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...
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 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...
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...
