TS EAPCET (Engineering) Permutations and Combinations — practice questions
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Practice TS EAPCET (Engineering) 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?The value of $5!$ is:The number of ways to arrange $n$ distinct objects in a row is: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:A **random variable** is best defined as:A **discrete** random variable is one whose possible values:For a continuous random variable $X$, the probability that $X$ equals any specific value is:The **cumulative distribution function (c.d.f.)** $F(x)$ of a discrete random variable is:When two fair dice are rolled and $X$ denotes the sum of the upper faces, the range of $X$ is:If a fair coin is tossed twice and $X$ = number of heads, then $P[X = 1]$ equals:If two cards are drawn with replacement from a deck of 52, $P[X = 2]$ where $X$ = number of aces equals:A fair die is thrown. Let $X$ = number of factors of the number on the upper face. $P[X = 2]$ equals:$f(x) = 3x^2$ for $0 < x < 1$ is the p.d.f. of $X$. The probability $P[1/2 < X < 1]$ is:If $f(x) = kx^2(1 - x)$ for $0 < x < 1$ is the p.d.f. of $X$, the value of $k$ is:For p.d.f. $f(x) = x/8$, $0 < x < 4$, the probability $P[x < 1.5]$ is:Find $k$ if $f(x) = kx$ for $0 < x < 2$ and 0 otherwise is a valid p.d.f.The c.d.f. $F(x)$ of the p.d.f. $f(x) = 3x^2$ for $0 < x < 1$ is:Two cards are drawn with replacement. $X$ = number of aces. The probability $P[X \geq 1]$ equals:For p.d.f. $f(x) = x^2/3$ for $-1 < x < 2$, the probability $P[0 < X \leq 1]$ equals:For p.d.f. $f(x) = k(4 - x^2)$ for $-2 \leq x \leq 2$ (and 0 elsewhere), the value of $k$ is:For the c.d.f. $F(x) = 3x - 2x^3$ (from p.d.f. $f(x) = 3(1 - 2x^2)$ on $[0, 1]$), $F(0.5)$ equals:If a fair coin is tossed $n$ times, the probability of any exact pattern (like all heads) is:If a die is thrown and 'getting an odd number' is success, then $p$ and $q$ are:A bag has balls marked 0–9. Four balls drawn with replacement. Probability that **none** is marked '0' is:Probability of bomb hitting target = 0.8. Out of 10 bombs dropped, probability that **exactly 2 miss** 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:Mohan owns 3 pants and 2 shirts. How many different pant-shirt pairs can he wear?The value of 0! is defined to beHow many 3-letter words, without repeating a letter, can be formed from the letters of NUMBER?If repetition is allowed, how many 3-letter words can be formed from the letters of NUMBER?What is the value of 7P2?In how many ways can nothing be selected from n different things?Which of the following equals 12C10?The expression n!/(n - 2)! simplifies toGiven that 10C3 = 120, what is 10P3?Twelve people each shake hands once with every other. How many handshakes occur?How many distinct arrangements are there of the letters of the word ROOT?A lock has 4 wheels marked 0 to 9. The first digit is 7 and no digit repeats. How many sequences remain?How many 4-digit numbers have no repeated digit?A chairman and a vice chairman are chosen from 8 persons. How many ways?How many words can be formed using all letters of EQUATION once each?How many distinct arrangements does MISSISSIPPI have?Which statement describes a combination?A permutation is best described asFrom 6 candidates, how many ways can a president and a secretary be chosen?In how many ways can 5 people occupy 3 chairs in a row, one person per chair?How many 2-letter codes come from A, B, C, D, E if letters may repeat?If 15C4 = 15Cx and x is not 4, what is x?How many ways can 4 cards be chosen from a standard deck of 52?How many 5-card hands from 52 cards contain exactly one ace?A team of 5 has 3 boys and 2 girls from 5 boys and 4 girls. How many ways?How many diagonals does a hexagon have?How many triangles can be formed from 7 points, no three of them collinear?In how many ways can 4 different books be arranged on a shelf?In how many ways can 7 students stand in a row?Five people stand in a row with two named persons always together. How many ways?In how many ways can 6 people sit around a round desk, rotations being the same?In nPr = nCr x r!, what does the factor r! count?Which Jain scholar, around 850, is credited with general formulae for permutations and combinations?Which Sanskrit scholar's Chhanda Sutra gives a method of counting combinations of letters?Bhaskaracharya treated permutations and combinations under which name in Lilavati?Sushruta Samhita says 6 different tastes give how many combinations when taken one, two, and so on?Who wrote Ars Conjectandi?In which year did Levi Ben Gerson give the general formula for nCr?Which Chinese book of changes contains early beginnings of permutations and combinations?The number nCk is also known by which name?The identity C(n, k) = C(n, n - k) can be explained byPascal's triangle is built from which recursion on combinations?Why is n!/(k!(n-k)!) the count of k-combinations?What is the value of 0! by the standard definition?A coach picks a captain and a vice-captain from 6 players. In how many ways can this be done?In how many ways can a group of 3 prizes-winners' names be drawn as a set of 3 from 10 entries, order ignored?A phone passcode has 4 digits chosen from 0 to 9 with repetition allowed. How many passcodes exist?The number of distinct arrangements of the letters of MISSISSIPPI isA garland uses 7 different flowers; reversed orders count as one. How many garlands?A committee of 3 is to be chosen from 8 members. How many different committees are possible?If nC8 = nC6, then the value of n isEvery pair among 12 friends shakes hands once. How many handshakes occur?Using Pascal's rule, 5C2 + 5C3 equals which value?In how many ways can 5 boys and 4 girls be seated in a row of 9 chairs with no restriction?Five friends stand in a line and two particular friends insist on standing together. How many lines are possibA team of 4 is formed from 6 men and 5 women with exactly 2 women. How many teams are possible?How many 4-digit numbers with all different digits can be formed from 0 to 9?The ratio 12P4 : 12C4 is equal toEight points lie in a plane with no three collinear. How many straight lines do they determine?How many triangles can be drawn using 7 points on a circle as vertices?A club of 10 members elects a president and a secretary, both different persons. How many outcomes exist?Which expression is always equal to 10C4?A traveller can reach a town by 4 bus routes or by 3 train routes. In how many ways can one route be chosen?With 5 shirts and 3 trousers, how many different outfits of one shirt and one trouser can be worn?How many subsets, including the empty set, does a 6-element set have?When all n objects are distinct and arranged in a line, nPn equalsWhat distinguishes a combination from a permutation?An ordered sequence of k distinct elements of a set is called what?Which Indian mathematician's Lilavati contains the rule for counting permutations of n objects?The rule for permutations of n objects was known in India around which year?Fabian Stedman in 1677 described factorials while explaining the permutations of what?