CAT Modern Mathematics — practice questions
120 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice CAT Modern Mathematics in the app →Euclid'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, unThe mean of observations is the sum of all values divided by:The Greek letter used to write summation in short form is:The exact mean of the 30 students' maths marks was:Students who scored exactly 40 marks go into which class interval?The class mark of a class interval is the:For the class 10-25, the class mark is:Using class marks with frequencies to compute the mean is the:The grouped mean came to 62 while the exact mean was 59.3 because of the:In the assumed mean method, d equals:The mean obtained by direct, assumed mean and step-deviation methods is:The mean percentage of female teachers in rural primary schools came to:The mean number of wickets taken by the 45 bowlers was:The value that occurs most often in the data is the:Data with more than one value sharing the maximum frequency is:In grouped data, the class with the maximum frequency is the:For the household survey with modal class 3-5, the mode came to:Among the 30 students, mode marks were 52 while mean marks were 62, so the mode was:The middle-most observation in ordered data is the:With 100 students, the median is the average of which two observations?The class whose cumulative frequency is greater than and nearest to n/2 is the:For the 53 students, the median marks came to about:The empirical relation between the three measures is 3 Median equals:An 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:For a closed plane figure, the distance around its boundary is the:A rectangular park is 30 m long and 20 m wide. The length of fence around it is:The land occupied by that 30 m by 20 m park is:If one bag of cement covers 4 square metres, the bags needed equal the path area divided by:A quadrilateral with only one pair of parallel opposite sides is a:The area of a trapezium is half the height times the:Nazma's trapezium plot, split into a rectangle of 240 and a triangle of 60 square metres, has area:A general quadrilateral can be split into two triangles by drawing one:The area of a quadrilateral equals half the diagonal times the:A quadrilateral has diagonal 5.5 cm and offsets 2.5 cm and 1.5 cm. Its area is:The area of a rhombus is half the product of its:A rhombus has diagonals 10 cm and 8.2 cm. Its area is:A trapezium field of area 480 square metres has height 15 m and one parallel side 20 m. The other side is:A rhombus of area 240 square cm has one diagonal 16 cm. The other diagonal is:A regular hexagon of side 5 cm, split into two congruent trapeziums of 32 square cm each, has area:Ridhima found the same hexagon area as a rectangle of 40 plus two triangles of 12 each, which totals:The circumference of a circle is found with the expression:A flooring tile shaped like a parallelogram has base 24 cm and height 10 cm. Its area is:A pentagon can be divided into three parts by constructing:Splitting a polygon into triangles to find its area is called:The area of a trapezium whose parallel sides are 1 m and 1.2 m with height 0.8 m is:A trapezium of area 34 square cm has one parallel side 10 cm and height 4 cm. The other side 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:Mohan owns 3 pants and 2 shirts. The number of pant and shirt pairs he can wear is:Sabnam has 2 school bags, 3 tiffin boxes and 2 water bottles. Choosing one of each, she can carry them in:If one event can happen in m ways and then another in n ways, the pair happens in:Four letter words from the letters of ROSE, with no letter repeated, number:If letters may repeat, the number of four letter words from R, O, S and E becomes:With 4 flags of different colours, signals using 2 flags one below the other number:Two digit even numbers formed from the digits 1, 2, 3, 4, 5 with repetition allowed number:Using 5 different flags, signals of at least 2 flags on a staff number:Three digit numbers from the digits 1 to 5, with repetition allowed, number:Three digit numbers from the digits 1 to 5, with no digit repeated, number: