List of top Mechanical Engineering Questions on Calculus asked in AP PGECET

Consider the following statements: 
I. If \(f\) is a differentiable scalar field, then \[ \operatorname{curl}(\operatorname{grad} f)=\vec{0}. \] 
II. If \(\vec{f}\) is a differentiable vector field, then \[ \operatorname{div}(\operatorname{curl}\,\vec{f})=0. \] 
Which one of the following is correct?

The absolute maximum of the function \[ f(x)=x^3-3x+2 \] on the interval \[ [0,2] \] is ________. 

The values of a function \(f(x)\) obtained for different values of x are given below
Using Simpson's one-third rule, the value of \(\int_{0}^{1} f(x) dx\) is approximately equal to ______}
The solution of the differential equation \(x \frac{d^{2} y}{dx^{2}} + \frac{dy}{dx} = 0\) is
Consider the statements.
I. if \(s_{n} = \frac{1}{n}\), the sequence \(\{s_{n}\}\) is divergent.
II. if \(s_{n} = 1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n}\), the sequence \(\{s_{n}\}\) is convergent.
Which one of the following is correct?
The values of a function \(f(x)\) obtained for different values of x are given below
Using Simpson's one-third rule, the value of \(\int_{0}^{1} f(x) dx\) is approximately equal to ______}
Consider the statements.
I. if \(s_{n} = \frac{1}{n}\), the sequence \(\{s_{n}\}\) is divergent.
II. if \(s_{n} = 1 + \frac{1}{2} + \frac{1}{3} + \dots + \frac{1}{n}\), the sequence \(\{s_{n}\}\) is convergent.
Which one of the following is correct?
Consider the statements.
I. If \(f\) is a differentiable scalar field, then \(curl(grad\, f) = \vec{0\).
II. If \(\vec{f}\) is a differentiable vector field, then \(div(curl\, \vec{f}) = 0\).
Which one of the following is correct?
The solution of the differential equation \(x \frac{d^{2} y}{dx^{2}} + \frac{dy}{dx} = 0\) is
The absolute maximum of the function \(f(x) = x^{3 - 3x + 2\) in the interval \([0, 2]\) is ________}