CAT Maxima & Minima Practice Questions With Solutions

The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing 18 units. If she breaks it into four pieces with each piece having distinct integer weight, then the difference between the highest and lowest possible values of the total price of the four pieces will be 288000. Then, the price of the original precious stone is

If $p^{2}+q^{2}-29=2pq-20=52-2pq$, then the difference between the maximum and minimum possible value of $(p^{3}-q^{3})$

For some real numbers a and b, the system of equations $x + y = 4$ and $(a+5)x+(b^2-15)y=8b$ has infinitely many solutions for x and y. Then, the maximum possible value of ab is

Let $0 \leq a \leq x \leq 100$ and $f(x) = \mid x - a \mid + \mid x - 100 \mid + \mid x - a - 50\mid$. Then the maximum value of f(x) becomes 100 when a is equal to

If a and b are non-negative real numbers such that a+ 2b = 6, then the average of the maximum and minimum possible values of (a+ b) is

If $c=\frac{16x}{y}+\frac{49y}{x}$ for some non-zero real numbers x and y, then c cannot take the value

Consider six distinct natural numbers such that the average of the two smallest numbers is 14, and the average of the two largest numbers is 28. Then, the maximum possible value of the average of these six numbers is

The minimum possible value of $\frac{x^{2} - 6x + 10}{3-x}$, for $x < 3$, is

For all real values of x, the range of the function $f(x)=\frac{x^{2}+2x+4}{2x^{2}+4x+9}$ is:

If $f(x)=x^{2}-7x$ and $g(x)=x+3$, then the minimum value of $f(g(x))-3x$ is: