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(i) The number of sides of the
(a) 1 quadrilateral formed by the lines \( x^{2} y^{2}+1=x^{2}+y^{2} \) that touch the circle \( x^{2}+y^{2}-2 x=0 \) is
(ii) \( \vec{b}, \vec{c} \) are orthogonal unit vectors
(b) 0 and \( \vec{b} \times \vec{c}=\vec{a} \). Then \( [\vec{a}+\vec{b}+\vec{c} \vec{a}+\vec{b} \vec{b}+\vec{c}] \) equals
(iii) A line having direction ratios
(c) 2 \( 1,-1,5 \) is perpendicular to the plane \( O P Q \), where \( P=(\lambda, 2,1) \), \( Q=(-2, \mu, 1) \) and \( O \) is the origin. Then \( \lambda+\mu \) equals
(iv) If the projection of the vector
(d) 3 \( \vec{i}+\vec{j}+\vec{k} \) on the vector \( \overrightarrow{a i}+4 \vec{j}-5 \vec{k} \) be \( \frac{1}{3 \sqrt{5}} \) then \( a \) can have the value
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