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Quadratic Equation and Inequalities

304 Questions Start JEE Mains Test
All Exams JEE Mains JEE Advanced TS-EAMCET AP-EAPCET BITSAT
1978 Q301 JEE Advanced Numerical
14 Mar 2026
Solve the following equation for $x:\,\,2\,{\log _x}a + {\log _{ax}}a + 3\,\,{\log _{{a^2}x}}\,a = 0,a > 0$
1978 Q302 JEE Advanced Numerical
14 Mar 2026
If $\left( {m\,,\,n} \right) = {{\left( {1 - {x^m}} \right)\left( {1 - {x^{m - 1}}} \right).......\left( {1 - {x^{m - n + 1}}} \right)} \over {\left( {1 - x} \right)\left( {1 - {x^2}} \right).........\left( {1 - {x^n}} \right)}}$

where $m$ and $n$ are positive integers $\left( {n \le m} \right),$ show that
$\left( {m,n + 1} \right) = \left( {m - 1,\,n + 1} \right) + {x^{m - n - 1}}\left( {m - 1,n} \right).$

1978 Q303 JEE Advanced Numerical
14 Mar 2026
Find all integers $x$ for which $\left( {5x - 1} \right) < {\left( {x + 1} \right)^2} < \left( {7x - 3} \right).$
1978 Q304 JEE Advanced Numerical
14 Mar 2026
Solve for $x:\,\sqrt {x + 1} - \sqrt {x - 1} = 1.$