Mathematics · 2013
JEE Main · 23 April 2013, Shift 1 · Q83
The cost of running a bus from A to B, is Rs. ( av +b/v), where v km/h is the average speed of the bus. When the bus travels at 30 km/h, the cost…
The cost of running a bus from A to B , is Rs. $\displaystyle \left(\mathrm{av}+\frac{\mathrm{b}}{\mathrm{v}}\right)$, where v km/h is the average speed of the bus. When the bus travels at $\displaystyle 30$ km/h, the cost comes out to be Rs. $\displaystyle 75$ while at $\displaystyle 40$ km/h, it is Rs. 65. Then the most economical speed (in km/h) of the bus is :
Official answer
(3)
$\displaystyle 60$
More from Applications of Derivatives
- The intercepts on x - axis made by tangents to the curve, y=∫_0^x|t| dt, x ∈ R, which are parallel to the line y=2 x, are equal to:2013
- Let the function f(x)=x/3+3/x+3, x ≠ 0 be strictly increasing in (-∞, α_1) ∪(α_2, ∞) and strictly decreasing in (α_3, α_4) ∪(α_4, α_5). Then Σ_i=1^5…2025
- If an equation of a tangent to the curve, y= cos (x+y),-1 ≤ x ≤ 1+π, is x+2 y=k then k is equal to:2013
- Let f:(0,1) → R be a function defined by f(x)=1/(1-e^-x), and g(x)=(f(-x)-f(x)). Consider two statements (I) g is an increasing function in (0,1)…2023
- A wire of length 20 m is to be cut into two pieces. A piece of length l_1 is bent to make a square of area A_1 and the other piece of length l_2 is…2023
- Let f: R → R be a function defined by f(x)=(x-3)^n_1(x-5)^n_2, n_1, n_2 ∈ N. Then, which of the following is NOT true?2022
- Let f(x)=x cos^-1(- sin |x|), x ∈[-(π)/2, (π)/2], then which of the following is true?2020
- Let f(x)=2 x+ tan^-1 x and g(x)= log_e(√(1+x^2)+x), x ∈[0,3]. Then2023
JEE Main 2013 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.