The distance between two points P and Q is d and the lengths of projections of PQ on the coordinate planes are `l_(1),l_(2),l_(3)` then `(l_(1)+l_(2)^(2)+l_(3)^(2))/(d^(2)`

The chord of contact of tangents from a point P to a circle passes through Q. If l_(1) and l_(2) are the length of the tangents from P and Q to the circle,then PQ is equal to (l_(1)+l_(2))/(2) (b) (l_(1)-l_(2))/(2)sqrt(l_(1)^(2)+l_(2)^(2))(d)2sqrt(l_(1)^(2)+l_(2)^(2))

If a rectangle has length L and the width is one-half of the length,then the area of the rectangle is (a) L( b) L^(2)( c) (1)/(2)L^(2)( d ) (1)/(4)L^(2)( e) 2L

Let A be a relation on the set of all lines in a plane defined by (l_(2), l_(2)) in R such that l_(1)||l_(2) , the n R is

Let R be the relation over the set of all straight lines in a plane such that l_(1) R l_(2) iff l_(1) _|_ l_(2) . Then, R is

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 ?

Let nge4 be a positive integer and let l_(1),l_(2),.....,l_(n) be the lengths of the sides of arbitrary n-sided non-degenerate polygon P. Suppose l_(1)/(l_(2))+l_(2)/(l_(3))+....l_(n-1)/(l_(n))+l_(n)/(l_(1))=n. Consider the following statements: I. The lengths of the sides of P are equal. II. The angles of P are equal. III. P is a regular polygon if it is cyclic. Then

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