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: […]
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 […]
Here is a variant of clueless Sudoku that I was trying for fun. In clueless Sudoku A n*n board is given No numbers are written on the board The board is divided in some blocks (typically in some pattern). Sum of numbers in each block must be constant. Numbers 1 to n must appear in […]
What is the value of \( \dfrac{11!-10!}{9!}\)? (A) 99 (B) 100 (C) 110 (D) 121 (E) 132 For what value of \( x \) does \( 10^x \cdot 100^{2x} = 1000^5 \)? (A) 1 (B) 2 (C) 3 (D) 4 (E) 5 For every dollar Ben spent on bagels, David spent 25 cents less. Ben paid $12.50 more than David. […]
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 […]