Mathematics

Single Correct Medium Published on 17th 09, 2020
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Q1 Single Correct Hard
A tank initially holds 10 lit. of fresh water. At t = 0, a brine solution containing $$\displaystyle \frac{1}{2}$$ kg of salt per lit. is poured into tank at a rate 1 lit/min while the well-stirred mixture leaves the tank at the same rate. Find the amount of salt in a tank at a particular time
  • A. $$5e^{-t} + 5 $$ 
  • B. $$5e^{-t} - 5 $$ 
  • C. $$-5e^{} - 5 $$ 
  • D. $$- 5e^{-t} + 5 $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Subjective Medium
Evaluate $$\displaystyle\int^{\pi/2}_0\sin^2xdx$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Subjective Medium

Evaluate the following definite integral:

$$\displaystyle\int_{0}^{\pi/2} \sin x \cos x\ dx$$ 

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Subjective Hard
Integrate the following function
$$x\ \sin^{-1}x$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Passage Medium
Consider two differentiable functions $$f(x), g(x)$$ satisfying $$\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$$ & $$\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$$. where $$\displaystyle f(x)>0    \forall  x \in  R$$

On the basis of above information, answer the following questions :

Asked in: Mathematics - Limits and Derivatives


1 Verified Answer | Published on 17th 08, 2020

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