1
JEE Main 2021 (Online) 31st August Evening Shift
Numerical
+4
-1
Let f(x) be a cubic polynomial with f(1) = $$-$$10, f($$-$$1) = 6, and has a local minima at x = 1, and f'(x) has a local minima at x = $$-$$1. Then f(3) is equal to ____________.
2
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 ___________.
3
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 _____________.
4
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 _____________.