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JEE Basics of Mathematics PYQs with Solutions

88 previous year questions from Basics of Mathematics (JEE Main & Advanced IOQM) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

88 questionsIOQMAnswers + solutions

About Basics of Mathematics PYQs

Basics of Mathematics has 88 previous year questions in the Quantrex Academy JEE Main & Advanced IOQM bank. The 88 questions in this list come from Olympiad workbook (88). Each question opens on its own page with the options, the correct answer and the worked solution where available.

JEE Basics of Mathematics PYQs with Solutions

About Basics of Mathematics PYQs

Basics of Mathematics questions with solutions

Find the sum of all positive integers n for which |2^n+5^n-65| is a perfect square.

A total fixed amount of N thousand rupees is given to three persons A, B, C , every year, each being given an amount proportional to her age. In the first year, A got half the

A five digit number n= a b c d e is such that when divided respectively by 2,3,4,5,6 the remainders are a, b, c, d, e . What is the remainder when n is divided by 100 ?

Find the largest 2-digit number N which is divisible by 4 , such that all integral powers of N end with N .

For any real number t , let [t] denote the largest integer ≤ t . Suppose that N is the greatest integer such that [ [ [ N ] ] =4 . Find the sum of digit of N .

Find the number of integer solutions to ||x|-2020| < 5 .

For a natural number n , let n^ denote the number obtained by deleting zero digits, if any. (For example, if n=260, n^ =26 ; if n=2020 , n^ =22 .) Find the number of 3 -digit

Find the number of pairs (a, b) of natural numbers such that b is a 3 -digit number, a+1 divides b-1 and b divides a^2+a+2 .

Positive integers a, b, c satisfy (a b)/(a-b)=c . What is the largest possible value of a+b+c not exceeding 99?

Let X be the set of all even positive integers n such that the measure of the angle of some regular polygon is n degrees. Find the number of elements in X .

Let x, y be positive integers such that x^4=(x-1)(y^3-23)-1 . Find the maximum possible value of x+y .

Find the number of triples of real numbers (a, b, c) such that a^ 20 +b^ 20 +c^ 20 =a^ 24 +b^ 24 +c^ 24 =1 .

Determine the number of positive integral value of p for which there exists a triangle with side a, b and c which satisfy a^2+(p^2+9) b^2+9 c^2-6 a b-6 p b c=0

Find the number of elements in the set \ (a, b) ∈ N: 2 ≤ a, b ≤ 2023, _a(b)+6 _b(a)=5\ .

Find the number of positive integers n such that n + n+1 < 11 .

What is the least positive integer by which 2^5 · 3^6 · 4^3 · 5^3 · 6^7 should be multiplied so that, the product is a perfect square?

The prime numbers a, b and c are such that a+b^2 =4 c^2 . Determine the sum of all possible values of a+b+c .

Find the number of ordered pairs (a, b) such that a, b ∈\ 10,11, …, 29,30\ and GCD(a, b)+LCM(a, b)=a+b .

If x and y are positive integers such that (x-4) (x-10)=2^y , find the maximum possible value of x+y .

For a positive integer n , let n denote the perfect square integer closest to n . For example, 74 =81 , 18 =16 . If N is the smallest positive integer such that 91 · 120 · 143 ·

The positive real numbers a, b, c satisfy: aligned & (a)/(2 b+1)+(2 b)/(3 c+1)+(3 c)/(a+1)=1 & (1)/(a+1)+(1)/(2 b+1)+(1)/(3 c+1)=2 aligned What is the value of

A contractor has two teams of workers : team A and team B. Team A can complete a job in 12 days and team B can do the same job in 36 days. Team A starts working on the job and

A pen costs ₹ 11 and a notebook costs ₹ 13 . Find the number of ways in which a person can spend exactly ₹ 1000 to buy pens and notebooks.

Let m, n be natural numbers such that m+3 n-5=5 LCM(m, n)-11 GCD(m, n) Find the maximum possible value of m+n .

In a class, the total numbers of boys and girls are in the ratio 4: 3 . On one day it was found that 8 boys and 14 girls were absent from the class and that the number of boys was

How many positive integers less than 1000 have the property that the sum of the digits of each such number is divisible by 7 and the number itself is divisible by 3 ?

Find the smallest positive integer n ≥ 10 such that n+6 is a prime and 9 n+7 is a perfect square.

An integer n is such that [(n)/(9)] is a three digit number with equal digits, and [(n-172)/(4)] is a 4 digit number with the digits 2,0,2,4 in some order. What is the remainder

For each positive integer n , consider the highest common factor h_ n of the two numbers n!+1 and (n+1)! . For n < 100 , find the largest value of h_n .

Let p, q be two-digit numbers neither of which are divisible by 10 . Let r be the four-digit number by putting the digits of p followed by the digits of q (in order). As p, q

Let α and β be positive integers such that (16)/(37) < (α)/(β) < (7)/(16) . Find the smallest possible value of β .

Let X be the set consisting of twenty positive integers n, n+2, …, n+38 . The smallest value of n for which any three numbers a, b, c ∈ X , not necessarily distinct, form the

Let the rational number p / q be closest to but not equal to 22 / 7 among all rational numbers with denominator < 100 . What is the value of p-3 q ?

Find the number of positive integers less than 101 that can not be written as the difference of two squares of integers.

Let T be the smallest positive integers which, when divided by 11,13,15 leaves remainders in the sets \ 7,8,9\ ,\ 1,2,3\ ,\ 4,5,6\ respectively. What is the sum of the square of

Let a and b natural numbers such that 2 a-b, a-2 b and a+b are all distinct squares. What is the smallest possible value of b ?

Let N denote the number of all natural numbers n such that n is divisible by a prime p> n and p < 20 . What is the value of N ?

Let E denote the set of all natural numbers n such that 3 < n < 100 and the set \ 1,2,3, …, n\ can be partitioned in to 3 subsets with equal sums. Find the number of elements of E

Let N be the smallest positive integer such that N+2 ~N+3 ~N+…+9 ~N is a number all whose digits are equal. What is the sum of the digits of N ?

A pen costs Rs. 13 and a note book costs Rs. 17. A school spends exactly Rs. 10000 in the year 2017-18 to buy x pens and y note books such that x and y are as close as possible

Let a b c be a three digit number with nonzero digits such that a^2+b^2=c^2 . What is the largest possible prime factor of a b c ?

Consider all 6-digit numbers of the form abccba where b is odd. Determine the number of all such 6-digit numbers that are divisible by 7 .

A book is published in three volumes, the pages being numbered from 1 onwards. The page numbers are continued from the first volume to the second volume to the third. The number

If a, b, c ≥ 4 are integers, not all equal, and 4 a b c=(a+3)(b+3)(c+3) , then what is the value of a+b+c ?