1
JEE Main 2021 (Online) 31st August Morning Shift
Numerical
+4
-1
If 'R' is the least value of 'a' such that the function f(x) = x2 + ax + 1 is increasing on [1, 2] and 'S' is the greatest value of 'a' such that the function f(x) = x2 + ax + 1 is decreasing on [1, 2], then
the value of |R $$-$$ S| is ___________.
2
JEE Main 2021 (Online) 27th August Morning Shift
Numerical
+4
-1
The number of distinct real roots of the equation 3x4 + 4x3 $$-$$ 12x2 + 4 = 0 is _____________.
3
JEE Main 2021 (Online) 26th August Morning Shift
Numerical
+4
-1
A wire of length 36 m is cut into two pieces, one of the pieces is bent to form a square and the other is bent to form a circle. If the sum of the areas of the two figures is minimum, and the circumference of the circle is k (meter), then $$\left( {{4 \over \pi } + 1} \right)k$$ is equal to _____________.
4
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 _________.