The sum of the series `a-(a+d)+(a+2d)-(a+3d)+` up to `(2n+1)` terms is- a. `-n d`. b. `a+2n d`. c. `a+n d`. d. `2n d`

If the sum of n terms of an A.P.is 2n^(2)+5n then its nth term is 4n-3 b.3n-4 c.4n3 d.3n+4

Assertion: The sum of 'n' terms of the series 2+8+14+.. is 3n^(2)-n Reason : If the series is an A.P.with c.d.6 the sum of 'n' terms is 3n^(2)-n

Statement-1: The sum of n terms of the series a+(a+d)+(a+2d)+...(a+(n-1)d)=(n)/(2)[2n+(n-1)d] Statement-2:- Mathematical induction is valid only for natural numbers.

In an arithmetic series, the sum of the first 2n terms is half the sum of the first 3n terms. If a = 12 and d = 3, find the value of n.

In an A.P. with first term 'a' and the common difference d(a, d!= 0) , the ratio 'rho' of the sum of the first n terms to sum of n terms succedding them does not depend on n . Then the ratio (a)/(d) and the ratio 'rho' , respectively are

The sum of first n odd natural numbers is 2n-1 (b) 2n+1 (c) n^2 (d) n^2-1

In a parallelogram A B C D diagonals A C\ a n d\ B D intersect at O\ a n d\ A C=6. 8\ c m\ a n d\ B D=5. 6 c m . Find the measures of O C\ a n d\ O D .

Let f,\ g\ a n d\ h be real-valued functions defined on the interval [0,\ 1] by f(x)=e^x^2+e^-x^2,\ g(x)=x e^x^2+e^-x^2\ a n d\ h(x)=x^2e^x^2+e^-x^2 . If a , b ,\ a n d\ c denote respectively, the absolute maximum of f,\ g\ a n d\ h on [0,\ 1], then a=b\ a n d\ c!=b (b) a=c\ a n d\ a!=b a!=b\ a n d\ c!=b (d) a=b=c