If the lines `a x+y+1=0,x+b y+1=0,` and `x+y+c=0(a , b , c` being distinct and different from 1) are concurrent, then `(1/(1-a))+(1/(1-b))+(1/(1-c))=` (a)0 (b) 1 (c)`1/((a+b+c))` (d) none of these

If the lines a x+y+1=0,x+b y+1=0a n dx+y+c=0(a ,b ,c being distinct and different from 1) are concurrent, then prove that 1/(1-a)+1/(1-b)+1/(1-c)=1.

If the lines ax + 2y + 1 = 0, bx + 3y + 1 = 0, cx + 4y + 1 = 0 are concurrent, then a, b, c are in

If y=tan^(-1)((2^x)/(1+2^(2x+1))),t h e n(dy)/(dx)a tx=0 is (a)1 (b) 2 (c) 1n 2 (d) none of these

lim_(x -> oo)(x(log(x)^3)/(1+x+x^2) equals 0 (b) -1 (c) 1 (d) none of these

The straight lines 4a x+3b y+c=0 , where a+b+c are concurrent at the point a) (4,3) b) (1/4,1/3) c) (1/2,1/3) d) none of these

("lim")_(xvec0)1/xcos^(-1)((1-x^2)/(1+x^2)) is equal to (a)1 (b) 0 (c) 2 (d) none of these

The straight lines x+2y-9=0,3x+5y-5=0 , and a x+b y-1=0 are concurrent, if the straight line 35 x-22 y+1=0 passes through the point (a) (a , b) (b) (b ,a) (c) (-a ,-b) (d) none of these

a ,b ,c are distinct real numbers not equal to one. If a x+y+z=0,x+b y+z=0,a n dx+y+c z=0 have nontrivial solution, then the value of 1/(1-a)+1/(1-b)+(1)/(1-c) is equal to a. 1 b. -1 c. z e ro d. none of these

If the straight lines 2x+3y-1=0,x+2y-1=0 ,and a x+b y-1=0 form a triangle with the origin as orthocentre, then (a , b) is given by (a) (6,4) (b) (-3,3) (c) (-8,8) (d) (0,7)

If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 (b) 1 (c) -1 (d) non of these