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## Problem on Inequality | ISI – MSQMS – B, 2018 | Problem 2a

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...

## Data, Determinant and Simplex

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 =...

## Problem on Integral Inequality | ISI – MSQMS – B, 2015

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...

## Inequality Problem From ISI – MSQMS – B, 2017 | Problem 3a

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...

## Problem on Natural Numbers | TIFR B 2010 | Problem 4

Try this problem of TIFR GS-2010 using your concepts of number theory and congruence based on natural numbers. Problem on Natural Numbers | TIFR 201O| PART B | PROBLEM 4 Which of the following statements is false? There exists a natural number which when divided by...

## Definite Integral Problem | ISI 2018 | MSQMS- A | Problem 22

Try this problem from ISI-MSQMS 2018 which involves the concept of Real numbers, sequence and series and Definite integral. DEFINITE INTEGRAL | ISI 2018| MSQMS | PART A | PROBLEM 22 Let $I=\int_{0}^{1} \frac{\sin x}{\sqrt{x}} d x$ and \$J=\int_{0}^{1} \frac{\cos...