Quadratic Equation and Inequalities
106 Questions
1978
JEE Advanced
Numerical
IIT-JEE 1978
Solve for $x:{4^x} - {3^{^{x - {1 \over 2}}}}\, = {3^{^{x + {1 \over 2}}}}\, - {2^{2x - 1}}$
Correct Answer: $${3 \over 2}$$
1978
JEE Advanced
Numerical
IIT-JEE 1978
Show that the square of $\,{{\sqrt {26 - 15\sqrt 3 } } \over {5\sqrt 2 - \sqrt {38 + 5\sqrt 3 } }}$ is a rational number.
Correct Answer: Solve it.
1978
JEE Advanced
Numerical
IIT-JEE 1978
Solve the following equation for $x:\,\,2\,{\log _x}a + {\log _{ax}}a + 3\,\,{\log _{{a^2}x}}\,a = 0,a > 0$
Correct Answer: $${a^{{\raise0.5ex\hbox{$\scriptstyle { - 1}$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}}},\,\,{a^{{\raise0.5ex\hbox{$\scriptstyle { - 4}$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 3$}}}}$$
1978
JEE Advanced
Numerical
IIT-JEE 1978
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
$\left( {m,n + 1} \right) = \left( {m - 1,\,n + 1} \right) + {x^{m - n - 1}}\left( {m - 1,n} \right).$
Correct Answer: Solve it.
1978
JEE Advanced
Numerical
IIT-JEE 1978
Find all integers $x$ for which $\left( {5x - 1} \right) < {\left( {x + 1} \right)^2} < \left( {7x - 3} \right).$
Correct Answer: 3
1978
JEE Advanced
Numerical
IIT-JEE 1978
Solve for $x:\,\sqrt {x + 1} - \sqrt {x - 1} = 1.$
Correct Answer: $${5 \over 4}$$