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

Write the maximum value of f(x) = \[\frac{\log x}{x}\], if it exists .

The maximum value of x^1/x, x > 0 is __________ .

If \[ax + \frac{b}{x} \frac{>}{} c\] for all positive x where a,b,>0, then _______________ .

The minimum value of \[\frac{x}{\log_e x}\] is _____________ .

For the function f(x) = \[x + \frac{1}{x}\]

Let f(x) = x³+3x² \[-\] 9x+2. Then, f(x) has _________________ .

The minimum value of f(x) = \[x4 - x2 - 2x + 6\] is _____________ .

The number which exceeds its square by the greatest possible quantity is _________________ .

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 ___________ .