1
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
2
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
3
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.
4
WB JEE 2022
+1
-0.25

A particle moving in a straight line starts from rest and the acceleration at any time t is $$a - k{t^2}$$ where a and k are positive constants. The maximum velocity attained by the particle is

A
$${2 \over 3}\sqrt {{{{a^3}} \over k}}$$
B
$${1 \over 3}\sqrt {{{{a^3}} \over k}}$$
C
$$\sqrt {{{{a^3}} \over k}}$$
D
$$2\sqrt {{{{a^3}} \over k}}$$
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