CAT Number System — practice questions
120 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice CAT Number System in the app →If $a + b = 7$ and $a - b = 3$, what is $a^2 - b^2$?Expand $(x + 5)^2$.If $a + b + c = 0$, what is the value of $a^3 + b^3 + c^3$?Factorise $a^3 - b^3$.If $x + \dfrac{1}{x} = 5$, find $x^3 + \dfrac{1}{x^3}$.If $a + b + c = 6$ and $a^2 + b^2 + c^2 = 14$, find $ab + bc + ca$.What is the prime factorisation of 360?For which value of n does $6^n$ end with the digit zero?How many divisors does the number $N = 2^3 \times 3^2 \times 5$ have?What is the HCF of 18 and 24?What is the LCM of 12 and 18?HCF of two positive integers a and b is 5. Their LCM is 200. If a = 25, what is b?Which of the following is a rational number?Which fraction has a TERMINATING decimal expansion?The product of a non-zero rational number and an irrational number is always:Every composite number can be expressed as:The prime factorisation of 253 is:The HCF of 96 and 404 is 4. Their LCM is:The LCM of 6, 72 and 120 is:What is the HCF of 96 and 404?The smallest number that is exactly divisible by every number from 1 to 10 is:The product 2 x 3 x 7 x 11 x 23 equals:A number leaves remainder 3 when divided by 7 and remainder 3 when divided by 5. The smallest such number abovHow many prime factors, counted with repetition, does 21252 = 2^2 x 3 x 7 x 11 x 23 have?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, 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: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 largest positive integer that divides both of two numbers is their:The algorithm that finds that largest common divisor by repeated division is named after:Using that algorithm on 455 and 42, the first step gives 455 = 42 times 10 plus:Continuing, 42 = 35 times 1 plus 7, then 35 = 7 times 5 plus 0. The largest common divisor is:The theorem saying every composite number can be written as a product of primes is the:Writing 20 as 2 times 2 times 5 is an example of:The highest common factor of 6 and 20 is:The lowest common multiple of 6 and 20 is:The highest common factor is found by taking, for each common prime, the:The lowest common multiple is found by taking, for each prime involved, the:For any two positive integers, the product of their highest common factor and lowest common multiple equals:The prime factorisation of 96 gives a highest common factor with 404 of:Using that result, the lowest common multiple of 96 and 404 is:The highest common factor of 6, 72 and 120 is:The lowest common multiple of 6, 72 and 120 is:For three numbers, the product of the numbers is:Knowing the highest common factor of two numbers lets you find their lowest common multiple by:If two numbers share no prime factor at all, their highest common factor must be:In that case, their lowest common multiple equals:A number like root 2, which cannot be written as a ratio of integers, is described as:If a prime p divides the square of a number a, the theorem states that p also divides:The two main tools introduced for studying real numbers here are prime factorisation and:An equation p(x) = 0 where p is a polynomial of degree 2 is called a:The standard form of such an equation is written as:In that standard form, the one restriction placed on the coefficient a is that it is:The scholar credited with deriving the quadratic formula around 1025 CE was:The expression b squared minus 4ac is called the equation's:If that expression is greater than zero, the equation has:If that expression equals zero, the equation has:If that expression is less than zero, the equation has: