JEE Main Sequences and Series — practice questions
107 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice JEE Main Sequences and Series 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 arithmetic mean and geometric mean of two positive numbers are 10 and 8 respectively. The numbers are:For two distinct positive real numbers, their arithmetic mean A and geometric mean G always satisfy:The value of $1^3 + 2^3 + 3^3 + \cdots + 10^3$ is:The sum to infinity of the series $1 + \tfrac{1}{3} + \tfrac{1}{9} + \cdots$ is:In a G.P. the 5th term is 81 and the 2nd term is 3. The common ratio is:The sum of the first 20 terms of an A.P. with first term 2 and common difference 3 is:For $x > 0$, the minimum value of $x + \dfrac{4}{x}$ is:If the sum of two positive numbers is 6 times their geometric mean, the numbers are in the ratio:The value of $n$ for which $\dfrac{a^{n+1}+b^{n+1}}{a^{n}+b^{n}}$ is the geometric mean of $a$ and $b$ is:Three numbers in G.P. have product 216 and sum 19. The numbers are:If the A.M. and G.M. of the roots of a quadratic equation are 8 and 5 respectively, the equation is:For two positive numbers, the arithmetic mean equals the geometric mean if and only if:The sum $1^2 + 2^2 + \cdots + n^2$ equals: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 10th term of the AP $3, 7, 11, 15, \ldots$ is:The sum to $n$ terms of a GP with first term $a = 2$ and ratio $r = 3$ is:The sum of the infinite GP $1 + 1/3 + 1/9 + 1/27 + \cdots$ is:The sum $1^2 + 2^2 + 3^2 + \cdots + 10^2$ equals: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:Sequences that follow specific patterns are called:A sequence containing a finite number of terms is called a:The number at the nth position of a sequence is called the:Adding the terms of a sequence produces what is called the associated:The sequence 1, 1, 2, 3, 5, 8 generated by a recurrence relation is called the:In a geometric progression, the fixed multiplier between terms is called the:A sequence is a geometric progression if the ratio of any term to its preceding term is:For a sequence to be a geometric progression, each of its terms must be:The geometric mean of two positive numbers a and b is which quantity?A series is finite when the sequence behind it is:The compact notation for a series uses which Greek letter?The sequence of successive quotients that never ends is given as an example of an:A progression built by repeatedly adding a fixed number is called an:For two positive real numbers, how does the arithmetic mean compare with the geometric mean?If the arithmetic mean of two positive numbers is 10, their sum must be:If the geometric mean of two positive numbers is 8, their product must be:For a geometric progression with first term 2 and ratio 2, the sum of ten terms is:Inserting 4, 16 and 64 between 1 and 256 makes the resulting sequence a: