Mathematics

Single Correct Medium Published on 17th 09, 2020
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Q1 Subjective Medium
The acceleration of a motorcycle is given by $$a_{x}(t) = At - Br^{2}$$, where $$A = 1.50\ ms^{-2}$$ and $$B = 0.120\ ms^{-4}$$. The motorcycle is at rest at the origin at time $$t = 0$$.
Find its position and velocity as functions of time.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q2 Assertion & Reason Hard
ASSERTION

The value $$\displaystyle\int_{-4}^{-5}\sin (x^{2}-3)dx+\int_{-2}^{-1}\sin (x^{2}+12x+33)$$ is zero.

REASON

$$\displaystyle\int_{-a}^{a}f(x)dx=0$$ if f(x) is an odd function.

  • A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  • B. Assertion is correct but Reason is incorrect
  • C. Both Assertion and Reason are incorrect
  • D. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q3 Subjective Medium
Evaluate : $$\displaystyle \int_{\pi/6}^{\pi/3}{\cfrac{1}{1+\sqrt{\tan{x}}}}dx$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q4 Subjective Medium
$$\text { Evaluate: } \displaystyle \int_{-\pi / 2}^{\pi / 2} \dfrac{\cos x}{1+e^{x}} \mathrm{d} \mathrm{x}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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Q5 Single Correct Hard
If $$\displaystyle I = \int \frac {dx}{(1 + x^4)^{1/4}}$$, then I equals
  • A. $$\displaystyle \frac {1}{2} \tan^{-1} \left ( \frac {x}{(1 + x^4)^{1/4}} \right ) + C$$
  • B. $$\displaystyle \frac {1}{4} \log \left | \frac {1 - (1 + x^4)^{1/4}}{1 + (1 + x^4)^{1/4}} \right | + C$$
  • C. $$\displaystyle \frac {1}{2} \tan^{-1} \frac {(1 + x^4)^{1/4}}{x} - \frac {1}{4} \log \left | \frac {1 - (1 + x^4)^{1/4}}{1 + (1 + x^4)^{1/4}} \right | + C$$
  • D. $$\displaystyle \frac {1}{2} \tan^{-1} \frac {(1 + x^4)^{1/4}}{x} - \frac {1}{4} \log \left | \frac {x - (1 + x^4)^{1/4}}{x + (1 + x^4)^{1/4}} \right | + C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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