iitjee 2006

Q.17 A tangent at P(x,y) point on the curve y =f(x) intersects to the axes at A and B pointsrespectively such that AP : BP ≡ 1 : 3,given that f(1) = 1, then–(a) normal at (1, 1) is x + 3y = 4(b) equation of curve is 3y + xy′ = 0(c) curve passes through (2, 1/8)(d) equation of curve is xy′ – 3y = 0Ans. [b,c]Q. 18 f(x) is a cubic polynomial such that f(3) = 18,f(–1) = 2 and f(x) has local maximum atx = –1. If f ′(x) has local maximum at x =0, then(a) f(x) is increasing for x ∈ [1, 2, 5 ](b) the distance between (–1, 2) and (a, f(a))where x = a is the point of local minimumSection III :Questions based on comprehensionswith one correct answer.Passage – INow we define the definite integral using theformula ∫ b b − af (x) dx = (f(a) + f(b)), for morea2accurate result for c ∈ (a,b) ,b − a⎢⎣ 2b − c⎢⎣ 2⎡⎤ ⎡⎤F (c) = ( f(a) + f(c) ) ⎥⎦ + ( f(b) + f(c) ) ⎥⎦when c =a + b,2∫ b ⎛ b − a ⎞f (x) dx = ⎜ ⎟a ⎝ 4(f(a)+ f(b) + 2f(c))⎠is 2 5(c) f(x) has local minima at x = 1(d) the value of f(0) = 5Ans. [b c]Q.19 Let A is a vector parallel to line ofintersection of planes P 1and P 2throughorigin. P 1is parallel to the vectors 2 ĵ +3 kˆand 4 ĵ – 3 kˆ and P 2is parallel to ĵ – kˆπQ.21 Evaluate 2 sin x dx∫0π(a) (1 + 2 )8 2π(c) (1 2)4 +(b)π(18 + 2)(d)π(1 24 + 2)Ans [b]and 3 ĵ +3 kˆ than angle between vectorsA and 2 î + ĵ –2 kˆ is–π(a) 2(c)π6⎧ xe⎪Q.20 Let f(x) = ⎨ 2−ex−1⎪⎩ x −e(b) 4π3π(d)4Ans [b, d]0 ≤ x < 11