Real Numbers
CBSE 2026 Board Exam Set 2 (Code 30/1/2)
CBSE_BOARD_PYQ_2026_30_1_2
Grade 10
Question:
[Section B]
Prove that $\sqrt{5}$ is an irrational number.
OR
Explain why $7 \times 11 \times 13 + 13$ and $7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 + 5$ are composite numbers.
Step-by-Step Solution
Key Concept: Main: Proof by contradiction. OR: Factoring out common 13 and 5.
[Main Question Solution]
Assume $\sqrt{5} = p/q$. Proof by contradiction. [2.0 Marks]
-------------------------------
[OR Choice Question Solution]
$13(77+1) = 13 \times 78$ (composite). $5(1008+1) = 5 \times 1009$ (composite). [2.0 Marks]
Correct Answer: Proof shown for both choices.
Confused by the solution? Ask the AI to explain a specific step, tell you where you went wrong, or break down the key trap in this question.