The product of two consecutive integers is divisible by 2. Is this statement true or false? Give reason.

(a) True (b) False (c) True (d) False (e) True

Solution: True. Justification: Let a, a + 1 be two consecutive positive integers. By Euclid’s division lemma, we have a = bq + r, where 0 ≤ r < b For b = 2 , we...

Solution: True. Justification: At least one out of every three consecutive positive integers is divisible by 2. Therefore, The product of three consecutive positive integers is divisible by 2. At least one out of every...

Solution: Let the three consecutive positive integers be n, n + 1 and n + 2, where n is any integer. By Euclid’s division lemma, we have a = bq + r; 0 ≤...

(a) Androgens are produced by Sertoli cells. (False) Androgens are produced by Leydig cells found in seminiferous tubules of the testis. (b) Spermatozoa get nutrition from Sertoli cells. (True) (c) Leydig cells are...

Let the three consecutive integers bex, x+1and x+2. According to the question, x+x+1+x+2 = 51 => 3x+3=51 => 3x+3-3=51-3 [Subtracting 3 from both sides] => 3x=48 => 3x/3 = 48/3 [Dividing both sides by 3] X=16 Hence, first...

Let, (n – 1) and n be two consecutive positive integers ∴ Their product = n(n – 1) = n 2 −n We know that any positive integer is of the form 2q...

True, because n(n+1)(n+2) will always be divisible by 6, as least one of the factors will be divisible by 2 and at one of the factors will be divisible by...

(i) False If P = {m, n} and Q = {n, m}, then P × Q = {(m, m), (m, n), (n, m), (n, n)} (ii) True (iii) True

True, because n(n + 1) will always be even, as one out of the n or n+1 must be even.