Try this problem from ISI-MSQMS 2018 which involves the concept of Inequality. INEQUALITY | ISI 2018| MSQMS | PART B | PROBLEM 2a (a) Prove that if $x>0, y>0$ and $x+y=1,$ then $\left(1+\frac{1}{x}\right)\left(1+\frac{1}{y}\right) \geq 9$ Key Concepts Algebra...

This is a beautiful problem connecting linear algebra, geometry and data. Go ahead and delve into the glorious connection. Problem Given a matrix \( \begin{bmatrix}a & b \\c & d \end{bmatrix} \) with the constraint \( 1 \geq a, b, c, d \geq 0; a + b + c + d =...

Try this problem from ISI-MSQMS 2015 which involves the concept of Integral Inequality. INTEGRAL INEQUALITY | ISI 2015 | MSQMS | PART B | PROBLEM 7b Show that $1<\int_{0}^{1} e^{x^{2}} d x<e$ Key Concepts Real Analysis Inequality Numbers Check The Answer ISI...

Try this problem from ISI-MSQMS 2017 which involves the concept of Inequality. INEQUALITY | ISI 2017| MSQMS | PART B | PROBLEM 3a (a) Prove that $a^{5}+b^{5}+c^{5}>a b c(a b+b c+c a),$ for all positive distinct values of $a, b, c$ Key Concepts Algebra Inequality...

Try this problem from ISI-MSQMS 2018 which involves the concept of Inequality and Combinatorics. INEQUALITY | ISI 2018 | MSQMS | PART B | PROBLEM 4 Show that $\sqrt{C_{1}}+\sqrt{C_{2}}+\sqrt{C_{3}}+\ldots+\sqrt{C_{n}} \leq 2^{n-1}+\frac{n-1}{2}$ where$C_k={n\choose...

Try this problem from ISI-MSQMS 2018 which involves the concept of Inequality. INEQUALITY | ISI 2018| MSQMS | PART B | PROBLEM 4b Let $a>0$ and $n \in \mathbb{N} .$ Show that”$$\frac{a^{n}}{1+a+a^{2}+\ldots+a^{2 n}}<\frac{1}{2 n}$$ Key Concepts Algebra...