CAT Algebra — practice questions
120 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice CAT Algebra in the app →The sample space of a single throw of a fair six-faced die isIf a fair coin is tossed once, the probability of getting a HEAD isA fair die is rolled. The probability of getting an ODD number isTwo fair dice are rolled. The probability that the SUM of the numbers showing is 7 isFor any two events $A$ and $B$, the probability of $A \cup B$ (A or B) is given byA card is drawn from a well-shuffled standard deck of 52 cards. The probability of drawing a KING isA fair die is rolled. The probability of getting a PRIME number isThree fair coins are tossed simultaneously. The probability of getting EXACTLY two heads isA card is drawn from a standard deck of 52. The probability that it is a KING or a QUEEN isIf $P(A) = 0.4$ and $P(B) = 0.5$ and $P(A \cap B) = 0.2$, then $P(A \cup B)$ isWhat is the probability that a randomly drawn card from a 52-card deck is a FACE CARD (King, Queen, or Jack)?Two events $A$ and $B$ are MUTUALLY EXCLUSIVE ifTwo fair coins are tossed. The probability of getting AT LEAST ONE head isIf the probability that a student passes a CAT mock test is $0.6$, what is the probability that the student FAEuclid's division lemma: for positive integers a and b there exist unique integers q and r with a = bq + r andIn a = bq + r, the integers q and r are called the:Euclid's division lemma was first recorded in which book of Euclid's Elements?The word algorithm comes from the name of a 9th century mathematician from:The HCF of 455 and 42, found by Euclid's algorithm, is:Euclid's algorithm works because HCF(c, d) equals:The HCF of 12576 and 4052 is:A sweetseller has 420 kaju and 130 badam barfis and wants equal stacks using the least tray area. Each stack hThe Fundamental Theorem of Arithmetic says every composite number is a product of primes in a way that is:The first correct proof of the Fundamental Theorem of Arithmetic was given by:How many prime numbers are there?Can 4 to the power n end in the digit zero for any natural number n?HCF(6, 20) is 2 and LCM(6, 20) is:HCF is the product of the smallest power of each common prime; LCM is the product of the:For two positive integers a and b, HCF(a, b) x LCM(a, b) equals:LCM(6, 72, 120) is:A number that cannot be written as p/q with integers p and q (q not zero) is:The proof that root 2 is irrational uses the technique of:If p is a prime and p divides a squared, then p divides:The sum of a rational and an irrational number is:A rational number has a terminating decimal expansion only when its denominator's prime factors are:Counting eggs that leave remainders 1, 2, 3, 4, 5 in pairs, threes, fours, fives, sixes and none in sevens, unAn equation of the form ax + by + c = 0, with a and b not both zero, is a linear equation in:Substituting x = 1 and y = 1 in 2x + 3y = 5 gives 5, so this pair of values is:Each solution of a linear equation in two variables corresponds to:Two lines drawn in a plane can intersect, be coincident, or be:If the two lines of a pair of linear equations intersect at one point, the pair has:A pair of linear equations that has no solution is called:A pair of linear equations whose lines coincide has:A pair of equations which are equivalent, with infinitely many common solutions, is called:Akhila's rides and games gave x - 2y = 0 and 3x + 4y = 20. The lines meet at:From that solution, the number of rides Akhila had on the Giant Wheel was:Romila paid 9 for 2 pencils and 3 erasers; Sonali paid 18 for 4 pencils and 6 erasers. Their lines are:Two rails are x + 2y - 4 = 0 and 2x + 4y - 12 = 0. Do they cross?For x + 3y = 6 and 2x - 3y = 12, the common point is:If a1/a2 is not equal to b1/b2, the two lines are:If a1/a2 = b1/b2 = c1/c2, the two lines are:If a1/a2 = b1/b2 but this differs from c1/c2, the two lines are:A pair of linear equations that has a solution is called:A coach buys 3 bats and 6 balls for 3,900 and later 1 bat and 3 balls for 1,300. This is a situation of:2 kg apples with 1 kg grapes cost 160, and 4 kg apples with 2 kg grapes cost 300. The unknowns here are:Putting x = 0 in the equation 3x + 4y = 20 gives y equal to:Choosing y = 2 in 3x + 4y = 20 was preferred because it gives x as:The graphical representation of a linear equation in two variables is:Probability based on the results of actual experiments is called:A coin tossed 1000 times gave 455 heads. The empirical probability of a head was:Comte de Buffon tossed a coin 4040 times and got how many heads?Karl Pearson made 24000 tosses of a coin and obtained a head probability of:Theoretical probability is the number of outcomes favourable to E divided by:The classical definition of probability was given in 1795 by:Who wrote the first book on probability, The Book on Games of Chance?Throwing a fair die gives outcomes 1 to 6 that are:A bag has 4 red balls and 1 blue ball. Drawing a red ball and a blue ball are:An event having only one outcome of the experiment is called:The sum of the probabilities of all elementary events of an experiment is:For any event E, P(E) plus P(not E) equals:Throwing a die once, the probability of getting a number greater than 4 is:The probability of getting the number 8 in a single throw of a die is:An event whose probability is 0 is called:The probability of getting a number less than 7 in a single throw of a die is:For any event E, the value of P(E) always lies between:A standard deck has 52 cards divided into how many suits?Drawing one card from a well-shuffled deck of 52, the probability it is an ace is:Kings, queens and jacks in a deck are together called:If the probability of Sangeeta winning a tennis match is 0.62, the probability Reshma wins is:Ignoring a leap year, the probability that two friends have different birthdays is:A list of numbers in which each term comes from adding a fixed number to the one before it is called:The fixed number added each time in such a list is called the:Shakila's money box holds 100, 150, 200, 250 rupees on successive birthdays. The common difference is:For the list 6, 3, 0, minus 3, the common difference is:Reena starts on 8000 rupees a month with a yearly rise of 500. Her salary in the fifth year is:With a starting salary of 8000 and a rise of 500 a year, the salary in the fifteenth year is:The nth term of a progression with first term a and common difference d is:The tenth term of the list 4, 10, 16, 22 is:Which of these lists is an arithmetic progression?The list minus 2, 2, minus 2, 2 is not a progression because the differences are:A progression with a last term is described as:To list a progression completely, the minimum information you need is:With first term 6 and common difference 3, the first four terms are:When the common difference is zero, as in 2, 2, 2, 2, the list is:Gauss found the sum of the whole numbers from 1 to 100 to be:The sum of the first n terms of a progression can be written as n by 2 times:The sum of the first 22 terms of the list 8, 3, minus 2 is:If the last term of a finite progression is l, the sum of all its terms is n by 2 times:The sum of the first 1000 positive integers is:If a, b and c are in a progression, then b equals:The middle term b of such a triple is called the:A well costs 150 rupees for the first metre and rises by 50 for each further metre. The cost for the fourth meThe distance between two points in a plane is worked out using which theorem?Since distance can never be negative, the distance formula takes:The distance between the points (4, 6) and (6, 8) is:The distance between the points (2, 3) and (4, 1) is:The distance between the points (0, 0) and (36, 15) is:The distance of the point (6, 4) from the point (minus 5, minus 3) comes to:The distance of any point P from the origin uses which coordinates?The points (3, 2), (minus 2, minus 3) and (2, 3) form which kind of triangle?The points (1, 7), (4, 2), (minus 1, minus 1) and (minus 4, 4) are the vertices of a:Ashima, Bharti and Camella sit at (3, 1), (6, 4) and (8, 6). Are they in a line?The relation satisfied by every point equidistant from (7, 1) and (3, 5) is:The graph of that relation is the:The point on the y-axis equidistant from (6, 5) and (minus 4, 3) is:The formula giving the point dividing a segment in a given ratio is the:The point dividing the join of (4, minus 3) and (8, 5) in the ratio 3 to 1 is:A midpoint divides a line segment in which ratio?Because of that, the midpoint of the join of two points is found by:The area of the triangle with vertices (1, minus 1), (minus 4, 6) and (minus 3, minus 5) is: