If `(x^2+p x+1)` is a factor of `(a x^3+b x+c),t h e n` a.`a^2+c^2=-a b` b. `a^2-c^2=-a b` c. `a^2-c^2=a b` d. none of these

If a!=0 and the line 2b x+3c y+4d=0 passes through the points of intersection of the parabolas y^2=4a x and x^2=4a y , then (a) d^2+(2b+3c)^2=0 (b) d^2+(3b+2c)^2=0 (c) d^2+(2b-3c)^2=0 (d)none of these

If af(x+1)+bf(1/(x+1))=x ,x!=-1,a!=b ,t h e nf(2) is equal to (a) (2a+b)/(2(a^2-b^2)) (b) a/(a^2-b^2) (c) (a+2b)/(a^2-b^2) (d) none of these

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

Let f(x)=(1+x)/(1-x) . If A is matrix for which A^3=O ,t h e nf(A) is (a) I+A+A^2 (b) I+2A+2A^2 (c) I-A-A^2 (d) none of these

If both roots of the equation a x^2+x+c-a=0 are imaginary and c > -1, then a. 3a >2+4c b. 3a<2+4c c. c < a d. none of these

If in the expansion of (1+x)^n ,a ,b ,c are three consecutive coefficients, then n= (a c+a b+b c)/(b^2+a c) b. (2a c+a b+b c)/(b^2-a c) c. (a b+a c)/(b^2-a c) d. none of these

The area of a parallelogram formed by the lines a x+-b x+-c=0 is (a) (c^2)/((a b)) (b) (s c^2)/((a b)) (c) (c^2)/(2a b) (d) none of these

If the equations a x^2+b x+c=0a n dx^3+3x^2+3x+2=0 have two common roots, then a. a=b=c b. a=b!=c c. a=-b=c d. none of these

If A=[a b c d] (where b c!=0 ) satisfies the equations x^2+k=0,t h e n a+d=0 b. K=-|A| c. k=|A| d. none of these

If the ratio of the roots of a x ^2+2b x+c=0 is same as the ratios of roots of p x^2+2q x+r=0, then a. (2b)/(a c)=(q^2)/(p r) b. b/(a c)=(q^)/(p r) c. (b^2)/(a c)=(q^2)/(p r) d. none of these