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NDA 2025 Maths · Mathematics · Three Dimensional Geometry · medium

The radius of the sphere with centre at the origin which touches the plane 2x+3y+6z=35 is

Single correct option

The radius of the sphere with centre at the origin which touches the plane 2x+3y+6z=352x+3y+6z=35 is
  1. A. 55
  2. B. 77
  3. C. 3535
  4. D. 57\dfrac57
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Answer: (A) 55

The sphere touches the plane when its radius equals the distance from the centre to the plane: ∣35∣4+9+36=357=5\frac{|35|}{\sqrt{4+9+36}}=\frac{35}{7}=5. The value 3535 forgets the normalisation, 77 is the denominator, and 57\frac57 inverts the ratio before simplifying.
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Original question written in the NDA 2025 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake