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 a^2x^4+b^2y^4=c^6, then the maximum value of x y is (a) (c^2)/(sqrt(a b)) (b) (c^3)/(a b) (c) (c^3)/(sqrt(2a b)) (d) (c^3)/(2a b)

The line x/a+y/b=1 meets the x-axis at A , the y-axis at B , and the line y=x at C such, that the area of "Delta"A O C is twice the area of "Delta"B O C . Then the coordinates of C are (b/3, b/3) (b) ((2a)/3,(2a)/3) ((2b)/3,(2b)/3) (d) none of these

C F is the internal bisector of angle C of A B C , then C F is equal to (2a b)/(a+b)cosC/2 (b) (a+b)/(2a b)cosC/2 (c) (b sinA)/(sin(B+C/2)) (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

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

In A B C , if the orthocentre is (0,0) and the circumcenter is (1,2), then centroid of A B C) is (a) (1/2,2/3) (b) (1/3,2/3) (c) (2/3,1) (d) none of these

If the quadrilateral formed by the lines a x+b y+c=0,a^(prime)x+b^(prime)y+c=0,a x+b y+c^(prime)=0,a^(prime)x+b^(prime)y+c^(prime)=0 has perpendicular diagonals, then (a) b^2+c^2=b^('2)+c^('2) (b) c^2+a^2=c^('2)+a^('2) (c) a^2+b^2=a^('2)+b^('2) (d) none of these

A B C is a variable triangle such that A is (1,2) and B and C lie on line y=x+lambda (where lambda is a variable). Then the locus of the orthocentre of triangle A B C is (a) (x-1)^2+y^2=4 (b) x+y=3 (c) 2x-y=0 (d) none of these

If alpha,beta are the roots of the equation a x^2+b x+c=0, then the value of aalpha^2+c//aalpha+b+(abeta^2+c)//(abeta+b) is (b(b^2-2a c))/(4a) b. (b^2-4a c)/(2a) c. (b(b^2-2a c))/(a^2c) d. none of these

In A B C ,a=5,b=12 ,c=90^0a n dD is a point on A B so that /_B C D=45^0dot Then which of the following is not true? C D=(60sqrt(2))/(17) (b) B D=(65)/(17) A D=(60sqrt(2))/(17) (d) none of these