CAT Inequalities Practice Questions With Solutions

If $\sqrt{5x+9} + \sqrt{5x - 9} = 3(2 + \sqrt{2})$, then $\sqrt{10x+9}$ is equal to

In an examination, the average marks of 4 girls and 6 boys is 24. Each of the girls has the same marks while each of the boys has the same marks. If the marks of any girl is at most double the marks of any boy, but not less than the marks of any boy, then the number of possible distinct integer values of the total marks of 2 girls and 6 boys is

Let a, b, m and n be natural numbers such that $a>1$ and $b>1$. If $a^{m}b^{n}=144^{145}$, then the largest possible value of $n-m$ is

Any non-zero real numbers x,y such that $y\neq3$ and $\frac{x}{y}<\frac{x+3}{y-3}$, Will satisfy the condition.

Let a, b, c be non-zero real numbers such that $b^2 < 4ac$, and $f(x) = ax^2 + bx + c$. If the set S consists of all integers m such that f(m) < 0, then the set S must necessarily be

The largest real value of a for which the equation $\mid x + a \mid + \mid x - 1 \mid = 2$ has an infinite number of solutions for x is

Let $f(x)$ be a quadratic polynomial in $x$ such that $f(x) \geq 0$ for all real numbers $x$. If f(2) = 0 and f( 4) = 6, then f(-2) is equal to

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