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JEE Advanced Introduction to Trigonometry — practice questions

Explore 4 free Introduction to Trigonometry questions in JEE Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Introduction to Trigonometry questions and exercises with answers

Showing questions 1–4 of 4.

From a standard deck of 52 playing cards, what is the probability of drawing a heart?Read the answer and worked solution →Which property of conditional probability is correct?Read the answer and worked solution →Using standard limits, evaluate $\lim_{x\to 0}\dfrac{a^x-1}{x}$ for $a>0$.Read the answer and worked solution →The derivative of $a^x$ for $a>0$ and $a\neq 1$ isRead the answer and worked solution →

Worked practice questions

From a standard deck of 52 playing cards, what is the probability of drawing a heart?

  1. $\dfrac{1}{2}$
  2. $\dfrac{1}{4}$
  3. $\dfrac{13}{52}$
  4. Both B and C are correct
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Correct answer: D. Both B and C are correct

A standard deck has 13 hearts out of 52 cards. So the probability is $\dfrac{13}{52}=\dfrac14$. **Hence both options B and C represent the same correct value, so D is the intended correct choice.**

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Which property of conditional probability is correct?

  1. $P(A'/B)=P(A/B)$
  2. $P(A'/B)=1-P(A/B)$
  3. $P(A'/B)=1-P(B/A)$
  4. $P(A'/B)=P(A\cap B)$
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Correct answer: B. $P(A'/B)=1-P(A/B)$

Within the reduced sample space where $B$ has occurred, the events $A$ and $A'$ are complementary. **Therefore their conditional probabilities add to 1, so $P(A'/B)=1-P(A/B)$.**

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Using standard limits, evaluate $\lim_{x\to 0}\dfrac{a^x-1}{x}$ for $a>0$.

  1. $0$
  2. $1$
  3. $\ln a$
  4. $a$
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Correct answer: C. $\ln a$

A fundamental limit is $\lim_{x\to 0}\dfrac{a^x-1}{x}=\ln a$. It is closely related to the derivative of $a^x$ at $x=0$.

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