PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions

Let f(x) = (x \[-\] a)² + (x \[-\] b)² + (x \[-\] c)². Then, f(x) has a minimum at x = _____________ .

The sum of two non-zero numbers is 8, the minimum value of the sum of the reciprocals is ______________ .

The function f(x) = \[\sum^5_{r = 1}\] (x \[-\] r)² assumes minimum value at x = ______________ .

At x= \[\frac{5\pi}{6}\] f(x) = 2 sin 3x + 3 cos 3x is ______________ .

If x lies in the interval [0,1], then the least value of x² + x + 1 is _______________ .

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 = ______________ .