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NDA 2 2025 Maths, question 83

Topic: Differential calculus

Passage · Q83 to Q84

Consider the function f(x)={4(5x),x<08k+x,x≥0f(x)=\left\{ \begin{matrix} 4(5^{x}), & x<0 \\ 8k+x, & x\ge 0 \end{matrix} \right.

Q83

If the function is continuous, then what is the value of kk?

  1. (a) 0.50.5Correct answer
  2. (b) 11
  3. (c) 1.51.5
  4. (d) 22

Solution.

Answer: (a) 0.50.5

  1. At the joining point, the left limit is 4×5⁰=4 and the right limit and value are 8k.
  2. Continuity requires 8k=4, hence k=1/2.