Science (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

The Cartesian equation of a line is `(x-5)/3 = (y+4)/7 = (z-6)/2` Write its vector form.

Find the vector and the Cartesian equations of the lines that pass through the origin and (5, −2, 3).

Find the vector and the Cartesian equations of the line that passes through the points (3, −2, −5), (3, −2, 6).

Show that the lines `(x-5)/7 = (y + 2)/(-5) = z/1` and `x/1 = y/2 = z/3` are perpendicular to each other.

Show that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3, 5, – 1), (4, 3, – 1).

Find the maximum and minimum value, if any, of the following function given by f(x) = (2x − 1)² + 3. 

Find the maximum and minimum value, if any, of the following function given by f(x) = 9x² + 12x + 2

Find the maximum and minimum value, if any, of the following function given by f(x) = −(x − 1)² + 10 

Find the maximum and minimum value, if any, of the following function given by g(x) = x³ + 1.

Find the maximum and minimum value, if any, of the function given by f(x) = |x + 2| − 1.

Find the maximum and minimum value, if any, of the following function given by g(x) = − |x + 1| + 3.

Find the maximum and minimum value, if any, of the following function given by h(x) = sin(2x) + 5.

Find the maximum and minimum value, if any, of the following function given by f(x) = |sin 4x + 3|

Find the maximum and minimum value, if any, of the following function given by h(x) = x + 1, x ∈ (−1, 1)

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

f(x) = x²

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

g(x) = x³ − 3x

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

`h(x) = sinx + cosx, 0 < x < pi/2`

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

f(x) = sinx − cos x, 0 < x < 2π

Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

f(x) = x³ − 6x² + 9x + 15