सिद्ध कीजिए कि सरल रेखाएँ `x=mz+a,y=nz+b` और `x=m'z+a',y=n'z+b'` एक-दूसरे को काटेंगी यदि `(a-a')(n-n')=(b-b')(m-m')` हो।

The area of the parallelogram formed by the lines y=m x ,y=x m+1,y=n x ,a n dy=n x+1 equals. (a) (|m+n|)/((m-n)^2) (b) 2/(|m+n|) 1/((|m+n|)) (d) 1/((|m-n|))

If a = x^(m + n) . Y^(l), b = x^(n + l). Y^(m) and c = x^(l + m) . Y^(n) , Prove that : a^(m-n) . b^(n - 1) . c^(l-m) = 1

If a=x^(m+n)\ y^l,\ b=x^(n+l)\ y^m and c=x^(l+m)y^n , prove that a^(m-n)\ b^(n-l)\ c^(l-m\ )=1

The equation of the plane through the intersection of the plane a x+b y+c z+d=0\ a n d\ l x+m y+n+p=0 and parallel to the line y=0,\ z=0. (A) (b l-a m)y+(c l-a n)z+d l-a p=0 (B) (a m-b l)x+(m c-b n)z+m d-b p=0 (c) (n a-c l)d+(b n-c m)y+n d-c p=0 (D) None of these

The equation of the plane through the intersection of the plane a x+b y+c z+d=0\ a n d\ l x+m y+n+p=0 and parallel to the line y=0,\ z=0. (A) (b l-a m)y+(c l-a n)z+d l-a p=0 (B) (a m-b l)x+(m c-b n)z+m d-b p=0 (c) (n a-c l)d+(b n-c m)y+n d-c p=0 (D) None of these

If y=(x-a)^(m)(x-b)^(n) , prove that (dy)/(dx)=(x-a)^(m-1)(x-b)^(n-1)[(m+n)x-(an+bm) ].

If a, x_1, x_2, …, x_k and b, y_1, y_2, …, y_k from two A. Ps with common differences m and n respectively, the the locus of point (x, y) , where x= (sum_(i=1)^k x_i)/k and y= (sum_(i=1)^k yi)/k is: (A) (x-a) m = (y-b)n (B) (x-m) a= (y-n) b (C) (x-n) a= (y-m) b (D) (x-a) n= (y-b)m

if x=sum a^(n),y=sum b^(n),z=sum c^(n) where a,b,c are in AP then x,y,z are in

The area of the parallelogram formed by the lines y=m x ,y=x m+1,y=n x ,a n dy=n x+1 equals. (|m+n|)/((m-n)^2) (b) 2/(|m+n|) 1/((|m+n|)) (d) 1/((|m-n|))

If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove that x y z=1