List of top Mathematics Questions on Tangents and Normals asked in VITEEE

If \( n(A) = 4 \) and \( n(B) = 7 \), then the difference between the maximum and minimum value of \( n(A \cup B) \) is:
If \( 12\cot^2 \theta - 31\csc \theta + 32 = 0 \), then the value of \( \sin \theta \) is:
If the tangent to the function $y = f(x) $ at $(3,4)$ makes an angle of $\frac{3 \pi }{4}$ with the positive direction of x-axis in anticlockwise direction then $f ' (3)$ is
The triangle formed by the tangent to the curve $f (x) = x2 + bx - b$ at the point $(1,1)$ and the coordinate axes lies in the first quadrant. If its area is $2$, then the value of b is
If the normal to the curve $y = f(x)$ at $(3,4)$ makes an angle $\frac{3 \pi}{4}$ with the positive x-axis, then $f'(3)$ is equal to