1
JEE Main 2021 (Online) 26th February Evening Shift
Numerical
+4
-1
Change Language
Let $$\alpha$$ and $$\beta$$ be two real numbers such that $$\alpha$$ + $$\beta$$ = 1 and $$\alpha$$$$\beta$$ = $$-$$1. Let pn = ($$\alpha$$)n + ($$\beta$$)n, pn$$-$$1 = 11 and pn+1 = 29 for some integer n $$ \ge $$ 1. Then, the value of p$$_n^2$$ is ___________.
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2
JEE Main 2021 (Online) 26th February Morning Shift
Numerical
+4
-1
Change Language
The sum of 162th power of the roots of the equation x3 $$-$$ 2x2 + 2x $$-$$ 1 = 0 is ________.
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3
JEE Main 2021 (Online) 24th February Evening Shift
Numerical
+4
-1
Change Language
The number of the real roots of the equation $${(x + 1)^2} + |x - 5| = {{27} \over 4}$$ is ________.
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4
JEE Main 2020 (Online) 8th January Morning Slot
Numerical
+4
-0
Change Language
The least positive value of 'a' for which the equation

2x2 + (a – 10)x + $${{33} \over 2}$$ = 2a has real roots is
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