Test Codes: SIA (Multiple Choice Type) and SIB (Short Answer Type ...

(c) The integer n need not be a power of 2, but must be even.(d) None of the above is necessarily true.28. Water falls from a tap of circular cross section at the rate of 2 metres/secand fills up a hemispherical bowl of inner diameter 0.9 metres.If the inner diameter of the tap is 0.01 metres, then the time neededto fill the bowl is(A) 40.5 minutes;(C) 60.75 minutes;29. The value of the integral∫ 5π/2e tan−1 (sin x)e tan−1 (sin x) + e dxtan−1 (cos x)π/2(B) 81 minutes;(D) 20.25 minutes.equals (A) 1; (B) π; (C) e; (D) none of these.30. The set of all solutions of the equation cos 2θ = sin θ + cos θ is givenby(A) θ = 0.(B) θ = nπ + π 2, where n is any integer.(C) θ = 2nπ or θ = 2nπ − π 2 or θ = nπ − π 4, where n is any integer.(D) θ = 2nπ or θ = nπ + π 4, where n is any integer.31. For k ≥ 1, the value of( ( )n n + 1+ +0)1( n + 22)+ · · · +( ) n + kequals( )( )n + k + 1n + k(A); (B) (n + k + 1) ;n + kn + 1( ) n + k + 1(C); (D)n + 1k( n + k + 132. The value of{ ( √ )} √ √ ]sin −1 cot[sin −1 1 5 2 81 − + cos −12 63 + sec−1 3is(A) 0; (B) π/6; (C) π/4; (D) π/2.33. Which of the following graphs represents the functionf(x) =∫ √ x0n).e −u2 /x du, for x > 0 and f(0) = 0?6