Counter example to “product of two odd integers is even” is
A) 7 × 5 = 35
B) 3 × 4 = 12
C) 2 × 6 = 12
D) Not possible
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There are three odd numbers and one even number. What type of number is their sum ?
Correct option is (D) Odd number Sum of three odd numbers is odd. Sum of an odd number and an even number is odd. \(\therefore\) Sum of three odd numbers and one even number is odd.
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There are three odd numbers and one even number. What type of number is their sum ?
2 Answers
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Number of odd integers between 1000 and 8000 which have none of their digits repeated, is : (A) 1014 (B) 810 (C) 690 (D) 1736
There are two restrictions operating this question. 1. For a number to be odd, the unit digit should be either 1,3,5,7 or 9. 2. Thousand can not be filled with 8 or...
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If n is odd, then an + bn is divisible by (a + b) and an− bn is divisible by (a − b). If n is even, then an− bn is divisible by (a − b) and (a + b) .
12011 + 22011 + 32011 +...... +20102011 = (12011 + 20102011) + (22011 + 20092011) + (32011 + 20082011) ...... (10112011 + 10002011) These terms are of the form an + bn, so they will be divided by a + b, as n...
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The statement “the sum of two odd numbers is odd” is
B) always false
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A counter example to the statement “In any right triangle the square of the smallest side equals to sum of the other sides” is
Correct option is C) (6, 8, 10)
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The product of two consecutive even numbers is always divisible by
Correct option is C) 4
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Counter example to”2n^2 + 11 is a prime” is
Correct option is D) 11
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Use the definition of Odd and Even functions to determine whether each of the following functions is Odd, Even, or neither. Must show your work for credit II! 1) \( f(x)=\frac{x}{1-x^{3}} \) 2) \( f(x)=\frac{x^{2}}{1+x} \) 3) \( \quad f(x)=x-|x| \)
(1) f(x) = \(\frac{x}{1-x^3}\) f(-x) = \(\frac{-x}{1-(-x)^3}\) = \(\frac{-x}{1+x^3}\) ≠ -f(x) or f(x) ∴ f(x) is neither even nor odd function. (2) f(x) = \(\frac{x^2}{1+x}\) ∴ f(-x) = \(\frac{(-x^2)}{1+(-x)}\) = \(\frac{x^2}{1-x}\) ≠ -f(x) or f(x). (3) f(x) = x-|x| ∴ f(-x) = -x-|-x| = -x-|x| = -(x+|x|) ≠ -f(x)...
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Find the consecutive even integers whose squares have the sum 340.
Let the consecutive even integers be ‘a’ and a + 2 ⇒ a2 + (a + 2)2 = 340 ⇒ 2a2 + 4a – 336 = 0 ⇒ a2 + 2a – 168...
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