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

If `"sin"^-1 (1 - "x") - 2  "sin"^-1 ("x") = pi/2,` then x is equal to ____________.

If `3  "sin"^-1 ((2"x")/(1 + "x"^2)) - 4  "cos"^-1 ((1 - "x"^2)/(1 + "x"^2)) + 2 "tan"^-1 ((2"x")/(1 - "x"^2)) = pi/3` then x is equal to ____________.

Solve for x : `{"x cos" ("cot"^-1 "x") + "sin" ("cot"^-1 "x")}^2` = `51/50

If matrices A and B are inverse of each other then ____________.

If A `= [(5, "x"),("y", 0)]` and A = A' then ____________.

Find all the points of local maxima and local minima of the function f(x) = (x - 1)³ (x + 1)²

Find the local minimum value of the function f(x) `= "sin"^4" x + cos"^4 "x", 0 < "x" < pi/2`

Find the points of local maxima and local minima respectively for the function f(x) = sin 2x - x, where `-pi/2 le "x" le pi/2`

If y `= "ax - b"/(("x" - 1)("x" - 4))` has a turning point P(2, -1), then find the value of a and b respectively.

Find the maximum profit that a company can make, if the profit function is given by P(x) = 41 + 24x – 18x².

If y = x³ + x² + x + 1, then y ____________.

Find both the maximum and minimum values respectively of 3x⁴ - 8x³ + 12x² - 48x + 1 on the interval [1, 4].

The function f(x) = x⁵ - 5x⁴ + 5x³ - 1 has ____________.

Find the height of the cylinder of maximum volume that can be inscribed in a sphere of radius a.

Find the volume of the largest cylinder that can be inscribed in a sphere of radius r cm.

The area of a right-angled triangle of the given hypotenuse is maximum when the triangle is ____________.

Find the area of the largest isosceles triangle having a perimeter of 18 meters.

The coordinates of the point on the parabola y² = 8x which is at minimum distance from the circle x² + (y + 6)² = 1 are ____________.

The distance of that point on y = x⁴ + 3x² + 2x which is nearest to the line y = 2x - 1 is ____________.

The function `"f"("x") = "x" + 4/"x"` has ____________.