Chemegate
Home/Practice Tests/PYQ Archive/Mathematics

GATE 2025 Chemical Engineering, Q14 · Mathematics

The correct answer is D, (³C₁ × ⁷C₁) / ¹⁰C₂.

Question

A box contains 3 identical green balls and 7 identical blue balls. Two balls are randomly drawn without replacement from the box. The probability of drawing 1 green and 1 blue ball is

  • A. (3P1×7P1)/10P2(³P₁ \times ⁷P₁) / ¹⁰P₂
  • B. (10P3×10P7)/10P2(¹⁰P₃ \times ¹⁰P₇) / ¹⁰P₂
  • C. (10C3×10C7)/10C2(¹⁰C₃ \times ¹⁰C₇) / ¹⁰C₂
  • D. (3C1×7C1)/10C2(³C₁ \times ⁷C₁) / ¹⁰C₂

Official answer: (3C1×7C1)/10C2(³C₁ \times ⁷C₁) / ¹⁰C₂

Why

GATE 2025 official key: (D). Order doesn't matter, so use combinations: favorable ways =3C1(1= ³C₁ (1 of 3 green) ×7C1(1 \times ⁷C₁ (1 of 7 blue), over ¹0C2¹⁰C₂ total ways to pick any 2 of 10 balls. P =(3×7)/45=21/45=7/15.= (3 \times 7)/45 = 21/45 = 7/15.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

Mathematics Topic Guide →More Mathematics PYQs →Take the Full GATE 2025 Test →