For x,t ∈ R let p_t(x)=(\sin t)x^2-(2\cos t)x+\sin tbe a family of quadratic polynomials in x with variable coefficients. Let A(t)=∫↖{1}↙{0}p_t(x)dx. Which of the following statements are true?(I) A (t)

Question

For x,t ∈ R  let  p_t(x)=(\sin t)x^2-(2\cos t)x+\sin tbe a family of quadratic polynomials in x with variable  coefficients. Let A(t)=∫↖{1}↙{0}p_t(x)dx.   Which of the following   statements are true?(I) A (t) < 0 for all t.(II) A (t) has infinitely many critical points.(III) A (t) = 0 for infinitely many t.(IV) A'(t) < 0 for all t.

Examsnet · Accepted Answer

Correct Answer is :  (II) and (III) only

KVPY SX SB Exam 2013 Question Paper