Solution - Career Point

27. The area bounded by the curves y = 2x 2 | x |& y = xand x = 0 is equal to2 2 2(A) (B) 3 6(C)26(D) None28. Order and degree of the differential equationy " = (y´+ 3) 1/3 are respectively(A) 2, 2 (B) 2, 3 (C) 3, 2 (D) None29. If x 18 = y 21 = z 28 then 3, 3 log y x, 3 log z y, 7 log x z arein(A) A.P. (B) G.P. (C) H.P. (D) None30. If log 2 x + log 2 y ≥ 6 then least possible value of x + yis(A) 32 (B) 16 (C) 8 (D) None31. No. of real roots of the equationx 3 + x 2 + 10x + sin x = 0 is(A) 1 (B) 2 (C) 3 (D) ∞32. The roots of the equation ax 2 + bx + c = 0, a ∈R + aretwo consecutive odd positive integers then(A) |b| ≤ 4a (B) |b| ≥ 4a(C) |b| ≥ 2a(D) None of these33. The sum of the terms of an infinitely decreasing G.P.is equal to the greatest value of the functionf(x) = x 3 + 3x – 9 on the interval [–2, 3] and thedifference between the first two terms is f´(0) thensum of first terms is(A) 19 or – 37 (B) 19(C) –37(D) None of these34. If the complex number z 1 = a + i, z 2 = 1 + ib, z 3 = 0form an equilateral triangle (a, b are real numberbetween 0 & 1) then :(A) a = 3 – 1, b = 3 / 2(B) a = 2 – 3 , b = 2 − 31 3(C) a = , b = 2 4(D) None of thesen35. ∑(−1)r=0(A)21n −r n C r1⎛⎜1r⎝ 2(B)r r3 7 ⎞+ + + ..... ∞⎟is equal to2r 3r2 2⎠32n − 1(C) 22 1n −36. The coefficient of x 3 y 4 z in the expansion of(1 + x + y – z) 9 is(A) 2 . 9 C 7 . 7 C 4 (B) – 2 . 9 C 2 . 7 C 3(C) 9 C 7 . 7 C 4 (D) None of these(D) Nonee x37. If = B 0 + B 1 x + B 2 x 2 + .... then B n – B n–1 = ?1−x1 1 1(A) (B) (C) (D) Nonen n n −138. The number of point (x, y, z) in space whose eachcoordinate is a negative integer such that x + y + z +12 = 0 is(A) 55 (B) 110 (C) 75 (D) None39. Six boys and six girls sit along a line alternativelywith probability P 1 & along a circle (againalternatively) with probability P 2 then P 1 /P 2 is equalto(A) 1 (B) 1/5 (C) 6 (D) None40. If f(x) is a polynomial satisfyingf(x) = 21f (x)1⎛ 1 ⎞f ⎜ ⎟ − f (x)⎝ x ⎠and f(2) = 17⎛ 1 ⎞f ⎜ ⎟⎝ x ⎠then the value of f(5) is(A) 624 (B) –124 (C) 626 (D) 126⎡1x⎤41. If A = ⎢ ⎥ is idempotent then x =⎣02 ⎦(A) 0 (B) 2(C) no such x exist (D) None of these42. Let R be a relation on the set of integers given bya R b if a = 2 k b for some integer k then R is(A) an equivalence relation(B) reflexive and symmetric but not transitive(C) reflexive and transitive but not symmetric(D) symmetric and transitive but not reflxive43. Minimum value ofb + ca+c + ab+ve numbers a, b, c) is(A) 1 (B) 2 (C) 4 (D) 6+a + b , (for realc44. From mean value theorem f(b) – f(a) = (b – a) f´(x 1 );a < x 1 < b if f(x) = x1 then x1 =(A)ab (B)a + b2(C)2aba + b(D)b − aa + b45. If f(x) =∫cot 4 1x dx + cot 3 ⎛ π ⎞x – cot x and f ⎜ ⎟ 3 ⎝ 2 = π⎠ 2then f(x) is(A) π – x (B) x – π (C) x (D) NoneXtraEdge for IIT-JEE 84APRIL 2010