Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 80

HARD

JEE Main/Advance

IMPORTANT

Earn 100

The angle of intersection of $y = a^{x}$ and $y = b^{x}$ , is given by:

100% studentsanswered this correctly

Important Questions on Application of Derivatives

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 81

The angle between the curves

x^{2} + 4 y^{2} = 32

and

x^{2} - y^{2} = 12

, is:

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 82

Find the angle at which two curves

x^{3} - 3 x y^{2} + 2 = 0

and

3 x^{2} y - y^{3} - 2 = 0

intersect

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 84

The shortest distance between curves

y^{2} = 8 x

and

y^{2} = 4 (x - 3)

is

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 85

The shortest distance between the curves

\frac{x^{2}}{32} + \frac{y^{2}}{18} = 1

and

{(x - \frac{7}{4})}^{2} + y^{2} = 1

is

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 86

Water is poured into an inverted conical vessel of which the radius of the base is

2 m

and height

4 m

, at the rate of

77

litre/minute. The rate at which the water level is rising at the instant when the depth is

70 cm

is (use

π = \frac{22}{7}

)

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 87

On the curve

x^{3} = 12 y .

The interval in which abscissa changes at a faster rate then its ordinate

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 88

A kite is

300 m

high and there are

500 m

of cord out. If the wind moves the kite horizontally at the rate of

5 km / hr

directly away from the person who is flying it, find the rate in

km / hr

at which the cord is being paid out?

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 89

The approximate value of

\tan 46 °

is (take

π = \frac{22}{7}

):