Let's discuss a Common but deadly question in Group theory. Question: Is it possible to get an infinite group which has elements of finite order? Discussion To pursue this discussion which is basically a very good concept for the students who are new in group theory, they must know first about the QUOTIENT GROUPS. Particularly […]
Try this problem from TOMATO Problem 7 based on the Parity of the terms of a sequence. Problem: Parity of the terms of a sequence If \( a_0 = 1 , a_1 = 1 \) and \( a_n = a_{n - 1} a_{n - 2} + 1 \) for \( n > 1 \), then: […]
This is a problem from TOMATO Problem number 2, useful for ISI and CMI entrance exam based on Men and Job. Problem: If m men can do a job in d days, then the number of days in which m+r men can do the job is (A) d+r; (B) $\frac{d}{m} (m+r)$ ; (C) $\frac {d}{m+r}$ […]
This is a problem number 3 from TOMATO based on Calculating Average Speed. Problem: Calculating Average Speed. A boy walks from his home to school at 6 kmph. He walks back at 2 kmph. His average speed, in kmph is (A) 3; (B) 4; (C) 5; (D) $\sqrt {12}$; Discussion: Suppose the distance from home […]
This is a problem number 95 from TOMATO based on finding the Number of factors of 1800. Problem The number of different factors of $1800$ equals: (A) $12$; (B) $210$; (C) $36$; (D) $18$; Discussion: We may factor $1800$ as $2^3 \times 3^2 \times 5^2 $ Then the number of factors is: $(3+1) \times (2+1) […]
This is an objective problem from TOMATO based on finding the Number of Positive Divisors. Problem: The number of positive integers which divide $240$ is- (A) $18$; (B) $20$; (C) $30$; (D) $24$; Discussion: We use the formula for computing number of divisors of a number: Step 1: Prime factorise the given number $240 = […]
Let us discuss about 'inequality' related problems - Minimum Perimeter Problem. All algebraic inequality problems can be traced back to two key ideas: Positive times positive is positive Square of a real number is nonnegative Though these two notions seem trivial and obvious in nature, they lead to a very rich and diverse theory of […]
A worker suffers a 20% cut in wages. He regains his original pay by obtaining a rise of (A) 20% (B) 22.50% (C) 25% (D) 27.50 % If \( \mathbf {m} \) men can do a job in \( \mathbf {d} \) days , then the number of days in which \( \mathbf {m+r} \) […]
This post contains ISI TOMATO Solutions of Objective Problems from 101 to 200. The number of ways of distributing 12 identical oranges among children so that every child gets at least one and no child more than 4 is(A) 31;(B) 52;(C) 35;(D) 42. The number of terms in the expansion of $latex {[(a+3b)^2(a-3b)^2]^2}$ , when […]
Sine rule is an important rule relating to the sides and angles of any triangle. Here is a Subjective problem no. 120 from TOMATO. Try it. Problem: Sine Rule and Triangle (i) If $ A + B +C = n \pi $ and $ s=2 $, show that $ \sin 2A + \sin 2B + […]
Try this beautiful problem from Probability: positive factors AMC-10A, 2003. You may use sequential hints to solve the problem
Try this beautiful problem from AMC 10A, 2007 based on Numbers on cube. You may use sequential hints to solve the problem.
Try this beautiful problem from the Pre-RMO, 2017 based on Integers and Inequality. You may use sequential hints to solve the problem.
Try this beautiful problem from Singapore Mathematics Olympiad, SMO, 2011 based on Permutation. You may use sequential hints to solve the problem.
Try this beautiful problem from AMC-10A, 2009 based on Diamond Pattern. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1995 based on GCD and Ordered pair.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1997 based on Trigonometry and greatest integer.
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 Pre-RMO, 2017 based on Series Problem. You may use sequential hints to solve the problem.
Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1995 based on Trigonometry and positive integers.