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JEE Main & Advanced IOQM PYQs with solutions

Chapter-wise IOQM previous year questions for JEE Main & Advanced: 454 questions in 21 chapters. Largest chapters: Permutation and Combination (112), Basics of Mathematics (88) and Properties of Triangles (64). Open any question for options, correct answer and solution.

JEE Main & Advanced IOQM PYQs with solutions

JEE IOQM chapters

Permutation and Combination

Basics of Mathematics

Properties of Triangles

Sequences and Series

Quadratic Equation

Circle

Straight Lines

Functions

Binary Numbers

Vector Algebra

Binomial Theorem

Determinants

Sets and Relations

Statistics

Application of Derivatives

Matrices

Three Dimensional Geometry

Definite Integration

Complex Number

Trigonometric Equations

Area Under Curves

Sample IOQM questions

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 ?

If a, b, c are real numbers and (a+b-5)^2+(b+2 c+3)^2+(c+3 a-10)^2=0 find the integer nearest to a^3+b^3+c^3 .

If a, b, c are real numbers and (a+b-5)^2+(b+2 c+3)^2+(c+3 a-10)^2=0 find the integer nearest to a^3+b^3+c^3 .

A finite set M of positive integers consists of distinct perfect squares and the number 92 . The average of the numbers in M is 85 . If we remove 92 from M , the average drops to

If ∑_ k=1 ^N (2 k+1)/((k^2+k)^2)=0.9999 then determine the value of N .

A group of women working together at the same rate can build a wall in 45 hours. When the work started, all the women did not start working together. They joined the work over a

Find the number of maps f:\ 1,2,3\ arrow\ 1,2,3,4,5\ such that f(i) ≤ f(j) whenever i < j

For an integer n ≥ 3 and a permutation σ=(p_1, p_2, …, p_n) of \ 1,2, …, n\ , we say p_1 is a landmark point if 2 ≤ I ≤ n-1 and (p_ I-1 -p_I)(p_ I+1 -p_I)>0 . For example, for n=7

Ari chooses 7 balls at random from n balls numbered 1 to n . If the probability that no two of the drawn balls have consecutive numbers equals the probability of exactly one pair

Let A B C be a triangle in the x y plane, where B is at the origin (0,0) . Let B C be produced to D such that B C: C D=1: 1, C A be produced to E such that C A: A E=1: 2 and A B

Let A B C D be a unit square. Suppose M and N are points on B C and C D respectively such that the perimeter of triangle M C N is 2 . Let O be the circumcentre of triangle M A N

An ant leaves the anthill for its morning exercise. It walks 4 feet east and then makes a 160^ ∘ turn to the right and walks 4 more feet. It then makes another 160^ ∘ turn to the

The incircle Γ of a scalene triangle A B C touches B C at D, C A at E and A B at F . Let r_A be the radius of the circle inside A B C which is tangent to Γ and the sides A B and A

The sides x and y of a scalene triangle satisfy x+(2 Δ)/(x)=y+(2 Δ)/(y) , where Δ is the area of the triangle. If x=60, y=63 , what is the length of the largest side of the

In a triangle A B C , the median A D divides ∠ B A C in the ratio 1: 2 . Extend A D to E such that E B is perpendicular A B . Given that B E=3, B A=4 , find the integer nearest to

In base -2 notation, digits are 0 and 1 only and the places go up in powers of -2 . For example, 11011 stands for (-2)^4+(-2)^3+(-2)^1+(-2)^0 and equals number 7 in base 10 . If

The equation 166 × 56=8590 is valid in some base b ≥ 10 (that is 1,6,5,8,9,0 are digits in base b in the above equation). Find the sum of all possible values of b ≥ 10 satisfying

Consider the sequence 1,7,8,49,50,56,57,343, … which consists of sums of distinct powers of 7 , that is, 7^0, 7^1, 7^0+7^1, 7^2, … , in increasing order. At what position will

Suppose the prime numbers p and q satisfy q^2+3 p=197 p^2+q . Write (q)/(p) as l+(m)/(n) , where l, m, n are positive integers, m < n and GCD(m, n)=1 . Find the maximum value of

Let X=\ -5,-4,-3,-2,-1,0,1,2,3,4,5\ and S=\ (a, b) ∈ X × X: x^2+a x+b. and x^3+b x+a have at least a common real zero\ . How many elements are there in S ?

If x= 2 + 3 + 6 is a root of x^4+a x^3+b x^2+c x+d=0 where a, b, c, d are integers, what is the value of |a+b+c+d| ?

Let A and B be two finite sets such that there are exactly 144 sets which are subsets of A or subsets of B . Find the number of elements in A ∪ B .

Let A and B be two finite sets such that there are exactly 144 sets which are subsets of A or subsets of B . Find the number of elements in A ∪ B .

Five students take a test on which any integer score from 0 to 100 inclusive is possible. What is the largest possible difference between the median and the mean of the scores?

Five students take a test on which any integer score from 0 to 100 inclusive is possible. What is the largest possible difference between the median and the mean of the scores?

Let A B C D be a convex cyclic quadrilateral. Suppose P is a point in the plane of the quadrilateral such that the sum of its distances from the vertices of ABCD is the least. If

Let Ω_1 be a circle with centre O and let AB be diameter of Ω_1 . Let P be a point on the segment OB different from O . Suppose another circle Ω_2 with centre P lies in the

A triangle A B C with A C=20 is inscribed in a circle m . A tangent t to ω is drawn through B . The distance of t from A is 25 and that from C is 16 . If S denotes the area of the

In a parallelogram A B C D , the point P on a segment A B is taken such that (A P)/(A B)=(61)/(2022) and a point Q on the segment A D is taken such that (A Q)/(A D)=(61)/(2065) .

In parallelogram A B C D, A C=10 and B D=28 . The points K and L in the plane of A B C D move in such a way that A K=B D and B L=A C . Let M and N be the midpoints of C K and D L

Let D, E, F be points on the sides B C, C A, A B of a triangle A B C , respectively. Suppose A D, B E, C F are concurrent at P . If P F / P C=2 / 3, P E / P B=2 / 7 and P D / P

Let x, y be real numbers such that x y=1 . Let T and t be the largest and the smallest values of the expression ((x+y)^2-(x-y)-2)/((x+y)^2+(x-y)-2) If T+t can be expressed in the

Let x, y be real numbers such that x y=1 . Let T and t be the largest and the smallest values of the expression ((x+y)^2-(x-y)-2)/((x+y)^2+(x-y)-2) If T+t can be expressed in the

Let P_0=(3,1) and define P_ n+1 =(x_ n , y_ n ) for n ≥ 0 by x_ n+1 =-(3 x_n-y_n)/(2), y_ n+1 =-(x_n+y_n)/(2) Find the area of the quadrilateral formed by the points P_ 96 , P_ 97

Let P_0=(3,1) and define P_ n+1 =(x_ n , y_ n ) for n ≥ 0 by x_ n+1 =-(3 x_n-y_n)/(2), y_ n+1 =-(x_n+y_n)/(2) Find the area of the quadrilateral formed by the points P_ 96 , P_ 97

Determine the sum of all possible surface areas of a cube two of whose vertices are (1,2,0) and (3,3,2) .

Determine the sum of all possible surface areas of a cube two of whose vertices are (1,2,0) and (3,3,2) .

Find the largest positive integer n < 30 such that (1)/(2)(n^8+3 n^4-4) is not divisible by the square of any prime number.