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