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Surds, Indices and Simplification

SSC CGL Quant. Try each one first, then open its answer.

Top 10 SSC CGL PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 19 times: 9 in 2023, 10 in 2024. This one: 26 Sep 2024 S2 See all 19 of this type

    69
    Simplify the following expression. (60+64÷4 of 4)×{1000÷((10 of (3+2))×2 of 5)}−28+(100×3 of 3)(60 + 64 \div 4 \text{ of } 4) \times \{1000 \div ((10 \text{ of } (3 + 2)) \times 2 \text{ of } 5)\} - 28 + (100 \times 3 \text{ of } 3).

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  2. Question 2

    This type asked 17 times: 12 in 2023, 4 in 2024, 1 in 2025. This one: 12 Sep 2025 S1 See all 17 of this type

    53
    Evaluate: 714−[56÷{13−(12×(34−14))}]7\frac{1}{4} - \left[\frac{5}{6} \div \left\{\frac{1}{3} - \left(\frac{1}{2} \times \left(\frac{3}{4} - \frac{1}{4}\right)\right)\right\}\right]

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  3. Question 3

    This type asked 13 times: 14 Jul 2023 S3, 14 Jul 2023 S4, 20 Jul 2023 S3, 21 Jul 2023 S2, 21 Jul 2023 S3, 24 Jul 2023 S3, 26 Jul 2023 S1, 27 Jul 2023 S1, 9 Sep 2024 S2, 13 Sep 2024 S3, 18 Sep 2024 S3, 23 Sep 2024 S2, 23 Sep 2024 S3. This one: 23 Sep 2024 S3 See all 13 of this type

    52
    Simplify the following expression 0.07×0.28÷0.04+0.64−1.64÷0.040.07 \times 0.28 \div 0.04 + 0.64 - 1.64 \div 0.04

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  4. Question 4

    This type asked 12 times: 21 Jul 2023 S3, 26 Jul 2023 S3, 27 Jul 2023 S2, 11 Sep 2024 S3, 13 Sep 2024 S2, 17 Sep 2024 S1, 17 Sep 2024 S2, 17 Sep 2024 S3, 14 Sep 2025 S3, 15 Sep 2025 S1, 16 Sep 2025 S1, 16 Sep 2025 S2. This one: 16 Sep 2025 S2 See all 12 of this type

    53
    Simplify: (56+34)÷(78−13)\left(\frac{5}{6} + \frac{3}{4}\right) \div \left(\frac{7}{8} - \frac{1}{3}\right)

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  5. Question 5

    This type asked 9 times: 12 Sep 2025 S1, 13 Sep 2025 S2, 14 Sep 2025 S1, 14 Sep 2025 S2, 15 Sep 2025 S1, 15 Sep 2025 S2, 15 Sep 2025 S3, 16 Sep 2025 S1, 17 Sep 2025 S2. This one: 17 Sep 2025 S2 See all 9 of this type

    51
    Simplify: (2.4+3.125)×0.25−(0.75÷0.3)(2.4 + 3.125) \times 0.25 - (0.75 \div 0.3)

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  6. Question 6

    Asked 7 times: 14 Sep 2025 S1*, 16 Sep 2025 S2*, 17 Sep 2025 S2*, 18 Sep 2025 S1*, 18 Sep 2025 S2*, 18 Sep 2025 S3*, 19 Sep 2025 S3 (* = numbers or wording changed that year) See all 7 times it was asked

    75
    What is the value of (0.23+0.023)÷(0.43+0.043)(0.2^3 + 0.02^3) \div (0.4^3 + 0.04^3)?

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  7. Question 7

    This type asked 7 times: 14 Sep 2025 S1, 16 Sep 2025 S2, 17 Sep 2025 S2, 18 Sep 2025 S1, 18 Sep 2025 S2, 18 Sep 2025 S3, 19 Sep 2025 S3. This one: 18 Sep 2025 S1 See all 7 of this type

    75
    Simplify: ((0.5)3+(0.05)3+(0.005)3)÷((0.1)3+(0.01)3+(0.001)3)\left((0.5)^3 + (0.05)^3 + (0.005)^3\right) \div \left((0.1)^3 + (0.01)^3 + (0.001)^3\right)

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  8. Question 8

    This type asked 6 times: 15 Sep 2025 S2, 16 Sep 2025 S2, 18 Sep 2025 S1, 19 Sep 2025 S2, 21 Sep 2025 S1, 21 Sep 2025 S3. This one: 21 Sep 2025 S3 See all 6 of this type

    51
    What will come in place of ? to satisfy the equation : (6−1)2=?−26(\sqrt{6}-1)^2 = ?-2\sqrt{6}

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  9. Question 9

    This type asked 5 times: 17 Sep 2025 S1, 19 Sep 2025 S1, 21 Sep 2025 S2, 21 Sep 2025 S3, 22 Sep 2025 S3. This one: 22 Sep 2025 S3 See all 5 of this type

    72
    Simplify: 5+26+5−262\frac{\sqrt{5 + 2\sqrt{6}} + \sqrt{5 - 2\sqrt{6}}}{\sqrt{2}}

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  10. Question 10

    This type asked 4 times: 12 Sep 2025 S2, 14 Sep 2025 S3, 18 Sep 2025 S2, 19 Sep 2025 S1. This one: 19 Sep 2025 S1 See all 4 of this type

    53
    Which of the following is correct? (i) 7+2>6+3\sqrt{7} + \sqrt{2} > \sqrt{6} + \sqrt{3} (ii) 7+2<6+3\sqrt{7} + \sqrt{2} < \sqrt{6} + \sqrt{3} (iii) 7+2=6+3\sqrt{7} + \sqrt{2} = \sqrt{6} + \sqrt{3}

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