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Problem 33

(i) The points \((-1,0),(4,-2)\) and \((\cos 2 \theta, \sin 2 \theta)\) are collinear (ii) The points \((-1,0),(4,-2)\) and $\left(\frac{1-\tan ^{2} \theta}{1+\tan ^{2} \theta}, \frac{2 \tan \theta}{1+\tan ^{2} \theta}\right)$ are collinear (a) both statements are equivalent (b) statement (i) has more solution than statement (ii) for \(\theta\) (c) statement (ii) has more solution than statement (i) for \(\theta\) (d) none of the above

Expert verified

Option (c) statement (ii) has more solution than statement (i) for \( \theta \)

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Chapter 1

If circle passes through the point \(\left(3, \sqrt{\frac{7}{2}}\right)\) and touches \(x+y=1\) and \(x-y=1\), the centre of the circle is : then (a) \((4,0)\) (b) \((4,2)\) (c) \((6,0)\) (d) \((7,9)\)

Chapter 1

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Chapter 1

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Chapter 1

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