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BITSAT 2009
Exam
BITSAT
Year
2009
Subject
Mathematics
Chapter
Pair of Lines

BITSAT 2009 · Mathematics · Pair of Lines

If (∫_0^n[x] dx= 66), then n=

If (\int_0^n[x] dx=\mathrm{dx}=66), then n=n=

Options

  1. A24
  2. B9
  3. C12
  4. D7

Correct answer

C. 12

Step-by-step solution

∫0n[x]dx=∫010dx+∫121dx+∫232dx+……+∫n−1n(n−1)dx=1+2+3+….+(n−1)=(n−1)n2=66⇒n(n−1)=132⇒n=12\begin{aligned}& \int_0^n[x] d x=\int_0^1 0 d x+\int_1^2 1 d x+\int_2^3 2 d x+\ldots \ldots+ \\ & \int_{n-1}^n(n-1) d x \\ & =1+2+3+\ldots.+(n-1)=\frac{(n-1) n}{2}=66 \\ & \Rightarrow n(n-1)=132 \Rightarrow n=12 \end{aligned})
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