1
JEE Main 2023 (Online) 6th April Evening Shift
Numerical
+4
-1

The number of points, where the curve $$y=x^{5}-20 x^{3}+50 x+2$$ crosses the $$\mathrm{x}$$-axis, is ____________.

2
JEE Main 2023 (Online) 29th January Evening Shift
Numerical
+4
-1
Out of Syllabus

If the equation of the normal to the curve $$y = {{x - a} \over {(x + b)(x - 2)}}$$ at the point (1, $$-$$3) is $$x - 4y = 13$$, then the value of $$a + b$$ is equal to ___________.

3
JEE Main 2022 (Online) 29th July Evening Shift
Numerical
+4
-1
Out of Syllabus

If the tangent to the curve $$y=x^{3}-x^{2}+x$$ at the point $$(a, b)$$ is also tangent to the curve $$y = 5{x^2} + 2x - 25$$ at the point (2, $$-$$1), then $$|2a + 9b|$$ is equal to __________.

4
JEE Main 2022 (Online) 27th July Evening Shift
Numerical
+4
-1

A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semi-vertical angle is $$\tan ^{-1} \frac{3}{4}$$. Water is poured in it at a constant rate of 6 cubic meter per hour. The rate (in square meter per hour), at which the wet curved surface area of the tank is increasing, when the depth of water in the tank is 4 meters, is ______________.