Solution - Career Point

14. If line lies inside the region S 0 , then -(A) t ∈ (0, 0.28) (B) t ∈ (0, 1)(C) t ∈ (0.28, 1) (D) t ∈ [.28, 1]15. L 1 = 0 having maximum slope, is -y −1y −1(A) = cos 1 (B) = cos (0.28)x − πx − πy − π(C) = cos (1) (D) None of thesex −1Paragraph # 2 (Ques. 16 to 18)Two circles S 1 = 0 and S 2 = 0 are touching to eachother externally at point T, with centreC 1 , C 2 and radii r 1 and r 2 respectively.If P and Q be the points of contact of a directcommon tangent to the two circles and PQ meets theline joining C 1 , C 2 in S. Tangent at common point Tis intersecting to the tangent PQ at R point and to otherdirect tangent at V point. Let S 1 = x 2 + y 2 – 6x = 0 andS 2 = x 2 + y 2 + 2x = 0.16. Angle between the two direct tangents is–(A) 90º (B) 30º(C) 60º(D) None of these17. Direct tangents are–(A) y = 3 x + 3 , y = – 3 x + 3x − x(B) y = – 3 , y = – 333x − x(C) y = + 3 , y = – 333(D) None of these18. A circle S = 0 of radius 1 units rolls on the outside ofthe circle S 2 = 0, touching it externally, locus of thecentre of this outer circle is –(A) Circle(B) Ellipse(C) Parabola (D) None of theseSECTION – IVMatrix – Match TypeThis section contains 2 questions. Each questioncontains statements given in two columns, which haveto be matched. The statements in Column I are labeledA, B, C and D, while the statements in Column II arelabeled p, q, r, s and t. any given statement in Column Ican have correct matching with ONE OR MOREstatements (s) in column II. The appropriate bubbledcorresponding to the answers to these questions have tobe 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 correctdarkening of bubbles will look like the following.ABCD19. Match the following-:Column- Ip q r s tpp(A) The sum of the series10∑r=020 C isr(B) The coefficient of x 53100100∑r=0rqqC (x − 3)rrr100−r(C) ( 10 C 0 ) 2 –( 10 C 1 ) 2 +…….…..–( 10 C 9 ) 2 + ( 10 C 10 ) 2 equals(D) The value of95 C 4 + ∑j=5100−j3120. Match the following -C isColumn -Ix − 2 y − 3 z − 4(A) If the lines = =1 1 λx −1 y − 4 z − 5and = =λ 2 1intersect at (α, β, γ) then λ =⎛ π −1⎛x + 1 ⎞(B) If lim 4xx→∞⎟ ⎞⎜ − tan ⎜ ⎟ =⎝ 4 ⎝ x + 2 ⎠⎠y 2 + 4y + 5 then y =2rssin(C) If chord x + y + 1= 0 of parabolay 2 = ax subtends 90º at (0, 0)then a =(D) If a = î + ĵ +kˆ , a . b = 1isand a × b = ĵ– kˆ , then | b | isequal tottColumn- II(p) – 10 C 5(q) 100 C 4(r) 2 19 + 21 20C 10(s) – 100 C 53(t) 100 C 47Column -II(p) 0(q) –1(r) –2(s) 1(t) –3XtraEdge for IIT-JEE 57APRIL 2010