Roots of the equation `|x m n1a x n1a b x1a b c1|)=0` are
independent of `m ,and n`
independent of `a ,b ,and c`
depend on `m ,n ,and a ,b ,c`
independent of `m , n and a ,b ,c`

If A ,B ,C be three mutually independent events, then Aa n dBuuC are also independent events. Statement 2: Two events Aa n dB are independent if and only if P(AnnB)=P(A)P(B)dot

|[1/c,1/c,-(a+b)/c^2],[-(b+c)/a^2,1/a,1/a],[(-b(b+c))/(a^2c),(a+2b+c)/(ac),(-b(a+b))/(ac^2)]| is (a) dependent on a,b,c (b) dependent on a (c) dependent on b (d) independent on a,b and c

If alphaa n dbeta,alphaa n dgamma,alphaa n ddelta are the roots of the equations a x^2+2b x+c=0,2b x^2+c x+a=0a d nc x^2+a x+2b=0, respectively, where a, b, and c are positive real numbers, then alpha+alpha^2= a. a b c b. a+2b+c c. -1 d. 0

Events Aa n dC are independent. If the probabilities relating A ,B ,a n dC are P(A)=1//5, P(B)=1//6; P(AnnC)=1//20 ; P(BuuC)=3//8. Then (a)events Ba n dC are independent (b)events Ba n dC are mutually exclusive events.(c) Ba n dC are neither independent nor mutually exclusive (d)events Ba n dC are equiprobable

Consider a point A(m,n) , where m and n are positve intergers. B is the reflection of A in the line y=x , C is the reflaction of B in the y axis, D is the reflection of C in the x axis and E is the reflection of D is the y axis. The area of the pentagon ABCDE is a. 2m (m+n) b. m (m+3n) c. m(2m+3n) d. 2m(m+3n)

The total number of terms which are dependent on the value of x in the expansion of (x^2-2+1/(x^2))^n is equal to 2n+1 b. 2n c. n d. n+1

If roots of an equation x^n-1=0a r e1,a_1,a_2,..... a_(n-1), then the value of (1-a_1)(1-a_2)(1-a_3)(1-a_(n-1)) will be n b. n^2 c. n^n d. 0

If the ratio of the remainders when the polynomial (x^(2m)+1) is successively divided by (x + a) and (x + b), be b : a, prove that (a^(n)-b^(n))/(b-a)=1 , where n = 2m + 1 and m inN .

If sinthetaa n d-costheta are the roots of the equation a x^2-b x-c=0 , where a , ba n dc are the sides of a triangle ABC, then cosB is equal to 1-c/(2a) (b) 1-c/a 1+c/(c a) (d) 1+c/(3a)

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