Answers by KG

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 pos...

If $\left(\sqrt{\frac{7}{3}}\right)^{2 x-y}=\frac{875}{2401}$ and $\left(\frac{4 a}{b}\right)^{4 x-y}=\left(\frac{2 a}{b}\right)^{y-6 x}$, for all non-zero real values of...

Nitu has an initial capital of ₹ $20,000$. Out of this, she invests ₹$8,000$ at $5.5 \%$ in bank $\mathrm{A}$, ₹$5,000$ at $5.6 \%$ in bank $\mathrm{B}$ and the remaining...

If $c=\dfrac{16 x}{y}+\dfrac{49 y}{x}$ for some non-zero real numbers $x$ and $y,$ then $c$ cannot take the value$-60$ $-50$ $60$ $-70$

A donation box can receive only cheques of ₹$100$, ₹$250$, and ₹$500$. On one good day, the donation box was found to contain exactly $100$ cheques amounting to a total s...

The minimum possible value of $\frac{x^{2}-6 x+10}{3-x}$, for $x<3$, is$-2$$2$$\frac{1}{2}$$-\frac{1}{2}$

Let $r$ be a real number and $f(x)=\left\{\begin{array}{cl}2 x-r & \text { if } x \geq r \\ r & \text { if } x<r\end{array}\right.$. Then, the equation $f(x)=f(f(x))$ hol...

If $(3+2 \sqrt{2})$ is a root of the equation $a x^{2}+b x+c-0$, and $(4+2 \sqrt{3})$ is a root of the equation $a y^{2}+m y+n – 0$, where $a, b, c, m$ and $n$ are intege...