List of top Mathematics Questions on Differentiation asked in MHT CET

The difference between the maximum value and minimum value of objective function \( z = 3x + 5y \) subject to \( x + 3y \le 60, x + y \ge 10, x - y \ge 0, x, y \ge 0 \) is
Let A = \( \lim_{x \to 0^+} (1 + \tan^2 \sqrt{x})^{\frac{1}{2x}} \), then log\(_e\) A =}
The equation of the plane passing through the line of intersection of the planes $x + y + z = 1$ and $3x + 4y + 5z = 2$ and perpendicular to the XY- plane is
The differential equation whose solution represents the family $x^2y = 4e^x + c$, where c is an arbitrary constant, is
In a triangle ABC with usual notations, if a, b, c are in arithmetic progression, then, $\tan \frac{A}{2} \cdot \tan \frac{C}{2} =$}
If $y = x^x + x^{\frac{1}{x}}$, then $\frac{dy}{dx}$ is equal to}
If the directed line makes an angle $45^\circ$ and $60^\circ$ with the X and Y -axes respectively, then the obtuse angle $\theta$ made by the line with the Z -axis is
If the points $\text{A}(2 - x, 2, 2), \text{B}(2, 2 - y, 2), \text{C}(2, 2, 2 - z)$ and $\text{D}(1, 1, 1)$ are coplanar, then the locus of point $\text{P}(x, y, z)$ is
The order and degree of differential equation of all tangent lines to the parabola $x^2 = 4y$ is respectively.

If \[ \int \frac{2x^2+3}{(x^2-1)(x^2-4)} \, dx = \log \left[ \left( \frac{x-2}{x+2} \right)^a \cdot \left( \frac{x+1}{x-1} \right)^b \right] + c \] where \( c \) is the constant of integration, then the value of \[ a+b = \, ? \] 

The equation of the plane passing through the line of intersection of the planes $x + y + z = 1$ and $3x + 4y + 5z = 2$ and perpendicular to the XY- plane is
The value of the integral $\int_1^2 \frac{x \text{ d}x}{(x+2)(x+3)}$ is
Let $f$ be a function which is continuous and differentiable for all $x$. If $f(1) = 1$ and $f'(x) \leq 5$ for all $x$ in $[1, 5]$, then the maximum value of $f(5)$ is