alleryThe probability of getting an even number on a single throw of a die is:
- $\tfrac23$
- $\tfrac12$
- $\tfrac16$
- $\tfrac13$
Show answer and solution
Correct answer: B. $\tfrac12$
Even numbers on a die are {2,4,6}: 3 of 6 outcomes ⟹ 3/6 = 1/2.
JEE Main Application of Integrals — practice questions
Explore 26 free Application of Integrals questions in JEE Main Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 1–26 of 26.
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 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 →The angle 90° in radians is:Read the answer and worked solution →The exact value of cos 60° is:Read the answer and worked solution →The double angle formula sin 2A equals:Read the answer and worked solution →The function f(x) = tan x has vertical asymptotes at:Read the answer and worked solution →Elementary geometry formulae are described as inadequate for areas enclosed by:Read the answer and worked solution →The area under a curve is thought of as being composed of many thin:Read the answer and worked solution →An elementary strip of height y and width dx has an area equal to:Read the answer and worked solution →A systematic approach to the theory of calculus began in which century?Read the answer and worked solution →If a curve lies below the x-axis, the computed area comes out as:Read the answer and worked solution →When the computed area is negative, which value is taken instead?Read the answer and worked solution →A circle is described as symmetrical about how many axes?Read the answer and worked solution →The method of exhaustion was developed by mathematicians of ancient:Read the answer and worked solution →The method of exhaustion was used for areas, volumes and which other quantity?Read the answer and worked solution →Newton described his work on the calculus as the theory of:Read the answer and worked solution →Newton's name for the inverse function of a derivative was the:Read the answer and worked solution →Leibnitz called his 1684 article Calculas summatorius because it concerned:Read the answer and worked solution →
Worked practice questions
The probability of drawing a king from a standard pack of 52 cards is:
- $\tfrac{1}{13}$
- $\tfrac{1}{4}$
- $\tfrac{1}{52}$
- $\tfrac{4}{13}$
Show answer and solution
Correct answer: A. $\tfrac{1}{13}$
There are 4 kings in 52 cards: 4/52 = 1/13.
When two dice are thrown, the probability that the sum of the numbers is 7 is:
- $\tfrac{1}{12}$
- $\tfrac16$
- $\tfrac{1}{9}$
- $\tfrac{7}{36}$
Show answer and solution
Correct answer: B. $\tfrac16$
Sums of 7 occur in 6 of 36 equally-likely pairs ⟹ 6/36 = 1/6.
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