1. Xtra Edge February 2012 - Career Point

(D)
P
A
T
B
(S) Pressure is increasing
MATHEMATICS
Questions 1 to 9 are multiple choice questions. Each
question has four 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. + 3 marks will be given for each correct
answer and – 1 mark for each wrong answer.
1. In a ∆ABC, if r = r2 + r3 –r1 and ∠A > π/3 then range
s
of is equal toa
⎛ 1 ⎞ ⎛ 1 ⎞ ⎛ 1 ⎞
(A) ⎜ , 2⎟
(B) ⎜ , ∞⎟
(C) ⎜ , 3⎟
(D) (3, ∞)
⎝ 2 ⎠ ⎝ 2 ⎠ ⎝ 2 ⎠
2. Vector perpendicular to î – j ˆ – k ˆ and in the plane of
î + j ˆ + kˆ and – î + j ˆ + kˆ is
(A) î + kˆ (B) 2 î + j ˆ + kˆ (C) 3 î +2 j ˆ + k ˆ (D) 4 î – 2 j ˆ –2 k ˆ
3. If a, b ∈ R, a ≠ 0 and roots of ax 2 – bx + 1 = 0
imaginary, then a + b + 1 is
(A) Zero (B) Positive
(C) Negative (D) None of these
4. Number of distinct normals that can be drawn to the
curve x 2 = 4y from point (1, 2), is
(A) 0 (B) 1 (C) 2 (D) 3
5. ABC is a triangle whose medians AD and BE are
perpendicular to each other. If AD = p and BE = q
then area of ∆ABC is-
2
(A) pq
3
3
(B) pq
2
4
(C) pq
3
3
(D) pq
4
6. If (21.4) a = (0.00214) b =100, then the value of
1 1
– is :
a b
(A) rational but not integral
(B) prime
(C) irrational
(D) composite
7. For 3 ≤ r ≤ n
n
Cr + 3 n Cr–1 + 3 n Cr–2 + n Cr–3 is-
(A) n+3 Cr (B) 2 n+2 Cr+2 (C) 3 n+1 Cr+1 (D) 3 n Cr
8. Point of intersection of straight lines represented by
6x 2 + xy – 40y 2 – 35x – 83y + 11 = 0 is-
(A) (3, 1) (B) (3, –1) (C) (–3, 1) (D) (–3, –1)
9. Number of points outside the hyperbola
3x 2 – y 2 = 48 from where two perpendicular tangents
can be drawn to the hyperbola is/are -
(A) 1 (B) 2 (C) infinite (D) None
This section contains 4 questions numbered 10 to 13,
(Reason and Assertion type question). Each question
contains Assertion (A) and Reason (R). 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. +3 marks
will be given for each correct answer and – 1 mark for
each wrong answer.
The following questions given below consist of an
"Assertion" (A) and "Reason" (R) Type questions. Use
the following Key to choose the appropriate answer.
(A) If both (A) and (R) are true, and (R) is the correct
explanation of (A).
(B) If both (A) and (R) are true but (R) is not the
correct explanation of (A).
(C) If (A) is true but (R) is false.
(D) If (A) is false but (R) is true.
10. Assertion (A) : The length of the shortest intercept
made by the family of lines (1 + λ) x + (λ – 1) y
+ 2 (1– λ) = 0 on the parabola x 2 = 4(y – 1) is 5.
Reason (R) : Latus rectum is the shortest focal chord
of the parabola.
11. Assertion (A) : If S1 and S2 are non-concentric
circles then their radical axis must exist.
Reason (R) : S1,S2, S3 are three circles such that no two
are concentric then their radical centre is defined.
12. Assertion (A) : If two straight lines intersect the xaxis
at A and B and y-axis at C and D such that
OA.OB = OC.OD, O being origin then points A, B,
C, D are concyclic.
Reason (R) : If a secant through a point P intersects
a circle at Q and R then PQ.PR is independent of the
direction of the secant.
13. Assertion (A) : The equation
(log x) 2 – log x 3 + 2 = 0 has only one solution.
Reason (R) : log x 2 = 2 log x if x > 0
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.
XtraEdge for IIT-JEE 65 FEBRUARY 2012