NDA 2018 Paper 1 | Application of Derivatives Question 24 | Mathematics

Read the following information for the next three items that follow.

Three sides of a trapezium are each equal to 6 cm. Let $$\alpha \in \left( {0,{\pi \over 2}} \right)$$ be the angle between a pair of adjacent sides.

If the area of the trapezium is maximum, what is the length of the fourth side?

8 cm

9 cm

10 cm

12 cm

NDA 2018 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

What is the maximum area of the trapezium?

$$36\sqrt 3 $$ cm²

$$30\sqrt 3 $$ cm²

$$27\sqrt 3 $$ cm²

$$24\sqrt 3 $$ cm²

NDA 2019 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

Read the following information and answer the three items that follow:

A curve y = me^mx where m > 0 intersects Y-axis at a point P.

What is the slope of the curve at the point of intersection P?

m²

2m²

NDA 2019 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

Read the following information and answer the three items that follow:

A curve y = me^mx where m > 0 intersects Y-axis at a point P.

How much angle does the tangent at P make with y-axis?

tan^$$-$$1 m²

cot^$$-$$1 (1 + m²)

sin^$$-$$1$$\left( {{1 \over {\sqrt {1 + {m^4}} }}} \right)$$

sec^$$-$$1$${\sqrt {1 + {m^4}} }$$

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