Solution - Career Point

1. Let F denote the set of all onto functions from A ={a 1 , a 2 , a 3 , a 4 } to B = {x, y, z}. A function f is chosenat random from F. The probability that f –1 (x)consists of exactly two elements is(A) 2/3 (B) 1/3 (C) 1/6 (D) 02. A letter is known to have come from eitherTATANAGAR or CALCUTTA. On the envelope,just two consecutive letters TA are visible . Theprobability that the letter has come fromCALCUTTA is(A) 4/11 (B) 1/3 (C) 5/12 (D) None3. A person writes 4 letters and addresses 4 envelopes.If the letters are placed in the envelops at random, theprobability that not all letters are placed in correctenvelopes is(A) 1/24 (B) 11/24 (C) 5/8 (D) 23/244. The value of x for which the matrix⎡ 2 0 7⎤A =⎢ ⎥⎢0 1 0⎥is inverse of⎢⎣1 − 2 1⎥⎦⎡−xB =⎢⎢0⎢⎣x(A) 2114x1− 4x(B) 317x ⎤0⎥⎥− 2x⎥⎦is(C) 41(D) 515. The largest term in the expansion of (3 + 2x) 50 , wherex = 1/5, is(A) 5 th (B) 6 th (C) 8 th (D) 9 th6. If2z − = 2, then the greatest value of | z | isz(A) 1 + 2 (B) 2 + 2(C) 3 +1 (D) 5 + 116−17. The value of∫tan x −1 dx is(A)(C)116π + 3342 (B) π3– 2 3416π + 2 3 (D) π – 2 3338. The solution of(y + x + 5)dy = (y – x + 1) dx is(A) log ((y + 3) 2 + (x + 2) 2 ) + tan –1 y + 3x + 2= C(B) log ((y + 3) 2 + (x – 2) 2 ) + tan –1 y − 3x − 2= C(C) log ((y + 3) 2 + (x + 2) 2 ) + 2 tan –1 y + 3x + 2= C(D) log ((y + 3) 2 + (x + 2) 2 ) – 2 tan –1 y + 3x + 2= CSECTION – IIMultiple Correct Answers TypeThis section contains 4 multiple correct answer(s) typequestions. Each question has 4 choices (A), (B), (C) and(D), out of which ONE OR MORE is/are correct.9. If n > 1, then (1 + x) n – nx – 1 is divisible by -(A) x 2 (B) x 3(C) x 4 (D) x 51−sin 4A + 110. If y =, then one of the values of y is -1+sin 4A −1(A) – tan A (B) cot A⎛ π ⎞⎛ π ⎞(C) tan ⎜ + A ⎟ (D) – cot ⎜ + A ⎟⎝ 4 ⎠ ⎝ 4 ⎠11. Equation of a common tangent to the circlesx 2 + y 2 – 6x = 0 and x 2 + y 2 + 2x = 0 is -(A) x = 1 (B) x = 0(C) x + 3 y + 3 = 0 (D) x – 3 y + 3 = 02x t − 5t + 412. The points of extremum of∫are -0t2 + e(A) x = – 2 (B) x = 1(C) x = 0 (D) x = – 1SECTION – IIIComprehension TypeThis section contains 2 groups of questions. Each grouphas 3 multiple choice questions based on a paragraph.Each question has 4 choices (A), (B), (C) and (D) for itsanswer, out of which ONLY ONE is correct.Paragraph # 1 (Ques. 13 to 15)Consider the region S 0 which is enclosed by the curve2y ≥ 1− x and max. {|x|, |y| } ≤ 4. If slope of afamily of lines is defined asm(t) = cos t where point (t, 2t + 0.4) lies inside theregion S 0 . Any member of this family of lines is calledL 1 = 0 if it passes through (π, max {t}) and L 2 = 0 if itpasses through the (π, min m {t}).13. Area of region of S 0 is -(A) 8 + π/2 sq. units (B) 8 – π/2 sq. units(C) 8 sq. units (D) 8 + π sq. units2XtraEdge for IIT-JEE 56APRIL 2010