IIT-JEE 2007 · Paper 2 · Mathematics Q55

MathematicsAssertion and reason+3 / -1Question 55 of 66

STATEMENT-1: The curve $y=\dfrac{-x^2}{2}+x+1$ is symmetric with respect to the line $x=1$ .

because

STATEMENT-2: A parabola is symmetric about its axis.

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

Statement-1 is True, Statement-2 is False

Statement-1 is False, Statement-2 is True

Answer and worked solution

Official answer: A

Complete the square. $y=-\frac12(x-1)^2+\frac32$ , a parabola with axis $x=1$ .

So the curve is symmetric about $x=1$ because a parabola is symmetric about its axis. Both statements are true and Statement 2 explains Statement 1.

(A)

Topics:Parabola

IIT-JEE 2007 · Paper 2, Mathematics question 55