Arts (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

The least value of the function f(x) = \[x3 - 18x2 + 96x\] in the interval [0,9] is _____________ .

The maximum value of f(x) = \[\frac{x}{4 - x + x^2}\] on [ \[-\] 1, 1] is _______________ .

The point on the curve y² = 4x which is nearest to, the point (2,1) is _______________ .

If x+y=8, then the maximum value of xy is ____________ .

The least and greatest values of f(x) = x³\[-\] 6x²+9x in [0,6], are ___________ .

f(x) = \[\sin + \sqrt{3} \cos x\] is maximum when x = ___________ .

If a cone of maximum volume is inscribed in a given sphere, then the ratio of the height of the cone to the diameter of the sphere is ______________ .

The minimum value of \[\left( x^2 + \frac{250}{x} \right)\] is __________ .

If(x) = x+\[\frac{1}{x}\],x > 0, then its greatest value is _______________ .

If(x) = \[\frac{1}{4x^2 + 2x + 1}\] then its maximum value is _________________ .

Let x, y be two variables and x>0, xy=1, then minimum value of x+y is _______________ .

f(x) = 1+2 sin x+3 cos²x, `0<=x<=(2pi)/3` is ________________ .

The function f(x) = \[2 x^3 - 15 x^2 + 36x + 4\] is maximum at x = ________________ .

The maximum value of f(x) = \[\frac{x}{4 + x + x^2}\] on [ \[-\] 1,1] is ___________________ .

Let f(x) = 2x³\[-\] 3x²\[-\] 12x + 5 on [ 2, 4]. The relative maximum occurs at x = ______________ .

The minimum value of x log_e x is equal to ____________ .

Using properties of determinants show that

`[[1,1,1+x],[1,1+y,1],[1+z,1,1]] = xyz+ yz +zx+xy.`

A wire of length 34 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a rectangle whose length is twice its breadth. What should be the lengths of the two pieces, so that the combined area of the square and the rectangle is minimum?

The sum of the surface areas of a cuboid with sides x, 2x and \[\frac{x}{3}\] and a sphere is given to be constant. Prove that the sum of their volumes is minimum, if x is equal to three times the radius of sphere. Also find the minimum value of  the sum of their volumes.

Using properties of determinants, prove the following :