1. Xtra Edge February 2012 - Career Point

12. Assertion (A) : If eccentricities of two ellipse are
same then their areas are also same.
2 2
x y
Reason (R) : Area of the ellipse + = 1
2 2
a b
(a < b, a > 0, b > 0) is π ab square units.
13. Consider a circle S : (x – 2) 2 + (y – 3) 2 = 13 and a line
L : y = x – 12.
Assertion (A) : Chord of contact of pair of tangents
drawn from every point on L = 0 to S = 0 passes
through P(3, 2)
Reason (R) : Pole of polar L = 0 with respect to
S = 0 is P(3, 2)
This section contains 2 paragraphs; each has 3 multiple
choice questions. (Questions 14 to 19) Each question
has 4 choices (A), (B), (C) and (D) out of which ONLY
ONE is correct. Mark your response in OMR sheet
against the question number of that question. +4 marks
will be given for each correct answer and – 1 mark for
each wrong answer.
Passage # 1 (Ques. 14 to 16)
If f (xy) = f (x) . f (y) and f is differentiable at x = 1
such that f '(1) = 1 also f (1) ≠ 0, then
14. f (x) is -
(A) continuous for all x ∈ R
(B) discontinuous at x = –1, 0, 1
(C) differentiable for all x ≠ 0
(D) None of these
15. f '(7) equals-
(A) 7 (B) 14 (C) 1 (D) None
16. Area bounded by curve f(x), x axis and ordinate
x = 4, is-
(A) 64/3 (B) 8 (C) 16 (D) None
Passage # 2 (Ques. 17 to 19)
1
There exists a G.P. with first term and common
A
1
ratio A (A > 1). If we add in the sum of first n
2
terms of the sequence, it equals to the sum of the
coefficients of even power of x in the expansion of
(1 + x) n . If we interchange the first term & common
ratio of given G.P., the sum of new infinitely
decreasing G.P. is equal to B, where A, B and n are
related by the relation
B−2
∫
A−2
n 364
( 1+
x)
dx =
3
17.
( 1+
x)
− n − B
The value of lim
isx→A
x − A
(A) 3 (B) 6 (C) e (D) 8
A
18. Area bounded by f(x) = x A and g(x) = x B is-
A + B
(A)
n
2A
(C)
A + 2B
+ n
XtraEdge for IIT-JEE 58 FEBRUARY 2012
(B)
(D)
B − A
n
B
n + A + B
19. Number of real roots of the equation
(x B – nx A ) 1/A = 6 are
(A) 2 (B) 4 (C) 1 (D) 0
This section contains 3 questions (Questions 20 to 22).
Each question contains statements given in two columns
which have to be matched. Statements (A, B, C, D) in
Column I have to be matched with statements (P, Q, R, S)
in Column II. The answers to these questions have to be
appropriately bubbled as illustrated in the following
example. If the correct matches are A-P, A-S, B-Q, B-R,
C-P, C-Q and D-S, then the correctly bubbled 4 × 4
matrix should be as follows :
P Q R S
A P Q R S
B P Q R S
C P Q R S
D P Q R S
Mark your response in OMR sheet against the question
number of that question in section-II. + 6 marks will be
given for complete correct answer and No Negative
marks for wrong answer. However, 1 mark will be
given for a correctly marked answer in any row.
20. Match the Column :
Column-I Column-II
(A) The reflection of the point (P) 5
(t – 1, 2t + 2) in a line is
(2t + 1, t) then the line has
slope equal to
(B) If θ be the angle between (Q) 6
two tangents which are drawn
to the circle x 2 + y 2 – 6 3 x – 6y + 27 = 0
from the origin, then 2 3 tanθ
equals to
(C) The shortest distance between (R) 2 7
parabolas y 2 = 4x and y 2 = 2x – 6
is d then d 2 =
(D) Distance between foci of the (S) 1
curve represented by the equation
x = 1 + 4cosθ, y = 2 + 3sinθ is