Prove that :`(200 !)/((10 !)^(20)19 !)` is an integer

Prove that 19^(93) - 13 ^(99) is positive integer divisible by 162.

prove that sum_(k=0)^10 20^C_k=2^(19)

Prove that sqrt(10)[(sqrt(10)+1)^(100)-(sqrt(10)-1)^(100)] is an even integer .

Prove that sqrt(10)[(sqrt(10)+1)^(100)-(sqrt(10)-1)^(100)] is an even integer .

Prove that sqrt(10)[(sqrt(10)+1)^(100)-(sqrt(10)-1)^(100)] is an even integer .

. Let a_(1),a_(2),a_(3)... be in AP and g_(1),g_(2)... be in GP If a_(1),g_(1)=2 and a_(10)=g_(10)=3, then (A)a_(19*)g_(7) is an integer (B) a_(7)g_(19) is an integer (C) a_(19)g_(10) is not an integer (D) none of these

Prove that sqrt(10)[(sqrt(10)+1)^(100)-(sqrt(10)-1)^(100)] is an even integer.

.Let a_1, a_2, a_3... be in AP and g_1, g_2... be in GP If a_1, g_1=2 and a_(10) = g_(10)=3 , then (A) a_(19).g_7 is an integer (B) a_7g_(19) is an integer (C) a_(19)g_(10) is not an integer (D) none of these

Let a and b be the 2 consecutive integers selected from the first 20 natural numbers. The probability that sqrt(a^(2) + b^(2) + a^(2)b^(2)) is an odd positive integer is a) (9)/(13) b) (10)/(19) c) (13)/(19) d)1

Prove that 4(cos ^(3) 10^(@) + sin ^(3) 20^(@)) = 3 ( cos 10^(@) + sin 20^(@)).