Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2013MathematicsApplication of Derivatives

A man 1.6 m high walks at the rate of 30 ~m / min away from a lamp which is 4 m above ground. How fast is the man's shadow lengthening?

Options

  1. A22 ~m / min
  2. B20 ~m / min
  3. C15 ~m / min
  4. D25 ~m / min

Correct answer

B. 20 ~m / min

Step-by-step solution

Let P Q=4 m be the height of pole and, A B=1.6 ~m be height of man. Let the end of shadow is R and it is at a distance of l from A when the man is at a distance x from P Q at some instant. Since, P Q R and A B R are similar, array ll we have, P Q A B = P R A R & 4 1.6 = x+l l & 2 x=3 l array 2 d x d t =3 d l d t . given . d x d t =30 ~m / min d l d t = 2 3 30 ~m / min =20 ~m / min .

Practice Application of Derivatives on Quantrex Academy →

More from Application of Derivatives

Consider the quadratic equation a x^2+b x+c=0 , where 2 a+3 b+6 c=0 and let g(x)= a x^3 3 + b x^2 2 +c x . Statement-I : The given quadratic equation ax ^2+ bx + c =0 has at least 2025The difference between the absolute maximum and absolute minimum values of the function f(x)=2 x^3-15 x^2+36 x-30 on [-1,4] is 2025If f(x)=x e^ x(1-x) , x R , then f(x) is 2025The angle between the curves y ^2= x and x ^2= y at the point (1,1) is 2025If the tangent of the curve 4 y^3=3 a x^2+x^3 drawn at the point (a, a) forms a triangle of area 25 24 sq.units with the coordinate axes then a = 2025If the function f(x)= x- ^2 x is defined on the interval [- , ] , then f is strictly increasing in the interval 2025If the Lagrange's mean value theorem is applied to the function f(x)=e^x defined on the interval [1,2] and the value of c (1,2) is k , then e^ k-1 = 2025If the tangent to the curve x y+a x+b y=0 at (1,1) makes an angle Tan ⁻¹ 2 with X -axis, then ab a + b = 2025 Full Application of Derivatives list All Manipal MET PYQs