Prime numbers
It can only be divided by one or itself i.e., a prime number has no factors other than 1 and itself. e.g., 2, 3, 5, 7, 11, 13, 17, 19, 23, are examples of prime numbers..
Set of question and answer on Number Theory
Question 1 - Question: For the given sequence, suggest possible next three terms and find the general term. 7, 11, 15,---- Answer: First term = 7, Common Difference = 11 - 7 = 15 - 11 = 4 Next three terms are 15 + 4 = 19, 19 + 4 = 23, 23 +..
Introduction
.02 cm. The unit of accuracy required is hundredth of a centimeter. Therefore, only digit 2 is significant. The 0 after decimal indicates the magnitude of measurement. Therefore, the 0 after decimal point is not significant. .02 cm has one significant figure. To sum up the above examples:..
Question 2
Question: For given sequence, suggest possible next three terms and find the general term. 7,11,15,... Answer: First term=7, Common difference =11 -7 = 15 - 11 = 4 The three terms form an A.P. Next three terms are 15 + 4 = 19, 19..
Question: For given sequence, suggest possible next three terms and find the general term. 7,11,15,... Answer: First term=7, Common difference =11 -7 = 15 - 11 = 4 The three terms form an A.P. Next three terms are 15 + 4 = 19, 19..Approximation
Approximation - We know that the digits of a number, one by one in order from left to right decrease in value rapidly. Let us illustrate it by examples. Mass of a gold ornament is 23.473 g. Round off to (i) two decimal places, (ii) one decimal place. 23.473 g = (2 x 10) + (3 x 1..
Surd
is NOT a surd because and 3 is NOT an irrational number. Without using tables, simplify: (i) 36 - 1 / 2 (ii) (i) 36 - 1 / 2 = (6 2 ) - 1 / 2 = 6 - 1 (i..
is NOT a surd because and 3 is NOT an irrational number. Without using tables, simplify: (i) 36 - 1 / 2 (ii) (i) 36 - 1 / 2 = (6 2 ) - 1 / 2 = 6 - 1 (i..Numbers prime to each other
Such numbers have only 1 as common factor even though they may be composite numbers e.g., 21 and 32 are prime to each other. We generally write (21, 32) = 1, which means 21 and 32 are prime to each other i.e., they have only one factor in common viz., ..
Question 7
Question: The first term of an AP is 73, common difference is -7. If the last term of the AP is -95, find the number of terms. Answer: Hence, the number of terms is 25..
Question: The first term of an AP is 73, common difference is -7. If the last term of the AP is -95, find the number of terms. Answer: Hence, the number of terms is 25..Question 7
Question: Find the first five terms of the sequence defined by t n = 6 - 4n. Which term of the sequence is -50? Answer: t n = 6 - 4n When n = 1, t 1 = 6 - 4(1) = 2 When n = 2, t 2 = 6 - 4(2) = -2 When n = 3, t 3 = 6 - 4(3) = -6 When n = 4, t 4 = 6 - 4(4) = -10 When n = 5..
Question: Find the first five terms of the sequence defined by t n = 6 - 4n. Which term of the sequence is -50? Answer: t n = 6 - 4n When n = 1, t 1 = 6 - 4(1) = 2 When n = 2, t 2 = 6 - 4(2) = -2 When n = 3, t 3 = 6 - 4(3) = -6 When n = 4, t 4 = 6 - 4(4) = -10 When n = 5..Example 7:
If a:b=4:5, b:c=6:7, find a:c and a:b:..
Result
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