Let's understand one-one function and differentiability with the help of a problem. Try it yourself before reading the solution. Let f be real valued, differentiable on (a, b) and $ f'(x) \ne 0 $ for all $ x \in (a, b) $. Then f is 1-1. True Discussion: Suppose f is not 1-1. Then there […]
Lets understand direct product of two subgroups 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@dev.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@dev.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@dev.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 […]
Try this beautiful problem from Probability in Dice from AMC-10A, 2009. You may use sequential hints to solve the problem.
Try this beautiful Problem from Singapore Mathematics Olympiad, 2012 based on Functional Equations. You may use sequential hints to solve the problem.
Try this beautiful problem from Pre-Regional Mathematics Olympiad, PRMO, 2018 based on Triangles. You may use sequential hints to solve the problem.
Try this beautiful problem from Pattern based on Triangle from AMC-10A, 2003. You may use sequential hints to solve the problem
Try this beautiful problem from Number theory based on divisibility from AMC-10A, 2003. You may use sequential hints to solve the problem.
Try this beautiful Problem from Singapore Mathematics Olympiad, SMO, 2008 based on Trigonometry. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 2011 based on Rectangles and sides.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Function of Complex numbers.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on Squares and Triangles.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1999 based on A Parallelogram and a Line.