[" 11."13(y-4)-3(y-9)-5(y+4)=0],[" 13."6(3x+2)-5(6x-1)=3(x-8)-5(7x]

(x-4)(x-3)=(x-6)(x-5) (y-9)(y-3)= (y-4)(y-3)

( 5)/(x) + 6y = 13, (3)/(x) + 4y = 7 ( x ne 0 )

Find each of the following products: (i) (x + 3) (x - 3) (ii) (2x + 5)(2x - 5) (ii) (8 + x)(8 - x) (iv) (7x + 11y) (7x - 11y) (v) (5x^(2) + (3)/(4) y^(2)) (5x^(2) - (3)/(4) y^(2)) (vi) ((4x)/(5) - (5y)/(3)) ((4x)/(5) + (5y)/(3)) (vii) (x + (1)/(x)) (x - (1)/(x)) (viii) ((1)/(x) + (1)/(y)) ((1)/(x) - (1)/(y)) (ix) (2a + (3)/(b)) (2a - (3)/(b))

The line of intersection of the planes vecr.(3hati-hatj+hatk)=1 and vecr.(hati+4hatj-2hatk)=2, is (A) (x-6/13)/2=(y-5/13)/-7=z/-13 (B) (x-6/13)/2=(y-5/13)/7=z/-13 (C) (x-4/7)/-2=y/7=(z-5/7)/13 (D) (x-4/7)/-2=y/-7=(z+5/7)/13

Solve by cross-multiplication method. (i) 8x-3y=12,5x=2y +7 (ii) 6x+ 7y -11 =0, 5x+ 2y =13 (iii) (2)/(x)+(3)/(y) =5, (3)/(x) -(1)/(y) +9=0

Solve by the method of elimination 2x-y=3,3x +y=7 (ii) x-y=5, 3x+ 2y = 25 (iii) (x)/(10 ) +(y)/(5) =14 ,(x)/( 8) + (y)/( 6) =15 (iv) 3(2x+y) =7xy,3 (x+3y ) =11xy (v) (4)/(x) +5y =7,(3)/(x) +4y =5 (vi) 13x +11y = 70,11x +13y =74

Find the equations of the tangent and normal to the given curves at the indicated points : (i) y=x^(4)-6x+13x^(2)-10x+5" at "(0, 5) (ii) y=x^(4)-6x^(3)+13x^(2)-10x+5" at "(1, 3) . (iii) y= x^(3)" at " (1, 1) (iv) y=x^(2)" at " (1, 1) (v) x =cost, y = sin t" at "y=(pi)/(4) .

Solve for x and y : ( 3x )/( 2) - ( 5y )/( 3) = - 2, ( x)/(3) + ( y)/(2) = (13)/(6)

The locus of a point "P" ,if the join of the points (2,3) and (-1,5) subtends right angle at "P" is x^(2)+y^(2)-x-8y+13=0 x^(2)-y^(2)-x+8y+3=0 x^(2)+y^(2)-4x-4y=0,(x,y)!=(0,4)&(4,0) x^(2)+y^(2)-x-8y+13=0,(x,y)!=(2,3)&(-1,5)

If X = {1,2,3,4,5}, Y = {1,3,5,7,9} determins which of the following relations from X to Y are functions ? Give reasonfor your answer. If it is a function. State its type. (i) R_(1) = {(x,y) | y = x + 2, x in X , y in Y } (ii) R_(2) = {(1,1),(2,1),(3,3),(4,3),(5,5)} (iii) R_(3) { (1,1),(1,3),(3,5),(3,7),(5,7)} (iv) R_(4) {(1,3),(2,5),(4,7),(5,9),(3,1)}