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Agniveer Air Force Integral Calculus — practice questions

Explore 68 free Integral Calculus questions in Agniveer Air Force Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Integral Calculus questions and exercises with answers

Showing questions 1–30 of 68.

A fair coin is tossed twice. How many outcomes are there in the sample space?Read the answer and worked solution →A fair six-sided die is rolled once. What is the probability of getting an even number?Read the answer and worked solution →$\sin(180° - \theta)$ equals:Read the answer and worked solution →$\sin^2\theta + \cos^2\theta$ equals:Read the answer and worked solution →$\sin(A + B) = $Read the answer and worked solution →sin(0°) equals:Read the answer and worked solution →cos(90°) equals:Read the answer and worked solution →sin²θ + cos²θ equals:Read the answer and worked solution →tan(45°) equals:Read the answer and worked solution →In which quadrant is sin θ positive and cos θ negative?Read the answer and worked solution →The arithmetic mean of n values x1, x2, ..., xn is:Read the answer and worked solution →Median of an odd-length sorted data set is:Read the answer and worked solution →Probability of a certain event:Read the answer and worked solution →Probability of rolling a 6 on a fair die:Read the answer and worked solution →For independent events A and B, P(A and B) equals:Read the answer and worked solution →The probability of getting an even number on a single throw of a die is:Read the answer and worked solution →The probability of drawing a king from a standard pack of 52 cards is:Read the answer and worked solution →When two dice are thrown, the probability that the sum of the numbers is 7 is:Read the answer and worked solution →The probability of getting at least one head when a coin is tossed twice is:Read the answer and worked solution →If $P(A)=0.3$, $P(B)=0.4$ and A, B are mutually exclusive, then $P(A\cup B)$ is:Read the answer and worked solution →The probability of getting a number greater than 4 on a single throw of a die is:Read the answer and worked solution →The identity $1 + \tan^2\theta$ equals:Read the answer and worked solution →The period of the function $\sin x$ is:Read the answer and worked solution →The radian measure of $45^\circ$ is:Read the answer and worked solution →The value of $\sin\dfrac{\pi}{6}$ is:Read the answer and worked solution →The expansion of $\sin(A+B)$ is:Read the answer and worked solution →The maximum value of $3\sin\theta$ is:Read the answer and worked solution →The value of $\cos 180^\circ$ is:Read the answer and worked solution →Complete the arc length relationRead the answer and worked solution →Match each identity to its nameRead the answer and worked solution →

Worked practice questions

A fair coin is tossed twice. How many outcomes are there in the sample space?

  1. $2$
  2. $4$
  3. $6$
  4. $8$
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Correct answer: B. $4$

Each toss has 2 possible outcomes (H or T), and the tosses are independent. By the multiplication principle, the sample space has $2 \times 2 = 4$ outcomes: {HH, HT, TH, TT}.

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A fair six-sided die is rolled once. What is the probability of getting an even number?

  1. $\dfrac{1}{6}$
  2. $\dfrac{1}{2}$
  3. $\dfrac{1}{3}$
  4. $\dfrac{2}{3}$
Show answer and solution

Correct answer: B. $\dfrac{1}{2}$

The even outcomes are {2, 4, 6}, so the number of favourable outcomes is 3. The total sample space has 6 outcomes. $P(\text{even}) = \dfrac{3}{6} = \dfrac{1}{2}$.

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$\sin(180° - \theta)$ equals:

  1. $-\cos\theta$
  2. $-\sin\theta$
  3. $\sin\theta$
  4. $\cos\theta$
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Correct answer: C. $\sin\theta$

Supplementary-angle identity: $\sin(180° - \theta) = \sin\theta$. Reason: sine is positive in the second quadrant (where $180° - \theta$ lies for $0° < \theta < 180°$), and the reference angle is $\theta$. Companion identities: - $\cos(180° - \theta) = -\cos\theta$ - $\tan(180° - \theta) = -\tan\theta$

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