Let's understand Fixed Point of continuous bounded function with the help of a problem. This problem is useful for College Mathematics.
Let's understand Fixed Point of continuous bounded function with the help of a problem. This problem is useful for College Mathematics.
Given any integer $n \ge 2 $ , we can always find an integer m such that each of the n-1 consecutive integers m + 2, m + 3,..., m + n are composite. True Discussion: Take m=n!. Then the consecutive integers n! + 2 , n! + 3 , ... n! + n are […]
Let's discuss a problem based on Least Value of a Sum of Complex Numbers. Try to solve it yourself before reading the solution. Problem: Least Value of a Sum of Complex Numbers If $ z_1 , z_2 , z_3 , z_4 \in \mathbb{C} $ satisfy $ z_1 + z_2 + z_3 + z_4 = 0 […]
A lamp is placed on the ground 100 feet away from a wall. A man six feet tall is walking at a speed of 10 ft/sec from the lamp to the nearest point on the wall. When he is midway between the lamp and the wall, the rate of change in the length of his shadow is (in ft/ sec)?
View the other sections of this test. Algebra || Geometry Try a online trial session of Cheenta I.S.I. M.Math, IIT JAM, TIFR Entrance Program. Mail us at helpdesk@cheenta.com View the other sections of this test. Algebra || Geometry Try a online trial session of Cheenta I.S.I. M.Math, IIT JAM, TIFR Entrance Program. Mail us at […]
Section 3: Geometry View the other sections of this test. Algebra || Analysis Try an online trial session of Cheenta I.S.I. M.Math, IIT JAM, TIFR Entrance Program. Mail us at helpdesk@cheenta.com Find the reflection of the point (2, 1) with respect to the line x=y in the xy-plane. Find the area of the circle in […]
Section 1: Algebra View the other sections of this test. Geometry || Analysis Try a online trial session of Cheenta I.S.I. M.Math, IIT JAM, TIFR Entrance Program. Mail us at helpdesk@cheenta.com Which of the following statements are true? Every group of order 11 is cyclic. Every group of order 111 is cyclic. Every group of […]
Any normal subgroup of order 2 is contained in the center of the group. True Discussion: Center of a group Z(G) is the sub group of elements that commute with all members of the group. A subgroup of order two has two elements: identity element and another element, say x, which is self inverse. Since […]
There is an element of order 51 in the multiplicative group (Z/103Z) True Discussion: First note that (Z/103Z) has 102 elements as 103 is a prime (in fact one of the twin primes of 101, 103 pair). Also 102 = 2317. So it has Sylow-3 subgroup of order 3 (prime order hence it is cyclic […]
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Triangle and Trigonometry.
Try this beautiful problem from Pre-Regional Mathematics Olympiad, PRMO, 2012 based on Triangle You may use sequential hints to solve the problem.
Try this beautiful problem from American Invitational Mathematics Examination, AIME, 1999 based on Probability in Games. You may use sequential hints.
Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2000 based on Least Positive Integer.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2015 based on Theory of Equations.
Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2013 based on HCF. You may use sequential hints to solve the problem.
Try this beautiful problem from Singapore Mathematics Olympiad based on area of triangle. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2019 based on Equations and Complex numbers.
Try this beautiful problem from American Invitational Mathematics Examination, AIME, 2009 based on Probability of tossing a coin.
Try this beautiful problem from the American Invitational Mathematics Examination, AIME, 2009 based on Equations with a number of variables.