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The Sum Of The Integers From 1 To 100 Which Are Divisible By 3 And 5 Is

Solution: LCM of 3 and 5 is 15. The numbers between 1 and 100 which are divisible by both 3... View Article

Solution: Let x = log2 7 Then 2x = 7 (since logb(x) = y, then by = x) This is... View Article

Solution: Let the numbers be x-d, x, x+d Sum = x-d+x+x+d = 18 3x = 18 x = 6 So... View Article

Let a1, a2, a3,… be terms of an AP. If (a1+a2+…ap.)/(a1+a2+…aq) = p2/q2, p not equal to q, then a6/a21... View Article

Solution: Let T1 = a, common difference = d Tm => a+(m-1)d = 1/n…(i) Tn => a+(n-1)d = 1/m…(ii) (i)... View Article

If the arithmetic mean of a and b is (an+bn)/(an-1 +bn-1) then the value of n is (1) -1 (2)... View Article

If a/(b+c), b/(c+a), c/(a+b) are in AP, then (1) a,b,c are in AP (2) c,a,b are in AP (3) a2,... View Article

Solution: Given a2, b2, c2 are in AP. b2-a2 = c2-b2 …(i) a/sin A = b/sin B = c/sin C... View Article

Solution: For an AP, nth term = a+(n-1)d pth term => a+(p-1)d = q ..(i) qth term => a+(q-1)d =... View Article

The sets S1 ,S2, S3,… are given by S1 = { 2/1}, S2 = { 3/2, 5/2}, S3 = {... View Article

Solution: Since a,b,c are in AP, we know 2b = a+c (a + 2b – c) = a+a+c-c = 2a... View Article

Solution: nth term of AP, an = a+(n-1)d a12 = a+(12-1)d = a+11d a22 = a+(22-1)d = a+21d Given sum... View Article

Solution: Given AP 2,5,8,11.. First term, a = 2 Common difference, d = 5-2 = 3 Sum of n terms... View Article

Solution: Given sum of n terms of AP = 2n+3n2 …(i) Put n = 1 in (i) S1 = 2+3... View Article

Solution: First n odd natural numbers are 1,3,5,..n This is an A.P. Here a = 1 d = 2 Sum... View Article

The sum of the first n terms of the series 1/2 + 3/4 + 7/8 + 15/16 + …….is equal... View Article

Solution: Given a,b,c in G.P. So b2 = ac Hence b = √ac ax2+2bx+c = 0 Put b = √(ac)... View Article

Solution: Let 1000x – x = 2355 999x = 2355 x = 2355/999 Hence option (3) is the answer.

Solution: Let a be the first term of G.P and r be the common ratio. Given 3rd term is 4.... View Article

An object that is moving under the absolute control of gravity is a free falling object. Any object that is... View Article