1
JEE Main 2021 (Online) 26th February Evening Shift
Numerical
+4
-1
Out of Syllabus
Let the normals at all the points on a given curve pass through a fixed point (a, b). If the curve passes through (3, $$-$$3) and (4, $$-$$2$$\sqrt 2$$), and given that a $$-$$ 2$$\sqrt 2$$ b = 3,
then (a2 + b2 + ab) is equal to __________.
2
JEE Main 2021 (Online) 26th February Evening Shift
Numerical
+4
-1
Let a be an integer such that all the real roots of the polynomial
2x5 + 5x4 + 10x3 + 10x2 + 10x + 10 lie in the interval (a, a + 1). Then, |a| is equal to ___________.
3
JEE Main 2021 (Online) 25th February Evening Shift
Numerical
+4
-1
Out of Syllabus
If the curves x = y4 and xy = k cut at right angles, then (4k)6 is equal to __________.
4
JEE Main 2021 (Online) 25th February Morning Shift
Numerical
+4
-1
Let f(x) be a polynomial of degree 6 in x, in which the coefficient of x6 is unity and it has extrema at x = $$-$$1 and x = 1. If $$\mathop {\lim }\limits_{x \to 0} {{f(x)} \over {{x^3}}} = 1$$, then $$5.f(2)$$ is equal to _________.