GATE (CE) 2022: MATHEMATICS #5 (App update required to attempt this test)

Statement 1: The function  has a local maxima at x = -1

Statement 2: The derivative of  is zero at x = -1

Messi accelerates from its goal post to opposite post and travels a distance of 90 m in 12 seconds. According to the mean value theorem, the virtual speedometer at a certain time during his acceleration must read exactly—

The maximum area (magnitude) of the rectangle whose vertices lies on the ellipse x² + 9y² = 1 is ---

The function  will have

Which one of the following is NOT a correct statement?

The right circular cone of largest volume that can be enclosed by sphere of 1 m radius has a diameter of