If `n in N >1` , then the sum of real part of roots of `z^n=(z+1)^n` is equal to `n/2` b. `((n-1))/2` c. ` n/2` d. `((1-n))/2`

A B C is a right-angled triangle in which /_B=90^0 and B C=adot If n points L_1, L_2, ,L_nonA B is divided in n+1 equal parts and L_1M_1, L_2M_2, ,L_n M_n are line segments parallel to B Ca n dM_1, M_2, ,M_n are on A C , then the sum of the lengths of L_1M_1, L_2M_2, ,L_n M_n is (a(n+1))/2 b. (a(n-1))/2 c. (a n)/2 d. none of these

If tanx=ntany ,n in R^+, then the maximum value of sec^2(x-y) is equal to (a) ((n+1)^2)/(2n) (b) ((n+1)^2)/n (c) ((n+1)^2)/2 (d) ((n+1)^2)/(4n)

If n >1 , show that the roots of the equation z^n=(z+1)^n are collinear.

sum_(k=1)^ook(1-1/n)^(k-1)= a. n(n-1) b. n(n+1) c. n^2 d. (n+1)^2

If omega is a complex nth root of unity, then sum_(r=1)^n(ar+b)omega^(r-1) is equal to A.. (n(n+1)a)/2 B. (n b)/(1+n) C. (n a)/(omega-1) D. none of these

The value of sum_(r=1)^n(-1)^(r+1)("^n C r)/(r+1) is equal to a. -1/(n+1) b. 1/n c. 1/(n+1) d. n/(n+1)

If a_1,a_2, .....,a_n are positive real numbers whose product is a fixed number c , then the minimum value of a_1+a_2+.........+a_(n-1)+2a_n is a. a_(n-1)+2a_n b. (n+1)c^(1//n) c. 2n c^(1//n) d. (n)(2c)^(1//n)

Two players P_1a n dP_2 play a series of 2n games. Each game can result in either a win or a loss for P_1dot the total number of ways in which P_1 can win the series of these games is equal to a. 1/2(2^(2n)-^ "^(2n)C_n) b. 1/2(2^(2n)-2xx^"^(2n)C_n) c. 1/2(2^n-^"^(2n)C_n) d. 1/2(2^n-2xx^"^(2n)C_n)

Let A be a set of n(geq3) distance elements. The number of triplets (x ,y ,z) of the A elements in which at least two coordinates is equal to a. ^n P_3 b. n^3-^n P_3 c. 3n^2-2n d. 3n^2-(n-1)

Matrix A such that A^2=2A-I ,w h e r eI is the identity matrix, the for ngeq2. A^n is equal to 2^(n-1)A-(n-1)l b. 2^(n-1)A-I c. n A-(n-1)l d. n A-I