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`

The mean deviation of the series a, a+d, a+2d, . . . , a+2n from its mean is -

Mean of the first n terms of the A.P a,(a+d),(a+2d),….. is

If the sum to infinity of the series 3+(3+d)1/4+(3+2d)1/(4^2)+......oo is (44)/9 , then find d ddot

The mean deviation of the series a , a+d , a+2d ,.....,a+2nd from its mean is (a) ((n+1)d)/(2n+1) (b) (n d)/(2n+1) (c) (n(n+1)d)/(2n+1) (d) ((2n+1)d)/(n(n+1))

If the sum of m terms of an A.P. is the same as the sum of its n terms, then the sum of its (m+n) terms is (a). m n (b). -m n (c). 1//m n (d). 0

If the 4th term in the expansion of (a x+1//x)^n is 5/2, then a. a=1/2 b. n=8 c. a=2/3 d. n=6

The position vectors of the vertices A ,Ba n dC of a triangle are three unit vectors vec a , vec b ,a n d vec c , respectively. A vector vec d is such that vec d ⋅ vec a = vec d ⋅ vec b = vec d ⋅ vec c a n d vec d=lambda( vec b+ vec c)dot Then triangle A B C is a. acute angled b. obtuse angled c. right angled d. none of these

The number of diagonal matrix, A or order n which A^3=A is a. is a a. 1 b. 0 c. 2^n d. 3^n

Sum of the first n terms of the series 1/2+3/4+7/8+(15)/(16)+......... is equals to (a). 2^n-n-1 (b). 1-2^(-n) (c). n+2^(-n)-1 (d).None of these

If x is real, then x//(x^2-5x+9) lies between a. -1a n d-1//11 b. 1a n d-1//11 c. 1a n d1//11 d. none of these