1
IIT-JEE 2011 Paper 1 Offline
Numerical
+4
-0
The minimum value of the sum of real numbers $${a^{ - 5}},\,{a^{ - 4}},\,3{a^{ - 3}},\,1,\,{a^8}$$ and $${a^{10}}$$ where $$a > 0$$ is
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2
IIT-JEE 2011 Paper 2 Offline
Numerical
+4
-0
The number of distinct real roots of $${x^4} - 4{x^3} + 12{x^2} + x - 1 = 0$$
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3
IIT-JEE 2009 Paper 2 Offline
Numerical
+3
-1
The smallest value of $$k$$, for which both the roots of the equation $$${x^2} - 8kx + 16\left( {{k^2} - k + 1} \right) = 0$$$ are real, distinct and have values at least 4, is
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