If `l_1=int_e^(e^2) dx/logx` and `l_2=int_1^2 e^x/xdx`, then (A) `l_1=2l_2` (B) `l_1+l_2=0` (C) `2l_1=l_2` (D) `l_1=l_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

The line l_1 x+ m_1 y+n=0 and l_2 x + m_2 y+n=0 will cut the coordinate axes at concyclic points if (A) l_1 m_1 = l_2 m_2 (B) l_1 m_2 = l_2 m_1 (C) l_1 l_2 = m_1 m_2 (D) l_1 l_2 m_1 m_2 = n^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

If int_(a)^(b)f(dx)dx=l_(1), int_(a)^(b)g(x)dx = l_(2) then :

If l=int_(0)^(pi//2)(cosx)/(1+sin^(2)x)dx , then (4)/(pi)l is _______.

Let l_(1)=int_(0)^(1)(e^(x))/(1+x)dx and l_(2)=int_(0)^(1)(x^(2))/(e^(x^(3))(2-x^(3)))dx. "Then"(l_(1))/(l_(2)) is equal to

Supose directioncoisnes of two lines are given by u l+vm+wn=0 and al^2+bm^2+cn^2=0 where u,v,w,a,b,c are arbitrary constnts and l,m,n are directioncosines of the lines. For u=v=w=1 if (n_1 n_2)/(l_1 l_2)=((a+b)/(b+c)) then (A) (m_1m_2)/(l_1 l_2)=((b+c))/((c+a)) (B) (m_1m_2)/(l_1 l_2)=((c+a))/((b+c)) (C) (m_1m_2)/(l_1 l_2)=((a+b))/((c+a)) (D) (m_1m_2)/(l_1 l_2)=((c+a))/((a+b))

If l_(1),l_(2) and l_(3) are the orders of the currents through our nerves, domestic appliances and average lightening, then the correct order of currents is (1) l_(1) gt l_(2) gt l_(3) (2) l_(1) gt l_(3) gt l_(2) (3) l_(1) lt l_(2) lt l_(3) (4) l_(1) = l_(2) = l_(3)

Let L be the set of all straight lines in plane. l_(1) and l_(2) are two lines in the set. R_(1), R_(2) and R_(3) are defined relations. (i) l_(1)R_(1)l_(2) : l_(1) is parallel to l_(2) (ii) l_(1)R_(2)l_(2) : l_(1) is perpendicular to l_(2) (iii) l_(1) R_(3)l_(2) : l_(1) intersects l_(2) Then which of the following is true ?

If l, l_(1), l_(2) and l _(3) be respectively the radii of the in-circle and the three escribed circles of a Delta ABC, then find l_(1)l_(2) l_(3)-l(l_(1)l_(2) +l_(2) l_(3)+l_(1) l_(3)).