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JEE Main & Advanced IOQM PYQs with solutions

Chapter-wise IOQM previous year questions for JEE Main & Advanced. Open any question for options, correct answer and solution.

454 questions21 chapters

Permutation Combination

112 PYQs

Basic of Mathematics

88 PYQs

Properties of Triangles

64 PYQs

Sequences and Series

38 PYQs

Quadratic Equation

38 PYQs

Circle

30 PYQs

Straight Lines

24 PYQs

Functions

20 PYQs

Binary Numbers

8 PYQs

Vector Algebra

6 PYQs

Binomial Theorem

6 PYQs

Determinants

2 PYQs

Sets and Relations

2 PYQs

Statistics

2 PYQs

Application of Derivatives

2 PYQs

Matrices

2 PYQs

Three Dimensional Geometry

2 PYQs

Definite Integration

2 PYQs

Complex Number

2 PYQs

Trigonometric Equations

2 PYQs

Area Under Curves

2 PYQs

1

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

Olympiad workbook Solution View → 2

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 tota

Olympiad workbook Solution View → 3

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 ?

Olympiad workbook Solution View → 4

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 .

Olympiad workbook Solution View → 5

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 .

Olympiad workbook Solution View → 6

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 8

Olympiad workbook Solution View → 7

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

Olympiad workbook Solution View → 8

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 pe

Olympiad workbook Solution View → 9

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

Olympiad workbook Solution View → 10

For an integer n 3 and a permutation = (p₁, p₂, , p_n ) of 1,2, , n , we say p₁ 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 , the perm

Olympiad workbook Solution View → 11

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 o

Olympiad workbook Solution View → 12

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 be

Olympiad workbook Solution View → 13

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

Olympiad workbook Solution View → 14

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 right

Olympiad workbook Solution View → 15

The incircle 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 and the sides A B and A C .

Olympiad workbook Solution View → 16

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

Olympiad workbook Solution View → 17

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 B

Olympiad workbook Solution View → 18

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 th

Olympiad workbook Solution View → 19

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 the equ

Olympiad workbook Solution View → 20

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 16856 oc

Olympiad workbook Solution View → 21

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 l+m+n .

Olympiad workbook Solution View → 22

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 ?

Olympiad workbook Solution View → 23

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 | ?

Olympiad workbook Solution View → 24

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 .

Olympiad workbook Solution View → 25

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 .

Olympiad workbook Solution View → 26

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? (Th

Olympiad workbook Solution View → 27

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? (Th

Olympiad workbook Solution View → 28

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 P

Olympiad workbook Solution View → 29

Let ₁ be a circle with centre O and let AB be diameter of ₁ . Let P be a point on the segment OB different from O . Suppose another circle ₂ with centre P lies in the interior of ₁

Olympiad workbook Solution View → 30

A triangle A B C with A C=20 is inscribed in a circle m . A tangent t to 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 tr

Olympiad workbook Solution View → 31

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 . If P Q inters

Olympiad workbook Solution View → 32

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 ,

Olympiad workbook Solution View → 33

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 A=m

Olympiad workbook Solution View → 34

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 form

Olympiad workbook Solution View → 35

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 form

Olympiad workbook Solution View → 36

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, P ₉

Olympiad workbook Solution View → 37

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, P ₉

Olympiad workbook Solution View → 38

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

Olympiad workbook Solution View → 39

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

Olympiad workbook Solution View → 40

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.

Olympiad workbook Solution View →
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