1
WB JEE 2024
+2
-0.5

Consider the function $$\mathrm{f}(x)=x(x-1)(x-2) \ldots(x-100)$$. Which one of the following is correct?

A
This function has 100 local maxima
B
This function has 50 local maxima
C
This function has 51 local maxima
D
Local minima do not exist for this function
2
WB JEE 2023
+1
-0.25

A missile is fired from the ground level rises x meters vertically upwards in t sec, where $$x = 100t - {{25} \over 2}{t^2}$$. The maximum height reached is

A
100 m
B
300 m
C
200 m
D
125 m
3
WB JEE 2023
+2
-0.5

The portion of the tangent to the curve $${x^{{2 \over 3}}} + {y^{{2 \over 3}}} = {a^{{2 \over 3}}},a > 0$$ at any point of it, intercepted between the axes

A
varies as abscissa
B
varies as ordinate
C
is constant
D
varies as the product of abscissa and ordinate
4
WB JEE 2023
+2
-0.5

Given $$f(x) = {e^{\sin x}} + {e^{\cos x}}$$. The global maximum value of $$f(x)$$

A
does not exist.
B
exists at a point in $$\left( {0,{\pi \over 2}} \right)$$ and its value is $$2{e^{{1 \over {\sqrt 2 }}}}$$.
C
exists at infinitely many points.
D
exists at $$x=0$$ only.
EXAM MAP
Medical
NEET