Solution - Career Point

X Y Z W0123456789012345678912. If z ≠ 0 and 2 + cos θ + i sin θ = 3/z, then find thevalue of 2 (z + z ) – |z| 2 .13. Find the sum of all the integral roots of(log 5 x) 2 + log 5x (5/x) = 1.14. Four different integers form an increasing A.P. suchthat one of them is the square of the remainingnumbers. Find the largest numbers.15. If n is a positive integer, andE = 2n + 1 C 1 + 2n + 1 C 2 + … + 2n + 1 C n – 2n + 1 C 2n + 1– 2n + 1 C 2n – … – 2n + 1 C n + 1 . Find |E|16. Find the number of values of t for which the systemof equations(a + 2t)x + by + by + cz = 0bx + (c + 2t)y + az = 0cx + ay + (b + 2t) z = 0has non-trivial solutions.17. A function f(x) is defined for x > 0 and satisfiesf(x 2 ) = x 3 for all x > 0. Then the value of f ′(4) is ___.18. If A is the area formed by the positive x-axis, and thenormal and tangent to the circle x 2 + y 2 = 4 at(1, 3 ) then A/ 3 is equal to _____.19. The area bounded by the curves x = y 2 andx = 3 – 2y 2 is ______.01234567890123456789PHYSICSSECTION – IStraight Objective TypeThis section contains 4 multiple choice questions. Eachquestion has 4 choices (A), (B), (C) and (D), out ofwhich ONLY ONE is correct.1. A thin conducting plate is inserted in half way betweenthe plates of a parallel plates capacitor of capacitance C.Conducting plateWhat does the value of capacitance, if both the plateof capacitor is shortened ?(A) C(B) 2C(C) 3C(D) 4C2. White light is incident normally on a glass surface(n = 1.52) that is coated with a film ofmg F 2 (n = 1.38). For what minimum thickness of thefilm will yellow light of wavelength 550 nm (in air)be missing in the reflected light ?(A) 99.6 nm(C) 19.6 nmmgF 2glass(B) 49.8 nm(D) 10.6 nm3. A circuit element is placed in a closed box. At timet = 0, a constant current generator supplying a current of Iamp is connected across the box. Potential diff. across thebox varies according to graph as shown in the figure. Theelement in the box is -8Volts(V)23 t(sec)Time(A) a resistance of 2Ω (B) a battery of emf 6V(C) an inductance of 2H (D) a capacitance4. Consider a usual set-up of Young's double slitexperiment with slits of equal intensity as shown inthe figure. Take 'O' as origin and the Y axis asindicated. If average intensity between y 1 = λD/4dand y 2 = λD/4d equals n times the intensity ofmaximum, then n equal is (take average over phasedifference) -y(A)d1 ⎛ ⎞⎜1+ 2 ⎟2 ⎝ π ⎠S 1S 2DO⎛ ⎞(B) 2 ⎜1+ 2 ⎟⎝ π ⎠⎛ ⎞(C) ⎜ + 21 ⎛ ⎞1 ⎟ (D) ⎜1− 2 ⎟⎝ π ⎠ 2 ⎝ π ⎠SECTION – IIMultiple Correct Answers TypeThis section contains 5 multiple correct answer(s) typequestions. Each question has 4 choices (A), (B), (C) and(D), out of which ONE OR MORE is/are correct.XtraEdge for IIT-JEE 66APRIL 2010