JEE Main Permutations and Combinations — practice questions
86 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice JEE Main Permutations and Combinations 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 kiThe value of $5!$ is:The number of ways to arrange $n$ distinct objects in a row is:$^{n}P_r$, the number of permutations of $n$ distinct objects taken $r$ at a time, equals:$^{n}C_r$, the number of combinations of $n$ distinct objects taken $r$ at a time, equals:How many different 4-digit numbers can be formed using the digits $1, 2, 3, 4, 5$ without repetition?In how many ways can a committee of $3$ persons be chosen from a group of $10$ people?$ in(180° - \theta)$ equals:$ in^2\theta + \cos^2\theta$ equals:$ in(A + B) = $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:sin(2θ) equals:If tan θ = 1/2 (acute), find sin 2θ:In triangle ABC with sides a, b, c opposite to angles A, B, C: sine rule states:General solution of cos θ = 0:If sin θ = 12/13 (acute θ in Q1), find tan(θ/2):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: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 number of ways to arrange the letters of the word DELHI is:The number of distinct arrangements of letters in the word MISSISSIPPI (4 S, 4 I, 2 P, 1 M) is:The number of ways to choose $3$ players from a class of $10$ for a team (order does not matter) is:Using Pascal's identity, $^7C_3 + ^7C_2$ 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:The angle 90° in radians is:The exact value of cos 60° is:The double angle formula sin 2A equals:An arrangement in a definite order of a number of objects is called a:In a combination, the order of the chosen objects is:The multiplication principle is also known as the fundamental principle of:The notation n factorial represents the product of the first n:Zero factorial is defined as which value?The principle for two events can be generalised to how many events?If one event can occur in m ways and then another in n ways, the total is:With 3 pants and 2 shirts, how many different pant and shirt pairs are there?Sabnam has 2 school bags, 3 tiffin boxes and 2 water bottles. How many combinations?A number lock has 4 wheels, each labelled with how many digits?The lock opens only if the 4 digits are arranged in a sequence with no:In the word ROOT, why are the letters not all treated as different?Listing every arrangement by hand is rejected as a method because it is:Choosing a 2 player team from X, Y and Z gives how many possible teams?A selection of 3 different objects taken 2 at a time is called a:Twelve people each shake hands with all the others. Order of the pair is:A team of 5 with at least 3 girls cannot be all girls. Why not?Five factorial can be rewritten as five times which quantity?