1
JEE Main 2021 (Online) 25th July Morning Shift
Numerical
+4
-1
If $$\alpha$$, $$\beta$$ are roots of the equation $${x^2} + 5(\sqrt 2 )x + 10 = 0$$, $$\alpha$$ > $$\beta$$ and $${P_n} = {\alpha ^n} - {\beta ^n}$$ for each positive integer n, then the value of $$\left( {{{{P_{17}}{P_{20}} + 5\sqrt 2 {P_{17}}{P_{19}}} \over {{P_{18}}{P_{19}} + 5\sqrt 2 P_{18}^2}}} \right)$$ is equal to _________.
2
JEE Main 2021 (Online) 26th February Evening Shift
Numerical
+4
-1
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 ___________.
3
JEE Main 2021 (Online) 26th February Morning Shift
Numerical
+4
-1
The sum of 162th power of the roots of the equation x3 $$-$$ 2x2 + 2x $$-$$ 1 = 0 is ________.
4
JEE Main 2021 (Online) 24th February Evening Shift
Numerical
+4
-1
The number of the real roots of the equation $${(x + 1)^2} + |x - 5| = {{27} \over 4}$$ is ________.