-(T,2x+3y=2;(c+2)x+(2c+1)y=2(c-1)

The value of cor which the system of equations (inx and y )x+y=2(c+1)x+(c+2)y=c+3 and (c+1)^(2)x+(c+2)^(2)y=(c+3)^(2) is consistent,is

xe^(-y)dx+ydy=0 A) 2x^(2)+(y-1)e^(y)=c B) (x^(2))/(2)+(y-1)e^(y)=c C) (y^(2))/(2)+(x-1)e^(x)=c D) 2y^(2)+(x-1)e^(x)=0

If (x_(1)-x_(2))^(2) + (y_(1)-y_(2))^(2)=a^(2) , (x_(2)-x_(3))^(2) + (y_(2) - y_(3))^(2)=b^(2) , (x_(3)-x_(1))^(2) + (y_(3) - y_(1))^(2) = c^(2) and k[|(x_(1),y_(1),1),(x_(2),y_(2),1),(x_(3),y_(3),1)|]^2=(a+b+c)(b+c-a)(c+a-b)(a+b-c) then the value of k a)1 b)2 c)4 d)none of these

If the circle x^(2)+y^(2)=a^(2) intersects the hyperbola xy=c^(2) in four points P (x_(1) ,y_(1)) Q (x_(2), y_(2)) R (x_(3) ,y_(3)) S (x_(4) ,y_(4)) then 1) x_(1)+x_(2)+x_(3)+x_(4)=2c^(2) 2) y_(1)+y_(2)+y_(3)+y_(4)=0 3) x_(1)x_(2)x_(3)x_(4)=2c^(4) 4) y_(1)y_(2)y_(3)y_(4)=2c^(4)

If x=a t^2,\ \ y=2\ a t , then (d^2y)/(dx^2)= -1/(t^2) (b) 1/(2\ a t^3) (c) -1/(t^3) (d) -1/(2\ a t^3)

If x=a t^2,\ \ y=2\ a t , then (d^2y)/(dx^2)= -1/(t^2) (b) 1/(2\ a t^3) (c) -1/(t^3) (d) -1/(2\ a t^3)

If x=a t^2,\ \ y=2\ a t , then (d^2y)/(dx^2)= (a) -1/(t^2) (b) 1/(2\ a t^3) (c) -1/(t^3) (d) -1/(2\ a t^3)

Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(c-z)^2|= |(1+a x)^2(1+b x)^2(1+c x)^2(1+a y)^2(1+b y)^2(1+c y)^2(1+a z)^2(1+b z)^2(1+c z)^2|= 2(b-c)(c-c)(a-b)xx(y-z)(z-x)(x-y)dot

(i) Find the value of 'a' if the lines 3x-2y+8=0 , 2x+y+3=0 and ax+3y+11=0 are concurrent. (ii) If the lines y=m_(1)x+c_(1) , y=m_(2)x+c_(2) and y=m_(3)x+c_(3) meet at point then shown that : c_(1)(m_(2)-m_(3))+c_(2)(m_(3)-m_(1))+c_(3)(m_(1)-m_(2))=0