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Algebraic Identities 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 10 times: 19 Jul 2023 S2, 19 Jul 2023 S4, 20 Jul 2023 S1, 20 Jul 2023 S3, 21 Jul 2023 S1, 25 Jul 2023 S4, 26 Jul 2023 S2, 26 Jul 2023 S4, 27 Jul 2023 S2, 10 Sep 2024 S1. This one: 10 Sep 2024 S1 See all 10 of this type

    72
    If the sum of three numbers is 18 and the sum of their squares is 36, then find the difference between the sum of their cubes and three times of their product.

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  2. Question 2

    This type asked 9 times: 18 Jul 2023 S3, 19 Jul 2023 S1, 20 Jul 2023 S4, 26 Jul 2023 S3, 27 Jul 2023 S3, 11 Sep 2024 S1, 17 Sep 2024 S3, 19 Sep 2024 S2, 22 Sep 2025 S1. This one: 22 Sep 2025 S1 See all 9 of this type

    71
    Given, x+1x=5x + \frac{1}{x} = 5, then determine the value of 2xx2−1\frac{2x}{x^2 - 1}

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  3. Question 3

    This type asked 7 times: 19 Jul 2023 S1, 24 Jul 2023 S3, 10 Sep 2024 S2, 11 Sep 2024 S2, 18 Sep 2024 S2, 24 Sep 2024 S2, 26 Sep 2024 S1. This one: 26 Sep 2024 S1 See all 7 of this type

    58
    If 3(163−63)(162+62+Q)=30\frac{3(16^3 - 6^3)}{(16^2 + 6^2 + Q)} = 30, then find the value of QQ.

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  4. Question 4

    This type asked 7 times: 14 Jul 2023 S1, 19 Jul 2023 S2, 20 Jul 2023 S2, 20 Jul 2023 S3, 24 Jul 2023 S4, 11 Sep 2024 S3, 23 Sep 2024 S3. This one: 23 Sep 2024 S3 See all 7 of this type

    57
    Let 3t−13t=33t - \frac{1}{3t} = 3, then which of the following expressions has the value equal to 12?

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  5. Question 5

    This type asked 7 times: 18 Jul 2023 S1, 19 Jul 2023 S4, 24 Jul 2023 S3, 25 Jul 2023 S3, 26 Jul 2023 S4, 27 Jul 2023 S1, 27 Jul 2023 S3. This one: 27 Jul 2023 S3 See all 7 of this type

    54
    The sum of the cubes of two given natural numbers is 9728, while the sum of the two given numbers is 32. What is the positive difference between the cubes of the two given numbers?

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  6. Question 6

    This type asked 6 times: 14 Jul 2023 S2, 24 Sep 2024 S3, 17 Sep 2025 S1, 17 Sep 2025 S3, 19 Sep 2025 S1, 19 Sep 2025 S2. This one: 19 Sep 2025 S2 See all 6 of this type

    74
    If a+b+c=0a + b + c = 0 and a=0.1a = 0.1, b=0.2b = 0.2, c=−0.3c = -0.3, then what is (a3+b3+c3)÷(3abc)(a^3 + b^3 + c^3) \div (3abc)?

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  7. Question 7

    This type asked 6 times: 17 Jul 2023 S4, 24 Jul 2023 S4, 10 Sep 2024 S1, 10 Sep 2024 S2, 13 Sep 2025 S2, 18 Sep 2025 S2. This one: 18 Sep 2025 S2 See all 6 of this type

    71
    Given, x+1x=4\sqrt{x} + \frac{1}{\sqrt{x}} = 4, then what is x+1xx + \frac{1}{x}?

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  8. Question 8

    This type asked 6 times: 14 Jul 2023 S3, 24 Jul 2023 S2, 24 Jul 2023 S3, 25 Jul 2023 S3, 19 Sep 2024 S1, 14 Sep 2025 S1. This one: 14 Sep 2025 S1 See all 6 of this type

    74
    Given, x+1x=4x + \frac{1}{x} = 4 find the value of x3+1x3x^3 + \frac{1}{x^3}.

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  9. Question 9

    This type asked 6 times: 17 Jul 2023 S2, 20 Jul 2023 S1, 25 Jul 2023 S2, 25 Jul 2023 S4, 9 Sep 2024 S1, 26 Sep 2024 S3. This one: 26 Sep 2024 S3 See all 6 of this type

    72
    Simplify 4x2−49y22x+7y+7y−2x\frac{4x^2 - 49y^2}{2x + 7y} + 7y - 2x

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  10. Question 10

    This type asked 6 times: 21 Jul 2023 S1, 21 Jul 2023 S3, 10 Sep 2024 S3, 19 Sep 2024 S3, 23 Sep 2024 S3, 25 Sep 2024 S3. This one: 25 Sep 2024 S3 See all 6 of this type

    56
    If a2+b2=148a^2 + b^2 = 148 and ab=54ab = 54, then find the value of a+ba−b\frac{a + b}{a - b}.

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