May 2011 - Career Point

6. If ∆ is area of ∆ABC and length of two sides are 3& 5 respectively, if third side is c, then22c + 16c + 64 c + 16c + 54(A) ∆ ≤(B) ∆ =12 38(C) ∆ >c2+ 16c + 7443(D) None of these7. A point Q is selected at random inside theequilateral triangle. If sum of lengths ofperpendicular dropped on sides from Q is P. Thenaltitude of triangle is -PP(A) (B) 2 3(C) P(D) None of theseQuestions 8 to 11 are multiple choice questions. Eachquestions has four choices (A), (B), (C) and (D), out ofwhich MULTIPLE (ONE OR MORE) is correct.8. If cotθ + tanθ = x and secθ – cosθ = y, then -(A) x sinθ . cosθ = 1(B) sin 2 θ = y cosθ(C) (x 2 y) 1/3 + (xy 2 ) 1/3 = 1(D) (x 2 y) 2/3 – (xy 2 ) 2/3 = 1θ9. If 0 ≤ θ ≤ π and sin = 1 + sin θ – 1 – sin θ2then possible values of tanθ is/are -43(A) (B) – 3 4(C) – 34(D) 0⎛ 2 1 ⎞10. If ⎜cos x + ⎟ (1 + tan 2 2y) (3 + sin 3z) = 42⎝ cos x ⎠then -(A) x is a multiple of π(B) x is a multiple of 2π(C) y is a multiple of π/2(D) None of these11. In a ∆ABC, if r = 1, R = 3, s = 5 which of thefollowing is/are correct (where a, b, c representsides of triangle) -(A) ar ∆ABC = 5(B) Product of sides of ∆ABC is 60(C) a 2 + b 2 + c 2 = 24(D) Sum of exradii of ∆ABC is 13This section contains 2 paragraphs, one has 3multiple choice questions and other has 2 multiplechoice questions (Question 12 to 16). Each questionshas 4 choices (A), (B), (C) and (D) out of which ONLYONE is correct.Passage : I (Q. No. 12 to 14)Let α ± β is not an odd multiple of π.α + βIf cos α + cos β = b, sin α + sin β = a, θ =2na(a – b)and sin 2θ + cos 2θ = 1 + where n ∈ I2 2a + bthen12. Value of n is -(A) 0 (B) 1(C) – 2(D) None of these13. If cosec n x = A then sin 3A. sin A is polynomial inx, whose degree is equal to -(A) 5 (B) 4 (C) 2 (D) 314. If degree of polynomial obtained in above questionis p then max. value of (p + 1) sin x + (p + 2) cos xis -(A) p + 2 (B) p + 3(C) p + 1(D) None of thesePassage : II (Q. No. 15 to 16)Let sides of a triangle are a = n + 1, b = n + 2 &c = n with sin C = 54 , then answer the following.15. Area of ∆ABC is -(A) 84 (B) 72(C) 60(D) None o these16. Largest exradius of circle escribing ∆ABC -(A) 12 (B) 14(C) 16(D) None of theseThis section contains 7 questions (Q.17 to 25).+4 marks will be given for each correct answer andno negative marking. The answer to each of thequestions is a SINGLE-DIGIT INTEGER, rangingfrom 0 to 9. The appropriate bubbles below therespective question numbers in the OMR have to bedarkened. For example, if the correct answers toquestion numbers X, Y, Z and W (say) are 6, 0, 9 and2, respectively, then the correct darkening of bubbleswill look like the following :X Y Z W0123456789012345678901234567890123456789XtraEdge for IIT-JEE 59 MAY 2011