Justin can do 10 math problems in 35 minutes. How long will he take to..
Justin can do 10 math problems in 35 minutes. How long will he take to complete 20 problems? => 65 minutes or 80 minutes or 75 minutes or 70 minutes ..
Examples:
i) A sequence of multiples of 5 5, 10, 15, 20, ii) A sequence of reciprocals of positive integers The above two sequences are clearly the infinite sequence..
i) A sequence of multiples of 5 5, 10, 15, 20, ii) A sequence of reciprocals of positive integers The above two sequences are clearly the infinite sequence..Jason started his lunch at 12:45 P.M. and took 20 minutes to finish hi..
Jason started his lunch at 12:45 P.M. and took 20 minutes to finish his lunch. How long did he eat? => 1:05 P.M. or 3:10 P.M. or 2:00 P.M. or 1:35 P.M...
Question 10
Question: Twelve students are participating in a competition. In how many ways can the first 3 prizes be won? Answer: Number of students participating in the competition = 12 The number of ways in which the first three prizes can be won = P (12,3) = 12 x 11 x 10 = 13..
Question 10
Question: The sides AB, BC, CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be drawn using these points as vertices. Answer: The points 3+4+5=12 points lie in a plane. To construct a triangle, we require three non-collinea..
Question: The sides AB, BC, CA of a triangle ABC have 3, 4 and 5 interior points respectively on them. Find the number of triangles that can be drawn using these points as vertices. Answer: The points 3+4+5=12 points lie in a plane. To construct a triangle, we require three non-collinea..Suggested answer:
Number of ways of filling hundred's place = 2 Number of ways of filling ten's place = 2 Number of ways of filling unit's place = 2 By the fundamental principle of counting, the total number of numbers = 2 x 2 x 2 =..
Example:
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..Question 6
Question: At an election, three wards of a town are canvassed by 4, 5 and 8 men respectively. If 20 men volunteer, in how many ways can they be allotted to the different wards? Answer: Let the three wards be labelled as A, B and C respectively. Let us select 4 men fo..
Question: At an election, three wards of a town are canvassed by 4, 5 and 8 men respectively. If 20 men volunteer, in how many ways can they be allotted to the different wards? Answer: Let the three wards be labelled as A, B and C respectively. Let us select 4 men fo..Example:
The matrices are scalar matrices of order 2 and 3 respectivel..
The matrices are scalar matrices of order 2 and 3 respectivel..Proof:
If r = s, there is nothing to prove. Now, If r < s, then n - r > n - s, then the above equation becomes Since both sides are products of (s-r), consecutive integers in Similarly it can be proved that n = r + s if r > s...
If r = s, there is nothing to prove. Now, If r < s, then n - r > n - s, then the above equation becomes Since both sides are products of (s-r), consecutive integers in Similarly it can be proved that n = r + s if r > s... Result
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