1
JEE Main 2021 (Online) 17th March Evening Shift
Numerical
+4
-1
Let f : [$$-$$1, 1] $$\to$$ R be defined as f(x) = ax2 + bx + c for all x$$\in$$[$$-$$1, 1], where a, b, c$$\in$$R such that f($$-$$1) = 2, f'($$-$$1) = 1 for x$$\in$$($$-$$1, 1) the maximum value of f ''(x) is $${{1 \over 2}}$$. If f(x) $$\le$$ $$\alpha$$, x$$\in$$[$$-$$1, 1], then the least value of $$\alpha$$ is equal to _________.
2
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 __________.
3
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 ___________.
4
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 __________.