JEE Main Application of Integrals — practice questions
83 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice JEE Main Application of Integrals in the app →A fair coin is tossed twice. How many outcomes are there in the sample space?A fair six-sided die is rolled once. What is the probability of getting an even number?Two fair dice are rolled simultaneously. What is the probability that the sum of the numbers on the two dice iA card is drawn at random from a standard $52$-card deck. What is the probability that the card is either a ki$ in(180° - \theta)$ equals:$ in^2\theta + \cos^2\theta$ equals:$ in(A + B) = $$\cos 2\theta$ equals:If $ in\theta + \cos\theta = 1$, then $ in\theta \cdot \cos\theta$ equals:$\cos 3\theta$ equals:sin(0°) equals:cos(90°) equals:sin²θ + cos²θ equals:tan(45°) equals:In which quadrant is sin θ positive and cos θ negative?sec θ is defined as:sin(A + B) equals:cos(A + B) equals:sin(60°) cos(30°) + cos(60°) sin(30°) equals:If sin θ = 3/5 (θ in Q1), find cos θ:Find cos(75°) using cos(A + B):sin(2θ) equals:cos(2θ) equals:Find sin(15°):If tan θ = 1/2 (acute), find sin 2θ:For 0 ≤ θ < 2π, solutions of sin θ = 1/2:1 - cos²θ equals:sin(A) + sin(B) equals (sum-to-product):In a right triangle, if hypotenuse = 13 and one leg = 5, sin θ for angle θ opposite to that leg:tan(A + B) equals:sin(180° - θ) equals:In triangle ABC with sides a, b, c opposite to angles A, B, C: sine rule states:If sin θ + cos θ = 1, then sin θ × cos θ equals:General solution of cos θ = 0:If tan θ + cot θ = 2, find sin 2θ:If sin θ = 12/13 (acute θ in Q1), find tan(θ/2):Minimum value of sin²θ + cos⁴θ:If sin θ = 12/13 (acute), find tan(θ/2):In triangle with sides 7, 8, 9, find cos of the angle opposite to side 9 (use cosine rule):General solution of sin θ = sin α:The arithmetic mean of n values x1, x2, ..., xn is:Median of an odd-length sorted data set is:Probability of a certain event:Probability of rolling a 6 on a fair die:For independent events A and B, P(A and B) equals:In the figure, the side $a$ is resolved into projections of the other two sides on the base. Which projection The probability of getting an even number on a single throw of a die is:The probability of drawing a king from a standard pack of 52 cards is:When two dice are thrown, the probability that the sum of the numbers is 7 is:The probability of getting at least one head when a coin is tossed twice is:If $P(A)=0.3$, $P(B)=0.4$ and A, B are mutually exclusive, then $P(A\cup B)$ is:The probability of getting a number greater than 4 on a single throw of a die is:In radian measure, $\pi$ radians equals:One radian is approximately equal to:The identity $1 + \tan^2\theta$ equals:The period of the function $ in x$ is:The radian measure of $45^\circ$ is:$ in(90^\circ - \theta)$ equals:The value of $ in\dfrac{\pi}{6}$ is:The expansion of $ in(A+B)$ is:The maximum value of $3 in\theta$ is:The value of $\cos 180^\circ$ is:The general solution of $\cos x = 1/2$ is:The area under the curve $y = x$ from $x = 0$ to $x = 4$ is:The area between $y = x^2$ and $y = x$ from $x = 0$ to $x = 1$ is:The area enclosed by the ellipse $x^2/a^2 + y^2/b^2 = 1$ is:The area enclosed by the parabola $y^2 = 4ax$ and its latus rectum is:The angle 90° in radians is:The exact value of cos 60° is:The double angle formula sin 2A equals:The function f(x) = tan x has vertical asymptotes at:Elementary geometry formulae are described as inadequate for areas enclosed by:The area under a curve is thought of as being composed of many thin:An elementary strip of height y and width dx has an area equal to:A systematic approach to the theory of calculus began in which century?If a curve lies below the x-axis, the computed area comes out as:When the computed area is negative, which value is taken instead?A circle is described as symmetrical about how many axes?The method of exhaustion was developed by mathematicians of ancient:The method of exhaustion was used for areas, volumes and which other quantity?Newton described his work on the calculus as the theory of:Newton's name for the inverse function of a derivative was the:Leibnitz called his 1684 article Calculas summatorius because it concerned: