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Surds, Indices and Simplification

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

Top 10 SSC CGL Tier II 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 4 times: 2 Mar 2023 Tier II, 3 Mar 2023 Tier II, 6 Mar 2023 Tier II, 18 Jan 2025 Tier II. This one: 18 Jan 2025 Tier II See all 4 of this type

    15
    The value of 43−02+(222)2−8+7×6=4^3 - 0^2 + \left(\frac{22}{2}\right)^2 - 8 + 7 \times 6 = ________

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  2. Question 2

    This type asked 4 times: 15 Nov 2020 Tier II, 29 Jan 2022 Tier II, 3 Feb 2022 Tier II, 26 Oct 2023 Tier II. This one: 26 Oct 2023 Tier II See all 4 of this type

    18
    What is the value of [18+{16×(3645÷2425)−(1221×1415÷2445)}+2736]\left[\frac{1}{8} + \left\{\frac{1}{6} \times \left(\frac{36}{45} \div \frac{24}{25}\right) - \left(\frac{12}{21} \times \frac{14}{15} \div \frac{24}{45}\right)\right\} + \frac{27}{36}\right]?

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  3. Question 3

    This type asked 4 times: 15 Nov 2020 Tier II, 29 Jan 2022 Tier II, 3 Feb 2022 Tier II, 8 Aug 2022 Tier II. This one: 8 Aug 2022 Tier II See all 4 of this type

    84
    If A=0.312‾A = 0.3\overline{12}, B=0.415‾B = 0.4\overline{15} and C=0.309‾C = 0.30\overline{9} , then what is the value of A + B + C?

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  4. Question 4

    This type asked 3 times: 15 Nov 2020 Tier II, 8 Aug 2022 Tier II, 26 Oct 2023 Tier II. This one: 26 Oct 2023 Tier II See all 3 of this type

    27
    Find the value of 1.24×2.792.64×5.94\frac{\sqrt{1.24} \times \sqrt{2.79}}{\sqrt{2.64} \times \sqrt{5.94}}

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  5. Question 5

    Asked 2 times: 18 Jan 2025 Tier II*, 20 Jan 2025 Tier II (* = numbers or wording changed that year) See all 2 times it was asked

    30
    (a5×b3×c7)(a4×b8×c9)\frac{(a^5 \times b^3 \times c^7)}{(a^4 \times b^8 \times c^9)} in simplified form is:

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  6. Question 6

    This type asked 2 times: 2 Mar 2023 Tier II, 6 Mar 2023 Tier II. This one: 6 Mar 2023 Tier II See all 2 of this type

    6
    Simplify the following. 10+25+108+154+22516+19.25×42\frac{\sqrt{10 + \sqrt{25 + \sqrt{108 + \sqrt{154 + \sqrt{225}}}}}}{\sqrt{16 + 19.25 \times 4^2}}

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  7. Question 7

    This type asked 2 times: 29 Jan 2022 Tier II, 3 Feb 2022 Tier II. This one: 3 Feb 2022 Tier II See all 2 of this type

    59
    If 1+32−1−32=c\sqrt{1 + \frac{\sqrt{3}}{2}} - \sqrt{1 - \frac{\sqrt{3}}{2}} = c, then the value of c is:

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  8. Question 8

    This type asked 2 times: 15 Nov 2020 Tier II, 29 Jan 2022 Tier II. This one: 29 Jan 2022 Tier II See all 2 of this type

    79
    The value of 14+[(20.35)2−(8.35)2]×0.0175(1.05)2+(1.05)(27.65)\frac{1}{4} + \frac{[(20.35)^2 - (8.35)^2] \times 0.0175}{(1.05)^2 + (1.05)(27.65)} is:

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  9. Question 9

    This type asked 2 times: 15 Nov 2020 Tier II, 29 Jan 2022 Tier II. This one: 29 Jan 2022 Tier II See all 2 of this type

    96
    If 22242−3+5=a+5b\frac{22\sqrt{2}}{4\sqrt{2} - \sqrt{3 + \sqrt{5}}} = a + \sqrt{5}b, with a,b>0a, b > 0, then what is the value of (ab):(a+b)(ab) : (a + b)?

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  10. Question 10

    Asked once: 6 Mar 2023 Tier II (same type asked 4 times) See all 4 of this type

    14
    Find the value of given expression. 3−(−6){−2−9−3}÷7{1+(−2)(−1)}3 - (-6)\{-2 - 9 - 3\} \div 7\{1 + (-2)(-1)\}

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