x + 2 = 0 is twice as
large as other is
(A) –3
1(B)
5
3(C) –
5
3(D)
3
1
44. If a, a1, a
2, a
3 , ......, a
100 , b are in A.P. and a, g
1, g
2, ...., g
100b , are in G.P. and h is harmonic mean of a and
b, then 501001
100321
)aa(
g....ggg
!+ 49
992
99432
)aa(
g....ggg
!+ 48
983
98543
)aa(
g....ggg
!+ ...+
)aa(
gg
5150
5150
! is equal to
(A)1h
)1h(h 50
"
"(B)
2h
)2h(h 5050
"
"(C)
)2h(2
)2h(h50
5050
"
"(D)
)2h(h
)2h(250
5050
"
"
45. The sum of the coefficient of all the terms in the expansion of (2x – y + z)20 in which y do not appear at allwhile x appears in even powers and z appears in odd powers is
(A) 0 (B)2
1220 "(C) 219 (D)
2
1320 "
46. The number of six letter words, each consisting of three consonants and 3 vowels, that can be formedusing the letters of the word "CIRCUMFERENCE" is
47. If in a #ABC the equation of angle bisector of angle B is y = x and angle C is y = –x. The equation of
line BC if the coordiates of A are (5, 7) is
(A) x + y + 1 = 0 (B) 7y + 5x – 3 = 0
(C) 7y = 5x (D) none of these
48. If two distinct chords of a parabola y2 = 4ax passing through the point (a, 2a) are bisected by the linex + y = 1, then length of the latus rectum can be(A) 2 (B) 7 (C) 4 (D) 5
49. The number of solutions of the equation xcos1" = sin x which lie in the interval [$, 5$], are
(A) 6 (B) 5 (C) 4 (D) 3
SECTION - II
True & False Statement Type This Section Contains 3 questions. Each questions contains 3 or 4 statements S
1, S
2, S
3or S
4. Each
statement is either true (T) or false (F). Each questions has 4 choices (A), (B), (C) and (D) each ofwhich contains whether S
1, S
2, S
3 or S
4are true or false. Exactly one choice contains the correct order
of truthness or falseness of S1, S
2, S
3 or S
4 respectively and is the correct choice.
50. Consider the following statements :
S1 : If two quadratic expressions f(x) = ax2 + bx + c and g(x) = ax2 + px + q, have equal discreminants and f(x) = g(x) has a root x = %, then arithematic mean of roots of f(x) + g(x) = 0 is %
51. Consider the following statements :S1 : If x + y = k is a normal to y2 = 12x, then k = 9S2 : The centre of ellipse 4x2 + 9y2 – 16x – 54y + 61 = 0 is (2, 3)
S3 : If in a triangle (a + b + c) ( – a + b + c) = kbc, then k & [0, 3]State, in order, whether S
1, S
2, S
3 are true or false
(A) T T F (B) T F T (C) F T F (D) F F T
52. Consider the following statementsS1 : If r and s are non negative integers and r + s = 2n + 1, then r! s! is least when value of |r – s| is 2.
S2 : 0xlim' (
( )
*++,
- !
)2 / x(tan
x2cos –xsinx12 = 6.
S3 : Number of values of ‘.’ in [0, 4$] satisfying the equation cos3. = 3cos., are 4State, in order, whether S
1, S
2, S
3 are true or false
(A) T F T (B) F T F (C) F F T (D) F T T
SECTION - III
Comprehension Type This section contains 2 paragraphs. Based upon each paragraph, there are 2 questions. Each question has4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
Paragraph for Question Nos. 53 to 54
Let 0(x, y) 1 x2 + y2 + 2gx + 2fy + c = 0 be a circle of radius k passing through the points (%, 0) and(0, %), % 2 0. If 0 (%, 0) = 0 has equal roots and 0(1, 1) = – 2 ,then
53. Value of k is(A) 1 (B) 2 (C) 4 (D) 8
54. Let the equation of tangent to the circle x2 + y2 – 2kx = 0 which is perpendicular to the normal drawn through
the origin be x + by = c, (where c 2 0 and k is obtained by Q.No. 53) then c =(A) 4 (B) 3 (C) 2 (D) 1
55. If f(x) = 4 has n solutions and product of these solutions is k, then k =
(A)2
n(B) n (C) 2n (D) 3n
56. If a = 2, then the greater solution of f(x) = 4 is (where k is obtained by Q.No. 55)
(A) 22k (B) 24k (C) 28k (D) 1
SECTION - IV
Integer Answer Type
This section contains 7 questions. The answer to each of the questions isa double digit integer, ranging from 00 to 99. The appropriate bubblebelow the respective question number in the ORS have to be darkened.
57. If set of all real value of a such that f(x) =40x2x
= kx2 + !x + m, then find the value of 2 – 5(k + ! + m).
60. The sum of the squares of the reciprocals of two perpendicular diameters of the ellipse 5x2 + 4y2 = 1is equal to k, then find the value of 8k.
61. If PQ is a double ordinate and e is eccentricity of the hyperbola 1b
y –
a
x2
2
2
2
4 such that OPQ is an
equilateral triangle, O being the centre of the hyperbola, then find the least possible integral value of 3e2.
62. PN is an ordinate of the parabola y2 = 4ax. A straight line is drawn parallel to the axis to bisect NP andmeets the curve in Q. NQ meets the tangent at the vertex in a point T such that AT = kNP, then find thevalue of 30k. (Where A is the vertex)
63. The number of different necklaces formed by using 30 identical diamonds and 3 different jewels when exactlytwo jewels are always together is 10x + y, where 0 5 x, y 5 9, then find the value of |x – y|.