JEE Advanced Binomial Theorem — practice questions
91 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice JEE Advanced Binomial Theorem 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:The number of terms in the expansion of $(a+b)^n$ is:The general term $T_{r+1}$ in the expansion of $(a+b)^n$ is:In the expansion of $(x+y)^8$, the middle term is the:The coefficient of $x^3$ in the expansion of $(1+x)^{10}$ is:The term independent of $x$ in the expansion of $\left(x+\dfrac{1}{x}\right)^6$ is:The value of $\binom{n}{0}+\binom{n}{1}+\cdots+\binom{n}{n}$ is:The constant term in the expansion of $\left(x^2+\dfrac{1}{x}\right)^6$ is:The coefficient of $x$ in the expansion of $(1+2x)^5$ is:The greatest binomial coefficient in the expansion of $(1+x)^{10}$ is:The number of middle terms in the expansion of $(a+b)^7$ is:If $\binom{10}{3}=\binom{10}{k}$ (with $k\neq 3$), then $k$ equals:The coefficient of $x^3$ in the expansion of $(2+x)^5$ is:The sum of all the coefficients in the expansion of $(2x+3)^4$ is: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:The identity $1 + \tan^2\theta$ equals:The period of the function $ in x$ is:The radian measure of $45^\circ$ is: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 expansion of $(a + b)^n$ contains how many terms?The general term in the expansion of $(x + 2)^{10}$ is:The sum of binomial coefficients $\binom{n}{0} + \binom{n}{1} + \cdots + \binom{n}{n}$ equals:The middle term in $(x + y)^6$ is the term with index:A fair coin is tossed twice. The probability of getting at least one head is:If $P(A) = 0.5, P(B) = 0.4, P(A \cap B) = 0.2$, then $P(A | B)$ is:Two events $A$ and $B$ are independent if:A binomial random variable $X$ has $n = 10$ trials and success probability $p = 0.3$. Its mean is:A card is drawn from a deck of 52. Given that the card is RED, what is the probability that it's a KING?If P(A) = 0.5, P(B) = 0.6, and P(A ∩ B) = 0.2, then P(A ∪ B) is:Two dice are rolled. The probability of getting AT LEAST ONE SIX is:Bayes' theorem is essentially used to:For a discrete random variable X with values 0, 1, 2 and probabilities 0.3, 0.5, 0.2 respectively, the mean E(In a binomial distribution B(n=10, p=0.5), the probability of EXACTLY 6 successes is:The 4 conditions required for a binomial distribution (Bernoulli trials) include all the following EXCEPT:For a binomial distribution B(n, p), the MEAN and VARIANCE are:The number of ways to choose 3 books out of 5 (order does NOT matter) is:The angle 90° in radians is:The function f(x) = tan x has vertical asymptotes at: