[4],[(1)mx-11y=m^(2)+11^(2)],[x+y=2m]

(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

(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

The angle between the rectangular hyperbola (y-mx)(my+x)=a^(2) and (m^(2)-1)(y^(2)x^(2))+4mxy=b^(2)

If [(1,1),(-1,1)][(x),(y)]=[(2),(4)], then the values of x and y respectively are

Find the (i) Net elongation rod approximately. (x xx 10^(-11)m) then x = (ii) Y_(eq) of the composite rod (x xx 0^(11) N..m^(2)) (assume A = area of cross section of each rod),. Then x = l_(1) = l(2) = 1m, F = 2N//m^(2), A = 1sq.m^(2) y_(1) = 2xx10^(11) N//m^(2)n, y_(2) = 3xx10^(11) N//m^(2) ltbr4gt

If m_(1) and m_(2) are the roots of the equation x^(2) + ( sqrt(3) + 2) x + sqrt(3) - 1 =0 then prove that area of the triangle formed by the lines y=m_(1) x, y=m_(2) x and y=c is (c^2)/( 4) ( sqrt(33) + sqrt(11)) .

If [(1,1),(-1,1)][(x),(y)]=[(2),(4)] ,then the values of x and y respectively are

Number of integral values of m for which lines x+y+1=0,mx-m^(2)y+3=0 and 2mx-(2m-1)y+(3m+2)=0 are concurrent

y=ae^(mx)+be^(-mx),(d^(2)y)/(dx^(2))=m^(2) yisequal rarr m^(2)(ae^(mx)-be^(mx))