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`

A ,B ,Ca n dD have position vectors vec a , vec b , vec ca n d vec d , respectively, such that vec a- vec b=2( vec d- vec c)dot Then a. A Ba n dC D bisect each other b. B Da n dA C bisect each other c. A Ba n dC D trisect each other d. B Da n dA C trisect each other

The total number of ways in which 2n persons can be divided into n couples is a. (2n !)/(n ! n !) b. (2n !)/((2!)^3) c. (2n !)/(n !(2!)^n) d. none of these

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

If k in R_ot h e ndet{a d j(k I_n)} is equal to K^(n-1) b. K^(n(n-1)) c. K^n d. k

a ,b ,c x in R^+ such that a ,b ,a n dc are in A.P. and b ,ca n dd are in H.P., then a b=c d b. a c=b d c. b c=a d d. none of these

xy=( x+y )^n and dy/dx = y/x then n= 1 b. 2 c. 3 d. 4

let a > 0 , d > 0 find the value of the determinant |[1/a,1/(a(a + d)),1/( (a + d) (a +2d))],[1/(a+ d),1/( (a+ d) (a + 2d)), 1/((a+2d) (a + 3d))],[1/(a +2d), 1/((a + 2d) (a +3d)), 1/((a+3d) (a + 4d))]|

If vec a , vec b , vec ca n d vec d are four vectors in three-dimensional space with the same initial point and such that 3 vec a-2 vec b+ vec c-2 vec d=0 , show that terminals A ,B ,Ca n d D of these vectors are coplanar. Find the point at which A Ca n dB D meet. Find the ratio in which P divides A Ca n dB Ddot

If ^n C_3+^n C_4>^(n+1)C_3 , then a. n >6 b. n >7 c. n<6 d. none of these

A B C D is a parallelogram. If La n dM are the mid-points of B Ca n dD C respectively, then express vec A La n d vec A M in terms of vec A Ba n d vec A D . Also, prove that vec A L+ vec A M=3/2 vec A Cdot