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

(A) * (B)(C) (D) *8. Let Q be a quadrilateral such that two of its sides are of length a andtwo other sides are of length b. If the area of Q is maximized, then(A) area of Q = ab.(B) area of Q > ab.(C) Q must be a parallelogram. (D) Q must be a rectangle.9. Let f(x) = 2 + cos x for all real x.Statement 1: For each real t, there exists a point c in [t, t + π] suchthat f ′ (c) = 0.Statement 2: For each real t, f(t) = f(t + 2π) holds.(A) Statement 1 is TRUE and Statement 2 is the CORRECT REA-SON for Statement 1.(B) Statement 1 is TRUE and Statement 2 is NOT the CORRECTREASON for Statement 1.(C) Statement 1 is TRUE and Statement 2 is FALSE.(D) Statement 1 is FALSE and Statement 2 is TRUE.10. Every integer of the form (n 3 − n)(n − 2) for n = 3, 4, . . . is(A) always divisible by 12. (B) always divisible by 24.(C) always divisible by 48. (D) always divisible by 18.11. Let a 1 = b 1 = 1, a 2 = 2, b 2 = 3, a n+1 = a n + b n , b n+1 = 2a n + b n .Then(A) b 2 n = 2a 2 n + 1, if n is odd.(B) b 2 n = 2a 2 n − 1, if n is odd. *(C) lim n→∞b nan= √ 2 − 1.(D) lim n→∞b nan= √ 2. *12. Let f(x) be any differentiable function such that f(x) = ∫ x0 g(y)dyand F (x) = ∫ x0 f(y)dy. Then ∫ b0 x2 f(x)dx equals12