JEE Main 2019 (Online) 10th January Evening Slot | Application of Derivatives Question 156 | Mathematics

A helicopter is flying along the curve given by y – x^3/2 = 7, (x $$ \ge $$ 0). A soldier positioned at the point $$\left( {{1 \over 2},7} \right)$$ wants to shoot down the helicopter when it is nearest to him. Then this nearest distance is -

$${1 \over 6}\sqrt {{7 \over 3}} $$

$${{\sqrt 5 } \over 6}$$

$${1 \over 2}$$

$${1 \over 3}$$$$\sqrt {{7 \over 3}} $$

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MCQ (Single Correct Answer)

-1

The shortest distance between the point $$\left( {{3 \over 2},0} \right)$$ and the curve y = $$\sqrt x $$, (x > 0), is -

$${{\sqrt 3 } \over 2}$$

$${5 \over 4}$$

$${3 \over 2}$$

$${{\sqrt 5 } \over 2}$$

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MCQ (Single Correct Answer)

-1

The maximum volume (in cu.m) of the right circular cone having slant height 3 m is :

2$$\sqrt3$$$$\pi $$

3$$\sqrt3$$$$\pi $$

6$$\pi $$

$${4 \over 3}\pi $$

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MCQ (Single Correct Answer)

-1

Let M and m be respectively the absolute maximum and the absolute minimum values of the function, f(x) = 2x³ $$-$$ 9x² + 12x + 5 in the interval [0, 3]. Then M $$-$$m is equal to :