1 hectate = ___________ `m^2`

The line joining the points (2m + 2 , 2m) and (2m + 1, 3) passes through (m +1 , 1) , if the values of m are "_______" .

ABCD is a square of length a, a in N, a > 1. Let L_1, L_2 , L_3... be points on BC such that BL_1 = L_1 L_2 = L_2 L_3 = .... 1 and M_1,M_2 , M_3,....be points on CD such that CM_1 = M_1M_2= M_2 M_3=... = 1. Then sum_(n = 1)^(a-1) ((AL_n)^2 + (L_n M_n)^2) is equal to :

If m + 1/( m - 2 ) = 4 , then find the value of ( m- 2)^2 + 1/ ( m-2 )^2

The direction ratios of the bisector of the angle between the lines whose direction cosines are l_1,m_1,n_1 and l_2,m_2,n_2 are (A) l_1+l_2,m_1+m_2+n_1+n_2 (B) l_1-l_2,m_1-m_2-n_1-n_2 (C) l_1m_2-l_2m_1,m_1n_2-m_2n_1,n_1l_2-n_2l_1 (D) l_1m_2+l_2m_1,m_1n_2+m_2n_1,n_1l_2+n_2l_1

In figure, find the velocity of m_1 in ms^-1 when m_2 falls by 9m . Given m_1=m , m_2=2m (take g=10ms^-2 ).

Two lines with direction cosines l_1,m_1,n_1 and l_2,m_2,n_2 are at righat angles iff (A) l_1l_2+m_1m_2+n_1n_2=0 (B) l_1=l_2,m_1=m_2,n_1=n_2 (C) l_1/l_2=m_1/m_2=n_1/n_2 (D) l_1l_2=m_1m_2=n_1n_2

If the direction cosines of two lines are (l_(1), m_(1), n_(1)) and (l_(2), m_(2), n_(2)) and the angle between them is theta then l_(1)^(2)+m_(1)^(2)+n_(1)^(2)=1=l_(2)^(2)+m_(2)^(2)+n_(2)^(2) and costheta = l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2) If the angle between the lines is 60^(@) then the value of l_(1)(l_(1)+l_(2))+m_(1)(m_(1)+m_(2))+n_(1)(n_(1)+n_(2)) is

If equation x^2-(2+m)x+1(m^2-4m+4)=0 has coincident roots then (A) m=0, m=1 (B) m=0, m=2 (C) m=2/3, m=6 (D) m=2/3, m=1