Simplification is the largest self-contained topic in the Punjab Police SI's Quantitative Aptitude section: 85 questions since 2016, and not one of them needs a concept. They need order — knowing which operation to do first — and they need you to spot the two or three places where an ugly-looking expression collapses to almost nothing.
Thirty of the 85 are straight BODMAS. Fifteen are fractions and decimals. Six hide a factorisation identity, four are about shifting decimal points, and thirty are indices and surds. You will learn (1) the BODMAS order including the step most candidates skip, (2) the left-to-right rule, (3) the four identities worth memorising, (4) the decimal and fraction habits that turn a two-minute question into twenty seconds, and (5) the seven laws of indices.
85
SI questions
2016–2023
30
plain BODMAS
order is the only skill
30
indices and surds
seven laws cover them
6
hide an identity
a³ ± b³ mostly
BODMAS, properly
Thirty questions rest on this one order.
The O is the step candidates lose marks on. It covers powers and the word “of”, and both come before division.
KEY TERM
“of” is not the same as ×
In an exam expression, “of” binds tighter than ÷ and ×. So 1/4 ÷ 1/4 of 1/4 means 1/4 ÷ (1/16) = 4, while 1/4 ÷ 1/4 × 1/4 means (1/4 ÷ 1/4) × 1/4 = 1/4. The SI builds whole questions out of that single difference, putting the two side by side so you have to notice.
1/4 of 1/4 = 1/16→1/4 ÷ 1/16 = 4
QUICK CHECK
What is the value of the following? ((3 + 3 × 3)/(3 × 3 × 3)) ÷ ((1/4 ÷ 1/4 of 1/4)/(1/4 ÷ 1/4 × 1/4)) (SI 14 Jul 2023)
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Answer: 1/36
Top of the first fraction: (3 + 9)/27 = 12/27 = 4/9. Second fraction: (1/4 ÷ 1/16) ÷ ((1/4 ÷ 1/4) × 1/4) = 4 ÷ (1/4) = 16. So the whole thing is (4/9) ÷ 16 = 4/144 = 1/36. Everything turns on “of” acting before ÷.
QUICK CHECK
Simplify the following expression. [(7/2 ÷ 5/2 × 3/2) / (7/2 ÷ 5/2 of 3/2)] ÷ 15/14 (SI 14 Jul 2023)
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Answer: 21/10
Numerator: (7/2 ÷ 5/2) × 3/2 = (7/5) × 3/2 = 21/10. Denominator: 7/2 ÷ (5/2 of 3/2) = 7/2 ÷ 15/4 = 14/15. Their ratio is (21/10) ÷ (14/15) = 9/4, and 9/4 ÷ 15/14 = 21/10.
Division and multiplication have equal rank, so you read them left to right. The same is true of addition and subtraction.
QUICK CHECK
What is the value of 90 + 55 ÷ 1.1 × 4 − 21? (SI 16 Oct 2022)
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Answer: 269
Left to right: 55 ÷ 1.1 = 50, then 50 × 4 = 200. So the expression is 90 + 200 − 21 = 269. Doing 1.1 × 4 first would give 55 ÷ 4.4 = 12.5 and the wrong answer 81.5.
CHECK YOURSELF
Find the value of 15 − [(7 × 8 ÷ 2) ÷ {44 − (32 − 20 ÷ 10)}] (SI 2 Jul 2023)
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Work from the innermost bracket outwards. 20 ÷ 10 = 2, so 32 − 2 = 30, so 44 − 30 = 14. Next, 7 × 8 ÷ 2 = 56 ÷ 2 = 28. Then 28 ÷ 14 = 2, and finally 15 − 2 = 13. Innermost first, every time — never try to hold two brackets in your head at once.
QUICK CHECK
Find the value of {4 + 3 + ((16 ÷ 8) ÷ 2)} + 6 × 9 ÷ 3 + 12. (SI 14 Jul 2023)
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Answer: 38
Inside: (16 ÷ 8) ÷ 2 = 2 ÷ 2 = 1, so the brace is 4 + 3 + 1 = 8. Then 6 × 9 ÷ 3 = 54 ÷ 3 = 18. Total = 8 + 18 + 12 = 38.
Innermost: 14 − 2 = 12, then 24 ÷ 12 = 2, so 34 − 2 = 32. Then 36 − 32 = 4, and 32 ÷ 4 = 8. Finally 14 − 8 = 6.
CHECK YOURSELF
The value of the expression 75 − 2(24 + 12 ÷ 3 × 6 − 4 × 5) + 9 is : (SI 18 Aug 2021)
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Inside the bracket: 12 ÷ 3 × 6 = 4 × 6 = 24, and 4 × 5 = 20. So the bracket is 24 + 24 − 20 = 28. Then 75 − 2(28) + 9 = 75 − 56 + 9 = 28. Note the 12 ÷ 3 × 6 — left to right again, not 12 ÷ 18.
COMMON TRAPS
“of” comes before ÷. It is the O in BODMAS, not another name for ×.
÷ and × are equal. 12 ÷ 3 × 6 is 24, not 12 ÷ 18.
A minus sign in front of a bracket flips every sign inside it. 75 − 2(24 + 4) is 75 − 48 − 8, not 75 − 48 + 8.
Mixed numbers must become improper fractions first. 3¼ is 13/4, and you cannot divide “three and a quarter” in parts.
THE LETTER-CODING QUESTIONS
“P means +, Q means −, R means ×, S means ÷.” Rewrite the line with real symbols, then apply BODMAS normally — the letters change nothing about the order. 70 Q 5 R 81 S 9 P 20 becomes 70 − 5 × 81 ÷ 9 + 20 = 70 − 45 + 20 = 45.
QUICK CHECK
If 'P' denotes '+', 'Q' denotes '−', 'R' denotes '×' and 'S' denotes '÷', then what will be the value of 70 Q 5 R 81 S 9 P 20? (SI 15 Jul 2023)
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Answer: 45
70 − 5 × 81 ÷ 9 + 20. Do × and ÷ left to right: 5 × 81 = 405, 405 ÷ 9 = 45. Then 70 − 45 + 20 = 45.
QUICK CHECK
If ‘P’ stands for ‘+’, ‘Q’ stands for ‘–’, ‘R’ stands for ‘×’ and ‘S’ stands for ‘÷’, then what will be the value of 120 Q 8 R 72 S 8 P 45? (SI 20 Jun 2023)
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Answer: 93
120 − 8 × 72 ÷ 8 + 45. Left to right: 8 × 72 = 576, 576 ÷ 8 = 72. Then 120 − 72 + 45 = 93.
When an ugly fraction is really an identity
Six questions, and each is over in ten seconds once you see it.
When you see two awkward decimals appearing over and over in a fraction — 0.943 and 0.057, 0.52 and 0.48, 2.3 and 0.3 — stop calculating. The paper has hidden a factorisation. Name the two numbers a and b, look at the shape of the top and the bottom, and the whole fraction will cancel to something tiny, usually 1 or a + b.
These four cover every identity question the SI has set. Memorise the right-hand sides — that is the half you have to recognise in the paper.
The top is a³ + b³ and the bottom is a² − ab + b², with a = 0.52 and b = 0.48. Since a³ + b³ = (a + b)(a² − ab + b²), the fraction is just a + b = 0.52 + 0.48 = 1.
QUICK CHECK
The value of (0.943×0.943 − 0.943×0.057 + 0.057×0.057)/(0.943×0.943×0.943 + 0.057×0.057×0.057) is : (SI 2 Jul 2023)
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Answer: 1
Here the top is a² − ab + b² and the bottom is a³ + b³ — the identity the other way up. So the fraction is 1/(a + b) = 1/(0.943 + 0.057) = 1/1 = 1.
CHECK YOURSELF
(7.85×7.85 − 2.15×2.15)/(7.85 − 2.15) + ((2.3)³ − 0.027)/((2.3)² + 0.69 + 0.09) is equal to ______. (SI 19 Aug 2021)
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First part: (7.85² − 2.15²)/(7.85 − 2.15) = (a² − b²)/(a − b) = a + b = 10. Second part: 0.027 = 0.3³ and 0.69 = 2.3 × 0.3, 0.09 = 0.3², so the bottom is a² + ab + b² with a = 2.3, b = 0.3 — and the top is a³ − b³. That part is a − b = 2. Total = 10 + 2 = 12.
QUICK CHECK
Simplify the following expression. ((0.25)⁴ + (0.25)² + 1)/((0.25)² + 0.25 + 1) = ? (SI 29 Jun 2023)
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Answer: 0.8125
With x = 0.25, the top is x⁴ + x² + 1 and the bottom is x² + x + 1. Since x⁴ + x² + 1 = (x² + x + 1)(x² − x + 1), the fraction is x² − x + 1 = 0.0625 − 0.25 + 1 = 0.8125.
QUICK CHECK
The value of ((2.697 − 0.498)² + (2.697 + 0.498)²) / (2.697 × 2.697 + 0.498 × 0.498) is : (SI 14 Jul 2023)
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Answer: 2
(a − b)² + (a + b)² = 2(a² + b²), always. So the fraction is 2(a² + b²)/(a² + b²) = 2, whatever a and b are — the decimals 2.697 and 0.498 never need to be touched.
Decimals and fractions
Fifteen questions, and most of them are about keeping track of the point.
Every number on the bottom is a tenth of the matching number on top. Squaring turns a factor of 10 into a factor of 100 — so the whole fraction is 100.
QUICK CHECK
What is the value of ((0.05)² + (0.55)² + (0.555)²) ÷ ((0.005)² + (0.055)² + (0.0555)²)? (SI 2 Jul 2023)
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Answer: 100
Each number on the bottom is exactly one tenth of the one above it. Squaring multiplies that ratio by itself, so every term on top is 100 times its partner. The whole fraction is therefore 100 — no arithmetic required.
Every number on the bottom is 1/10,000 of the matching one on top. Squared, that is 10⁸, so the fraction inside the bracket is 10⁸. The fourth root of 10⁸ is 10² = 100.
QUICK CHECK
0.5 × 0.5 + 0.5 − 0.5 is equal to which of the following? (SI 24 Aug 2021)
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Answer: 0.25
0.5 × 0.5 + 0.5 − 0.5 = 0.25 + 0 = 0.25. The +0.5 and −0.5 cancel, which is the whole point of the question.
CHECK YOURSELF
Ramesh spends 3/5 of his monthly salary on food and 1/3 of his salary on clothes and travel, and keeps the rest as savings. If his monthly salary is 45,000, how much will he save in 3 months? (SI 20 Jun 2023)
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Fraction spent = 3/5 + 1/3 = 9/15 + 5/15 = 14/15, so the saving is 1/15 of the salary. Monthly saving = 45,000/15 = ₹3,000. The question asks for three months: 3 × 3,000 = ₹9,000. The distractor ₹3,000 is the one-month figure — the commonest way to lose this mark.
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A tailor has 87.5 metres of cloth and has to make 8 pieces out of every one metre of cloth. How many pieces of cloth can be made in all? (SI 14 Jul 2023)
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87.5 metres, 8 pieces from every metre. 87.5 × 8 = 700 pieces. A one-line question, but note that the answer is a count, so it must be a whole number — and 87.5 × 8 obligingly is.
Also asked onceTap to open
CHECK YOURSELF
Simplify the following. 325 × 325 + 275 × 275 − 12 + (4140 ÷ 345) (SI 20 Jun 2023)
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325² + 275² − 12 + (4140 ÷ 345). 325² = 105,625 and 275² = 75,625, which add to 181,250. 4140 ÷ 345 = 12, so the −12 and +12 cancel exactly. The answer is 181,250.
CHECK YOURSELF
Find the value of '?' in the equation given below. (1/2) of 2558 + 42% of 1350 = (?)² − 7605 (SI 19 Aug 2021)
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Work the left side: half of 2558 = 1279, and 42% of 1350 = 567, so the left side is 1,846. That makes (?)² = 1846 + 7605 = 9,451 and ? ≈ 97.2 — which is not among the four choices. The printed figures do not close. The official key (the green tick on the response sheet) is 95, so treat this as a paper defect and move on; in the exam, pick the key.
CHECK YOURSELF
The value of (287.0134 × 0.0491 × 1.902)/(41.004 × 99.89) is closest to ______. (SI 19 Aug 2021)
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Round everything first: (287 × 0.05 × 1.9)/(41 × 100) ≈ 27.3/4100 ≈ 0.007. ‘Closest to’ questions are an invitation to approximate, not to multiply exactly.
CHECK YOURSELF
If A = (3/4) ÷ (5/6), B = 3 ÷ [(4 ÷ 5) ÷ 6], C = [3 ÷ (4 ÷ 5)] ÷ 6, D = (3 ÷ 4) ÷ (5 ÷ 6), then : (SI 29 Jun 2023)
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A = (3/4) ÷ (5/6) = 9/10. D = (3 ÷ 4) ÷ (5 ÷ 6) = (3/4) ÷ (5/6) = 9/10 — the same thing written differently. B and C come out as 45/2 and 45/8. So A and D are equal. Brackets, not the letters, decide the value.
CHECK YOURSELF
Find the value of '?' in the equation given below. (0.3³ + 0.33³) ÷ (0.3³ + 0.03³) = ? (SI 24 Aug 2021)
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Top: 0.3³ + 0.33³. Bottom: 0.3³ + 0.03³. Factor 0.03³ out of the bottom and 0.03³ out of the top as well: the ratio reduces to (10³ + 11³)/(10³ + 1³) = 2331/1001 = 2.33. Pulling out the common power of ten is the move.
The rest of the paper, question by question
Thirty-one more, grouped by the shape they take.
THE NESTED-BRACKET PATTERN, ASKED FOUR TIMES
Four SI questions share the exact shape [A ÷ {B − C(D − E)}] ÷ F, always with mixed numbers. Work strictly from the inside out:
1. Turn every mixed number into an improper fraction first — 3¼ becomes 13/4.
2. Do the innermost round bracket (D − E).
3. Multiply by C, subtract from B inside the curly bracket.
4. Divide A by that, then divide by F last.
If the final answer is not a tidy number, you have almost certainly done step 4 before step 3.
Simplify the following expression : [(9/4 ÷ 7/4 × 11/4)/(9/4 ÷ 7/4 of 11/4)] ÷ 1.75 (SI 29 Jul 2023)
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Answer: 4 9/28
The two halves look identical but are not, because “of” binds tighter than ÷.
Top: 9/4 ÷ 7/4 × 11/4 = (9/7) × (11/4) = 99/28.
Bottom: 9/4 ÷ (7/4 of 11/4) = 9/4 ÷ 77/16 = 36/77.
Their ratio is (99/28) ÷ (36/77) = 99 × 77 / (28 × 36) = 7623/1008 = 121/16. Dividing by 1.75 = 7/4 gives 121/28 = 4 9/28.
This single question is the clearest test of the “of” rule in the whole paper.
QUICK CHECK
The value of ((6/7)^{4} + (7/6)^{4} + 1) / ((6/7)^{2} + (7/6)^{2} − 1) is : (SI 14 Jul 2023)
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Answer: 3 169/1764
Put a = (6/7)² and b = (7/6)², so ab = 1. The expression is (a² + b² + 1) ÷ (a + b − 1).
Since ab = 1, a² + b² + 1 = a² + b² + ab, and the standard factorisation a² + ab + b² = (a + b)² − ab means the numerator is (a + b)² − 1 = (a + b + 1)(a + b − 1).
The bracket cancels, leaving a + b + 1 = 36/49 + 49/36 + 1. Over 1764 that is 1296 + 2401 + 1764 = 5461, so the value is 5461/1764 = 3 169/1764.
QUICK CHECK
Simplify the following expression : [ 71 – 14 ÷ 2 of 7 ] - [ 6 ÷ 6 of 6 + 6 ÷ 6 x 6 ] + ( 6 + 6 ) – 6 of 6 + 6x ( 6 x 8 ) ÷6 - ( 0.35 x 0.35 + 0.65 x 0.65 + 0.7 x 0.65 ). (SI 9 Jul 2023)
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Answer: 521/6
The longest expression in the whole paper, but it is only BODMAS. Take it in pieces.
[71 − 14 ÷ 2 of 7]: “of” first, 2 of 7 = 14, so 14 ÷ 14 = 1 and the bracket is 70.
[6 ÷ 6 of 6 + 6 ÷ 6 × 6]: 6 of 6 = 36, so 6 ÷ 36 = 1/6; and 6 ÷ 6 × 6 = 6. The bracket is 1/6 + 6 = 37/6.
(6 + 6) = 12. 6 of 6 = 36. 6 × (6 × 8) ÷ 6 = 48.
The last bracket: 0.35² + 0.65² + 0.7 × 0.65 = 0.1225 + 0.4225 + 0.455 = 1.
Putting it together: 70 − 37/6 + 12 − 36 + 48 − 1 = 93 − 37/6 = (558 − 37)/6 = 521/6.
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CHECK YOURSELF
The value of [3 1/4 ÷ {1 1/4 − 1/2(2 1/2 − 1/4 − 1/6)}] ÷ (1/2 of 4 1/3) is : (SI 14 Jul 2023)
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Round bracket: 2½ − ¼ − ⅙ = 5/2 − 1/4 − 1/6 = (30 − 3 − 2)/12 = 25/12. Half of that is 25/24, and 1¼ − 25/24 = 30/24 − 25/24 = 5/24.
Then 13/4 ÷ 5/24 = 78/5, and ½ of 4⅓ = 13/6. Finally 78/5 ÷ 13/6 = 36/5 = 7 1/5.
Find the value of the following expression. 316 − 3(20 + 16 ÷ 4 × 3 − 2 × 2) + 101 (SI 9 Jul 2023)
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Inside the bracket, division and multiplication come before the additions: 16 ÷ 4 × 3 = 12 and 2 × 2 = 4, so the bracket is 20 + 12 − 4 = 28.
Then 316 − 3(28) + 101 = 316 − 84 + 101 = 333.
CHECK YOURSELF
Simplify the following. 12.0737 − [5 + 0.05 of (4.1 − 1.3 × 2.02)] (SI 15 Jul 2023)
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Inner bracket: 4.1 − 1.3 × 2.02 = 4.1 − 2.626 = 1.474. “0.05 of 1.474” = 0.0737.
So the square bracket is 5 + 0.0737 = 5.0737, and 12.0737 − 5.0737 = 7.0.
CHECK YOURSELF
Find the value of 1 ÷ 3/7 of (6 + 8 × 1) + [1/5 ÷ 7/25 − 1]. (SI 15 Jul 2023)
Solve the equation given below. [10 + 8 − 2 × (2 + 78) − 45÷9 + (36÷9 + 5×3 − 20)] × (−3/2) (SI 19 Aug 2021)
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Work through the square bracket: 10 + 8 = 18; 2 × 80 = 160; 45 ÷ 9 = 5; and the inner bracket 4 + 15 − 20 = −1.
So the square bracket is 18 − 160 − 5 − 1 = −148, and −148 × (−3/2) = 222.
CHECK YOURSELF
Simplify the given expression. ((−4 − 6)⁴ − 6³ + 10/2)/(18 − 7 ÷ 7 − 4) (SI 20 Jun 2023)
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Top: (−10)⁴ = 10,000; minus 6³ = 216; plus 10/2 = 5. That gives 9,789.
Bottom: 18 − 1 − 4 = 13. And 9,789 ÷ 13 = 753.
An even power of a negative number is positive — that is the only trap here.
CHECK YOURSELF
Find the value of 96 ÷ 48 − {(4² − 6 × 2)² ÷ (4 ÷ 2) + 7} + (22/9 ÷ 11/8 × 2 1/4). (SI 20 Jun 2023)
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96 ÷ 48 = 2. Inside the curly bracket: 4² − 6 × 2 = 16 − 12 = 4, so 4² = 16, then 16 ÷ 2 = 8 and 8 + 7 = 15.
The last bracket: 22/9 ÷ 11/8 × 9/4 = (22/9)(8/11)(9/4) = 4.
Total = 2 − 15 + 4 = −9.
CHECK YOURSELF
Solve : [75 − 12 ÷ 3 of 2] + (18 − 6) ÷ 4 (SI 24 Aug 2021)
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“3 of 2” = 6, so 12 ÷ 6 = 2 and the square bracket is 75 − 2 = 73. Then (18 − 6) ÷ 4 = 3, and 73 + 3 = 76.
CHECK YOURSELF
8 − 1 1/6 of 1 5/7 ÷ 2 2/5 of 5/6 is equal to : (SI 29 Jun 2023)
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Both “of”s bind first: 1⅙ of 1 5/7 = (7/6)(12/7) = 2, and 2⅖ of ⅚ = (12/5)(5/6) = 2.
So the expression is 8 − 2 ÷ 2 = 8 − 1 = 7.
What is the value of 5 1/2 ÷ (3 1/2 + 7 1/2)? (SI 29 Jun 2023)
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3½ + 7½ = 11, and 5½ ÷ 11 = (11/2) ÷ 11 = 1/2.
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What is the value of 5/4 − 0.45 + 3.75 − 1/2 − 0.05 ? (SI 16 Oct 2022)
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Convert the fractions: 5/4 = 1.25 and 1/2 = 0.5. Then 1.25 − 0.45 + 3.75 − 0.5 − 0.05 = 4.
Group the numbers that make whole values: (1.25 + 3.75) = 5 and (0.45 + 0.5 + 0.05) = 1.
CHECK YOURSELF
Find the value of 'y' in the equation given below. −774.67 + 1742.52 − 873.43 − y = − 7472.78 (SI 19 Aug 2021)
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Collect the known terms first: −774.67 + 1742.52 − 873.43 = 94.42.
So 94.42 − y = −7472.78, giving y = 94.42 + 7472.78 = 7567.20.
CHECK YOURSELF
The length of a field is divided into three parts. The first part is 1/3 of the whole length, the second part is 3/5 of the first part, and the third part is 3.50 metres. Find the length of the field. (SI 20 Jun 2023)
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Let the length be L. The first part is L/3 and the second is 3/5 of that, which is L/5. Together the first two are L/3 + L/5 = 8L/15.
The third part is the rest: L − 8L/15 = 7L/15 = 3.50, so L = 3.50 × 15/7 = 7.50 metres.
CHECK YOURSELF
If (2 + 1/(1 + 4/5)) / (2 + 1/(1 + 1/(1 + 1/4))) = x, then what is the value of x? (SI 24 Aug 2021)
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Top: 1 + 4/5 = 9/5, so 1 ÷ (9/5) = 5/9 and the numerator is 2 + 5/9 = 23/9.
Bottom, from the inside: 1 + ¼ = 5/4; 1 ÷ (5/4) = 4/5; 1 + 4/5 = 9/5; 1 ÷ (9/5) = 5/9; so the denominator is also 2 + 5/9 = 23/9.
The two are equal, so x = 1. Continued fractions are always built from the bottom up.
CHECK YOURSELF
Raghu consumes 0.75 litre of milk every day, and Rani consumes 1/4 litre of milk every day. If the price of milk is ₹42.25 per litre, then find the total amount (in ₹) spent by the two of them on milk in 15 weeks. (SI 24 Aug 2021)
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Together they drink 0.75 + 0.25 = 1 litre a day — the fractions were chosen to add to one.
15 weeks is 105 days, so 105 litres at ₹42.25 costs 105 × 42.25 = ₹4,436.25.
If x = 0.3/10, then the value of (5x + 25x² + 125x³)/0.1³ is ________. (SI 29 Jul 2023)
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x = 0.3/10 = 0.03. Then 5x = 0.15, 25x² = 25(0.0009) = 0.0225 and 125x³ = 125(0.000027) = 0.003375.
Their sum is 0.175875, and dividing by 0.1³ = 0.001 shifts the point three places: 175.875.
Every factor on the bottom is 6/5 of the one above it, and there are five of them. So the whole fraction is (5/6)⁵ = 3125/7776 = 3125/7776.
Spotting the matching pattern saves multiplying ten decimals.
CHECK YOURSELF
3/4 of the difference between 2 1/6 and 1 1/9 is subtracted from 3/4 of 4 1/3. The resultant value is : (SI 31 Jul 2023)
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The difference: 2⅙ − 1 1/9 = 13/6 − 10/9 = (39 − 20)/18 = 19/18, and ¾ of that is 19/24.
Three-quarters of 4⅓ = ¾ × 13/3 = 13/4.
Subtracting, 13/4 − 19/24 = (78 − 19)/24 = 59/24.
Four small brackets: (9 − 3) = 6, (4 − 7) = −3, (49 − 25) = 24 and (81 − 1) = 80. Adding, 6 − 3 + 24 + 80 = 107.
The second bracket is negative, which is where the 131 option comes from.
CHECK YOURSELF
What is the approximate value that will come in place of (?) in the equation given below? 80% of (280 + √?) = 240 (SI 19 Aug 2021)
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Undo the percentage first: if 80% of something is 240, that something is 240 ÷ 0.8 = 300.
So 280 + √? = 300, giving √? = 20 and ? = 400.
Indices and surds
Thirty more questions, and only seven laws behind them.
Every indices question in the SI paper is one of these seven laws applied once or twice. There is nothing else to learn.
QUICK CHECK
Simplify algebraically (a^6)² / a^8 (SI 2016)
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Answer: a⁴
Two laws in a row: (a⁶)² = a¹² by the power-of-a-power rule, and then a¹² ÷ a⁸ = a⁴ by subtracting the indices.
QUICK CHECK
Simplify algebraically : a^6/a^{-5} (SI 2016)
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Answer: a^{11}
Dividing by a negative index means adding: a⁶ ÷ a⁻⁵ = a^(6 − (−5)) = a¹¹. The minus of a minus is the step most candidates drop.
CHECK YOURSELF
10^0 = ? (SI 2016)
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Any non-zero number raised to the power zero is 1, so 10⁰ = 1. It follows from the division rule: aⁿ ÷ aⁿ = a⁰, and anything divided by itself is 1.
QUICK CHECK
Find the value of (243)^{0.8} ÷ (243)^{0.4}. (SI 20 Jun 2023)
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Answer: 9
Dividing powers of the same base subtracts the indices: 243^0.8 ÷ 243^0.4 = 243^0.4. Now 243 = 3⁵, so 243^0.4 = 3^(5 × 0.4) = 3² = 9.
Recognising 243 as 3⁵ is the whole question — 3⁵ = 243, 3⁶ = 729 and 3⁸ = 6561 are worth memorising, since the SI paper uses all three.
QUICK CHECK
The value of ((243)^{0.13} × (243)^{0.07})/((7)^{0.25} × (49)^{0.075} × (343)^{0.2}) is : (SI 2 Jul 2023)
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Answer: 3/7
Group each base. On top, 243^0.13 × 243^0.07 = 243^0.2 = (3⁵)^0.2 = 3.
Below, write 49 = 7² and 343 = 7³, so the denominator is 7^0.25 × 7^0.15 × 7^0.6 = 7^1 = 7.
The value is 3/7. Converting every number to a power of a single base before adding the indices is the entire method.
Put everything on base 4. 256 = 4⁴, so 256^(n/4) = 4ⁿ, and 16 = 4², so 16ⁿ = 4^2n.
The numerator is 4ⁿ × 4^(2n+1) = 4^(3n+1); the denominator is 4^2n × 4^(n−1) = 4^(3n−1). Dividing leaves 4^2 = 16.
The n disappears, which is the signal that you have chosen the right base.
QUICK CHECK
The value of (3 × 9^{n+1} − 9 × 3^{2n})/(3 × 3^{2n+3} − 9^{n+1}) is : (SI 29 Jul 2023)
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Answer: 1/4
Write every term on base 3. 9^(n+1) = 3^(2n+2) and 9 × 3^2n = 3^(2n+2) as well.
Numerator = 3 × 3^(2n+2) − 3^(2n+2) = 3^(2n+2)(3 − 1) = 2 × 3^(2n+2).
Denominator = 3 × 3^(2n+3) − 3^(2n+2) = 3^(2n+2)(9 − 1) = 8 × 3^(2n+2).
The common factor cancels and the value is 2/8 = 1/4.
When two powers of the same base are added, factor out the smaller one. The bracket always turns into a simple fraction.
QUICK CHECK
If 3^{x-2} + 3^x = 7290, find the value of x. (SI 29 Jun 2023)
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Answer: 8
Factor out the smaller power: 3^(x−2) + 3^x = 3^x(1/9 + 1) = 3^x × 10/9 = 7290. So 3^x = 7290 × 9/10 = 6561 = 3⁸, giving x = 8.
Never try to split 7290 — factoring out the smaller power is always the first move.
QUICK CHECK
If 2^{a−4} + 2^{a+2} = 130, then the value of a is : (SI 2 Jul 2023)
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Answer: 5
Same move on base 2: 2^(a−4) + 2^(a+2) = 2^a(1/16 + 4) = 2^a × 65/16 = 130. So 2^a = 130 × 16/65 = 32 = 2⁵ and a = 5.
QUICK CHECK
If (8^k × 8³) − 1540 = 31228, then the value of k is : (SI 14 Jul 2023)
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Answer: 2
First tidy the equation: 8^k × 8³ = 31228 + 1540 = 32768. By the product rule the left side is 8^(k+3), and 32768 = 8⁵ (since 8⁵ = 32,768). So k + 3 = 5 and k = 2.
If you do not recall 8⁵, note that 32768 = 2¹⁵ and 8 = 2³, so the index is 15/3 = 5.
QUICK CHECK
If (2/3)^x × (3/2)^{2x} = 243/32, find the value of x. (SI 14 Jul 2023)
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Answer: 5
Flip the first bracket so both share a base: (2/3)^x = (3/2)^(−x), so the left side is (3/2)^(2x − x) = (3/2)^x.
The right side is 243/32 = 3⁵/2⁵ = (3/2)⁵, so x = 5.
QUICK CHECK
(81/256)^{-1/6} is equal to : (SI 29 Jul 2023)
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Answer: (4/3)^{2/3}
A negative index flips the fraction: (81/256)^(−1/6) = (256/81)^(1/6). Now 256 = 4⁴ and 81 = 3⁴, so this is ((4/3)⁴)^(1/6) = (4/3)^(2/3).
Option B (4/3) is what you get by forgetting to carry the 4 through the sixth root.
QUICK CHECK
Find the value of (4^{-1} × 3³)/(8^{-2}). (SI 29 Jul 2023)
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Answer: 432
Turn both negative indices the right way up: 4⁻¹ = 1/4 and 1/8⁻² = 8² = 64. So the expression is (27/4) × 64 = 27 × 16 = 432.
QUICK CHECK
Simplify the following expression. {(1/3)^{-3} − (1/2)^{-3}} ÷ {(1/5)^{-2} − (1/4)^{-2}} (SI 29 Jun 2023)
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Answer: 19/9
A negative index on a fraction simply flips it: (1/3)⁻³ = 3³ = 27 and (1/2)⁻³ = 2³ = 8; (1/5)⁻² = 25 and (1/4)⁻² = 16.
The expression is (27 − 8) ÷ (25 − 16) = 19/9.
QUICK CHECK
The value of (√(2401/49))³ is equal to ______. (SI 20 Jun 2023)
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Answer: 343
Simplify inside the root first: 2401/49 = 49, so √(2401/49) = 7. Then 7³ = 343.
2401 = 7⁴ is worth knowing — it turns the whole question into 7^(4/2 × 3 − 3) in one line.
QUICK CHECK
Which of the following is the value of the given expression? (16/72) × 81^{0.12} × 9^{0.06} × 3^{1.4} (SI 31 Jul 2023)
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Answer: 2
Put the three powers on base 3: 81^0.12 = 3^0.48, 9^0.06 = 3^0.12 and 3^1.4 stays. Their indices add to 0.48 + 0.12 + 1.4 = 2, so together they are 3² = 9.
Then 16/72 = 2/9, and (2/9) × 9 = 2.
QUICK CHECK
The value of (5²)/((3² + 4²)⁴) ÷ (1/625)^{1.5} × (2/3)^{-2} is : (SI 31 Jul 2023)
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Answer: 9/4
Take the pieces one at a time. 3² + 4² = 25, so 5²/25⁴ = 25/25⁴ = 25⁻³ = 5⁻⁶.
Next (1/625)^1.5 = 625^(−1.5) = (5⁴)^(−1.5) = 5⁻⁶, and dividing 5⁻⁶ by 5⁻⁶ gives 1.
What is left is (2/3)⁻² = (3/2)² = 9/4.
QUICK CHECK
If (9/4)^{3/2} × (16/81)² ÷ (2/3)^{4+a} = 9/4, then (5^a)/a is ________. (SI 31 Jul 2023)
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Answer: 125/3
Write everything as a power of 2/3. (9/4)^(3/2) = (3/2)³ = (2/3)⁻³, and (16/81)² = ((2/3)⁴)² = (2/3)⁸.
Multiplying gives (2/3)⁵, and dividing by (2/3)^(4+a) gives (2/3)^(1−a). The right-hand side 9/4 = (3/2)² = (2/3)⁻², so 1 − a = −2 and a = 3.
The question asks for 5^a/a = 125/3 = 125/3.
QUICK CHECK
Let x = ((3/2)³)/(3^6) × 5²(2⁴ + 3²)^{0.5}. Then the value of x^{-2/3} is : (SI 31 Jul 2023)
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Answer: 36/25
Evaluate the bracket first: 2⁴ + 3² = 25, and 25^0.5 = 5. So 5² × 5 = 125.
The front part is (3/2)³ ÷ 3⁶ = (27/8) ÷ 729 = 1/216. Hence x = 125/216, and x^(−2/3) = (216/125)^(2/3) = (6/5)² = 36/25.
216 = 6³ and 125 = 5³, which is why the two-thirds power comes out clean.
WHEN DIFFERENT BASES SHARE ONE VALUE
If 2^a = 3^b = 6^c, take logarithms of the common value k. Then 1/a = log2 / log k, 1/b = log3 / log k and 1/c = log6 / log k.
Because log 2 + log 3 = log 6, the combination 1/a + 1/b − 1/c is always 0. The SI paper has asked this twice, once directly and once dressed up as (xy + yz + zx)/xyz — which is just 1/x + 1/y + 1/z.
QUICK CHECK
If 2^a = 3^b = 6^c, then find the value of 1/a + 1/b − 1/c (SI 29 Jul 2023)
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Answer: 0
Let 2^a = 3^b = 6^c = k. Taking logarithms, a log2 = b log3 = c log6 = log k, so 1/a = log2 / log k and so on.
Then 1/a + 1/b − 1/c = (log2 + log3 − log6) / log k. Since 2 × 3 = 6, the numerator is log 6 − log 6 = 0.
QUICK CHECK
If 2^{x} = 3^{y} = 6^{-z}, then what will be the value of (xy+yz+zx)/xyz? (SI 2 Jul 2023)
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Answer: 0
First notice that (xy + yz + zx)/xyz = 1/z + 1/x + 1/y — divide each term by xyz.
With 2^x = 3^y = 6^(−z) = k, we get 1/x = log2/log k, 1/y = log3/log k and 1/z = −log6/log k. Adding, (log2 + log3 − log6)/log k = 0.
CHECK YOURSELF
If ((4^8)²)/(64(7)^8) × (36(6^9)^{1/4})/((4)^{15}) × 49 × (7^6)/(6^{1/4}) = (6/x)⁴ × 7^y, then find x and y. (SI 29 Jun 2023)
Show answer
Collect each base separately.
Powers of 4: (4⁸)² = 4¹⁶, and 64 = 4³, so 4¹⁶ ÷ (4³ × 4¹⁵) = 4⁻² = 1/16.
Powers of 6: 36 = 6² and (6⁹)^(1/4) = 6^(9/4), divided by 6^(1/4) gives 6^(2 + 9/4 − 1/4) = 6⁴.
Powers of 7: (1/7⁸) × 49 × 7⁶ = 7^(−8 + 2 + 6) = 7⁰ = 1.
So the left side is 6⁴/16. The right side is (6/x)⁴ × 7^y, so x⁴ = 16 giving x = 2, and 7^y = 1 giving y = 0. The answer is x = 2 and y = 0.
A conjugate pair always leaves a difference of squares. A sum of surds always simplifies once each perfect square is pulled out.
QUICK CHECK
The square root of (8 + √39) (8 − √39) is (SI 24 Aug 2021)
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Answer: 5
The two brackets are conjugates, so their product is a difference of squares: 8² − (√39)² = 64 − 39 = 25. The square root of 25 is 5.
Never multiply the brackets out term by term — the surd cancels itself.
QUICK CHECK
What is the value of √252/(√700 + √(1372))? (SI 24 Aug 2021)
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Answer: 1/4
Pull the perfect square out of each surd: √252 = √(36 × 7) = 6√7, √700 = √(100 × 7) = 10√7 and √1372 = √(196 × 7) = 14√7.
The expression becomes 6√7 ÷ (10√7 + 14√7) = 6√7 ÷ 24√7 = 1/4.
QUICK CHECK
Find the value of x. √(1 + 55/729) = (1 + x/27) (SI 19 Aug 2021)
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Answer: 1
Add inside the root first: 1 + 55/729 = 784/729. Both are perfect squares — 784 = 28² and 729 = 27² — so the root is 28/27.
Writing 28/27 as 1 + 1/27 shows that x = 1.
QUICK CHECK
Find the value of x in √144/4 = √196/x. (SI 24 Aug 2021)
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Answer: 14/3
√144 = 12, so the left side is 12/4 = 3. On the right √196 = 14, so 14/x = 3 and x = 14/3.
QUICK CHECK
If x = 5, then find the value of the expression 10x √(x³ − x²)? (SI 19 Aug 2021)
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Answer: 500
Substitute x = 5 inside the root first: x³ − x² = 125 − 25 = 100, and √100 = 10. Then 10x × 10 = 10(5) × 10 = 500.
Simplifying x³ − x² to x²(x − 1) first also works: 25 × 4 = 100.
QUICK CHECK
If a = 3^{0.5} + 1/3^{0.5} and b = 3^{0.5} − 1/3^{0.5}, then the value of the expression (a × b)² − 64/9 + (3/8) a × b is : (SI 2 Jul 2023)
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Answer: 1
You never need a or b separately — only their product. ab = (√3 + 1/√3)(√3 − 1/√3) = 3 − 1/3 = 8/3, another difference of squares.
Now (ab)² − 64/9 + (3/8)ab = 64/9 − 64/9 + (3/8)(8/3) = 0 + 1 = 1.
QUICK CHECK
Let x = (0.25)^{0.5} and y = (3.375)^{1/3}. The value of the expression (4x² − 9y²)/3.5 × 1/(x² − y²) is ______. (SI 20 Jun 2023)
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Answer: 11/4
Simplify x and y first: x = (0.25)^0.5 = 0.5 and y = (3.375)^(1/3) = 1.5, since 1.5³ = 3.375.
Then x² = 0.25 and y² = 2.25. The numerator 4x² − 9y² = 1 − 20.25 = −19.25, and x² − y² = 0.25 − 2.25 = −2.
So the value is (−19.25 ÷ 3.5) × (1 ÷ −2) = (−5.5)(−0.5) = 2.75 = 11/4.
CHECK YOURSELF
If [(√(1455) − √(1239))^{2/3} × (√(1239) + √(1455))^{2/3}] / [(8^{1/6} + 1/8^{1/6})(8^{1/3} − 1 + 1/8^{1/3})(8^{1/6} − 1/8^{1/6})(8^{1/3} + 1 + 1/8^{1/3})] = m m/n (a mixed number), where m and n are natural numbers, then find the value of 2m(n + 1) − n²? (SI 15 Jul 2023)
Show answer
Take the two halves separately.
Top: (√1455 − √1239)^(2/3) × (√1455 + √1239)^(2/3) = [(√1455 − √1239)(√1455 + √1239)]^(2/3) = (1455 − 1239)^(2/3) = 216^(2/3) = 36.
Bottom: let t = 8^(1/6), so 8^(1/3) = t² and t × (1/t) = 1. Then (t + 1/t)(t² − 1 + 1/t²) = t³ + 1/t³ and (t − 1/t)(t² + 1 + 1/t²) = t³ − 1/t³ — both are the cube identities. Their product is t⁶ − 1/t⁶ = 8 − 1/8 = 63/8.
So the fraction is 36 ÷ (63/8) = 288/63 = 32/7 = 4 4/7, which matches the stated form m m/n with m = 4 and n = 7. Finally 2m(n + 1) − n² = 2(4)(8) − 49 = 64 − 49 = 15.
COMMON TRAPS
Reading a⁶ ÷ a⁻⁵ as a¹. Subtracting a negative index adds, so the answer is a¹¹.
Expanding 3^(x−2) + 3^x instead of factoring out the smaller power. The bracket is always a tidy fraction; the expansion never is.
Leaving a surd under the root. √252 is 6√7, and once every term is a multiple of √7 the root cancels out of the fraction entirely.
Forgetting that a negative index flips a fraction rather than making it negative. (1/3)⁻³ is 27, not −27.
One-page revision
Read only this the night before.
QUICK BYTES
B → O → D → M → A → S, and O includes the word “of”.
÷ and × left to right. + and − left to right.
Brackets from the inside out: ( ) then { } then [ ].
Two repeated decimals in a fraction → look for a³ ± b³ before you calculate.
(a − b)² + (a + b)² = 2(a² + b²) — appears every other year.
Every number on the bottom a tenth of the top → the squared fraction is 100.
Letter codes (P, Q, R, S) change the symbols, never the order.
Pull the perfect square out of every surd before you divide.
2^a = 3^b = 6^c → 1/a + 1/b − 1/c = 0.
REMEMBER
Brackets, of, divide, multiply, add, subtract — and when two share a rank, read left to right. That one sentence answers thirty of the eighty-five, and the seven index laws answer thirty more.
3.Simplify the following expression: [ 71 – 14 ÷ 2 of 7 ] - [ 6 ÷ 6 of 6 + 6 ÷ 6 x 6 ] + ( 6 + 6 ) – 6 of 6 + 6x ( 6 x 8 ) ÷6 - ( 0.35 x 0.35 + 0.65 x 0.65 + 0.7 x 0.65 ).ਹੇਠ ਲਿਖੇ ਵਿਅੰਜਕ ਨੂੰ ਸਰਲ ਕਰੋ: [ 71 – 14 ÷ 2 of 7 ] - [ 6 ÷ 6 of 6 + 6 ÷ 6 x 6 ] + ( 6 + 6 ) – 6 of 6 + 6x ( 6 x 8 ) ÷6 - ( 0.35 x 0.35 + 0.65 x 0.65 + 0.7 x 0.65 ).#
SI · 9 Jul 2023 · Shift 1
1521/6521/6
2420/6420/6
3421/6421/6
4520/6520/6
4.Let a = [1/2 ÷ 1/3 + 3/4 × 10/6] × (2/3 ÷ 2/9 + 1/2) and b = [3(1/6 − 5/12 × 6/5) − (−3)] × 2 ÷ (5/2). The value of a/b is:ਮੰਨ ਲਓ a = [1/2 ÷ 1/3 + 3/4 × 10/6] × (2/3 ÷ 2/9 + 1/2) ਅਤੇ b = [3(1/6 − 5/12 × 6/5) − (−3)] × 2 ÷ (5/2). a/b ਦਾ ਮੁੱਲ ਹੈ:#
SI · 9 Jul 2023 · Shift 1
177/577/5
2385/64385/64
3385/128385/128
4385/32385/32
5.Find the value of the following expression. 316 − 3(20 + 16 ÷ 4 × 3 − 2 × 2) + 101ਹੇਠ ਲਿਖੇ ਵਿਅੰਜਕ ਦਾ ਮੁੱਲ ਪਤਾ ਕਰੋ। 316 − 3(20 + 16 ÷ 4 × 3 − 2 × 2) + 101#
SI · 9 Jul 2023 · Shift 1
13333
2333333
3323323
4313313
6.A tailor has 87.5 metres of cloth and has to make 8 pieces out of every one metre of cloth. How many pieces of cloth can be made in all?ਇੱਕ ਦਰਜ਼ੀ ਕੋਲ 87.5 ਮੀਟਰ ਕੱਪੜਾ ਹੈ ਅਤੇ ਉਸ ਨੂੰ ਇੱਕ ਮੀਟਰ ਕੱਪੜੇ ਵਿੱਚੋਂ 8 ਟੁਕੜੇ ਬਣਾਉਣੇ ਪੈਂਦੇ ਹਨ। ਕੱਪੜੇ ਦੇ ਕੁੱਲ ਕਿੰਨੇ ਟੁਕੜੇ ਬਣਾਏ ਜਾ ਸਕਦੇ ਹਨ?#
SI · 14 Jul 2023 · Shift 1
1525525
2700700
3400400
4375375
7.Simplify the following expression. [(7/2 ÷ 5/2 × 3/2) / (7/2 ÷ 5/2 of 3/2)] ÷ 15/14ਹੇਠਾਂ ਦਿੱਤੇ ਵਿਅੰਜਕ ਨੂੰ ਸਰਲ ਕਰੋ। [(7/2 ÷ 5/2 × 3/2) / (7/2 ÷ 5/2 of 3/2)] ÷ 15/14#
11.Simplify the following. 12.0737 − [5 + 0.05 of (4.1 − 1.3 × 2.02)]ਹੇਠਾਂ ਦਿੱਤੇ ਨੂੰ ਸਰਲ ਕਰੋ। 12.0737 − [5 + 0.05 of (4.1 − 1.3 × 2.02)]#
SI · 15 Jul 2023 · Shift 1
17.07.0
27.37.3
37.17.1
47.27.2
12.Find the value of 1 ÷ 3/7 of (6 + 8 × 1) + [1/5 ÷ 7/25 − 1].1 ÷ 3/7 of (6 + 8 × 1) + [1/5 ÷ 7/25 − 1] ਦਾ ਮੁੱਲ ਪਤਾ ਕਰੋ।#
SI · 15 Jul 2023 · Shift 1
1−5/42−5/42
25/425/42
3−1/42−1/42
4−5/47−5/47
13.If 'P' denotes '+', 'Q' denotes '−', 'R' denotes '×' and 'S' denotes '÷', then what will be the value of 70 Q 5 R 81 S 9 P 20?ਜੇਕਰ ‘P’, ‘+’ ਨੂੰ, ‘Q’, ‘−’ ਨੂੰ, ‘R’, ‘×’ ਨੂੰ ਅਤੇ ‘S’, ‘÷’ ਨੂੰ ਦਰਸਾਉਂਦਾ ਹੈ, ਤਾਂ 70 Q 5 R 81 S 9 P 20 ਦਾ ਮੁੱਲ ਕੀ ਹੋਵੇਗਾ?#
SI · 15 Jul 2023 · Shift 1
15555
24545
35858
44848
14.If ‘P’ stands for ‘+’, ‘Q’ stands for ‘–’, ‘R’ stands for ‘×’ and ‘S’ stands for ‘÷’, then what will be the value of 120 Q 8 R 72 S 8 P 45?ਜੇਕਰ ‘P’, ‘+’ ਨੂੰ ਦਰਸਾਉਂਦਾ ਹੈ, ‘Q’, ‘–’ ਨੂੰ ਦਰਸਾਉਂਦਾ ਹੈ, ‘R’, ‘×’ ਨੂੰ ਦਰਸਾਉਂਦਾ ਹੈ ਅਤੇ ‘S’, ‘÷’ ਨੂੰ ਦਰਸਾਉਂਦਾ ਹੈ, ਤਾਂ 120 Q 8 R 72 S 8 P 45 ਦਾ ਮੁੱਲ ਕਿੰਨਾ ਹੋਵੇਗਾ?#
18.The length of a field is divided into three parts. The first part is 1/3 of the whole length, the second part is 3/5 of the first part, and the third part is 3.50 metres. Find the length of the field.ਇੱਕ ਖੇਤਰ ਦੀ ਲੰਬਾਈ ਨੂੰ ਤਿੰਨ ਭਾਗਾਂ ਵਿੱਚ ਵੰਡਿਆ ਜਾਂਦਾ ਹੈ। ਪਹਿਲਾ ਹਿੱਸਾ ਪੂਰੀ ਲੰਬਾਈ ਦਾ 1/3 ਹੈ, ਦੂਜਾ ਹਿੱਸਾ ਪਹਿਲੇ ਹਿੱਸੇ ਦਾ 3/5 ਹੈ, ਅਤੇ ਤੀਜਾ ਹਿੱਸਾ 3.50 ਮੀਟਰ ਹੈ। ਖੇਤਰ ਦੀ ਲੰਬਾਈ ਪਤਾ ਕਰੋ।#
SI · 20 Jun 2023 · Shift 2
17.50 metres7.50 ਮੀਟਰ
215.50 metres15.50 ਮੀਟਰ
315 metres15 ਮੀਟਰ
445.50 metres45.50 ਮੀਟਰ
19.Ramesh spends 3/5 of his monthly salary on food and 1/3 of his salary on clothes and travel, and keeps the rest as savings. If his monthly salary is 45,000, how much will he save in 3 months?ਰਮੇਸ਼ ਆਪਣੀ ਮਹੀਨਾਵਾਰ ਤਨਖਾਹ ਦਾ 3/5 ਭੋਜਨ 'ਤੇ ਅਤੇ ਆਪਣੀ ਤਨਖਾਹ ਦਾ 1/3 ਕੱਪੜਿਆਂ ਅਤੇ ਸੈਰ-ਸਪਾਟੇ 'ਤੇ ਖ਼ਰਚ ਕਰਦਾ ਹੈ ਅਤੇ ਬਾਕੀ ਬਚਤ ਵਜੋਂ ਜਮ੍ਹਾਂ ਰੱਖਦਾ ਹੈ। ਜੇਕਰ ਉਸਦੀ ਮਹੀਨਾਵਾਰ ਤਨਖਾਹ 45,000 ਹੈ, ਤਾਂ ਉਹ 3 ਮਹੀਨਿਆਂ ਵਿੱਚ ਕਿੰਨੀ ਬਚਤ ਕਰੇਗਾ?#
30.3/4 of the difference between 2 1/6 and 1 1/9 is subtracted from 3/4 of 4 1/3. The resultant value is:2 1/6 ਅਤੇ 1 1/9 ਦੇ ਅੰਤਰ ਦਾ 3/4, 4 1/3 ਦੇ 3/4 ਵਿੱਚੋਂ ਘਟਾਇਆ ਜਾਂਦਾ ਹੈ। ਨਤੀਜਾ ਮੁੱਲ ਹੈ:#
SI · 31 Jul 2023 · Shift 1
159/4859/48
259/2459/24
378/2478/24
448/5948/59
31.Simplify the following using BODMAS rule. 26 + 11 − 5 × 1/2 of 12 − {36 ÷ (14 + 4)}BODMAS ਨਿਯਮ ਦੀ ਵਰਤੋਂ ਕਰਦਿਆਂ ਹੇਠਾਂ ਦਿੱਤੇ ਨੂੰ ਹੱਲ ਕਰੋ। 26 + 11 − 5 × 1/2 of 12 − {36 ÷ (14 + 4)}#
SI · 16 Oct 2022
155
277
31313
41515
32.What is the value of 90 + 55 ÷ 1.1 × 4 − 21?90 + 55 ÷ 1.1 × 4 − 21 ਦਾ ਮੁੱਲ ਕੀ ਹੈ?#
SI · 16 Oct 2022
1296296
2269269
3216216
4221221
33.What is the value of the following expression? (4/3 + 5/9) of 4/17 ÷ 2 1/3 × 1 3/4 − 1/4ਹੇਠਾਂ ਦਿੱਤੇ ਵਿਅੰਜਕ ਦਾ ਮੁੱਲ ਕਿੰਨਾ ਹੈ? (4/3 + 5/9) of 4/17 ÷ 2 1/3 × 1 3/4 − 1/4#
SI · 16 Oct 2022
112/1312/13
21/121/12
37/127/12
45/125/12
34.What is the value of 5/4 − 0.45 + 3.75 − 1/2 − 0.05 ?5/4 − 0.45 + 3.75 − 1/2 − 0.05 ਦਾ ਮੁੱਲ ਕੀ ਹੈ?#
36.What do we get on simplifying (9/−8) × ((7/3) − 2 + (5/6))?(9/−8) × ((7/3) − 2 + (5/6)) ਨੂੰ ਸਰਲ ਕਰਨ 'ਤੇ ਸਾਨੂੰ ਕੀ ਪ੍ਰਾਪਤ ਹੁੰਦਾ ਹੈ?#
SI · 19 Aug 2021 · Shift 1
121/1621/16
216/2116/21
3−21/16−21/16
4−16/21−16/21
37.Find the value of '?' in the equation given below. (1/2) of 2558 + 42% of 1350 = (?)2 − 7605ਹੇਠਾਂ ਦਿੱਤੀ ਸਮੀਕਰਨ ਵਿੱਚ '?' ਦਾ ਮੁੱਲ ਪਤਾ ਕਰੋ। 2558 ਦਾ (1/2) + 1350 ਦਾ 42% = (?)2 − 7605#
SI · 19 Aug 2021 · Shift 1
1105105
29494
39595
49696
38.The value of (287.0134 × 0.0491 × 1.902)/(41.004 × 99.89) is closest to ______.(287.0134 × 0.0491 × 1.902)/(41.004 × 99.89) ਦਾ ਮੁੱਲ ______ ਦੇ ਸਭ ਤੋਂ ਨੇੜੇ ਹੈ।#
40.Find the value of 'y' in the equation given below. −774.67 + 1742.52 − 873.43 − y = − 7472.78ਅੱਗੇ ਦਿੱਤੀ ਹੋਈ ਸਮੀਕਰਨ ਵਿੱਚ 'y' ਦਾ ਮੁੱਲ ਪਤਾ ਕਰੋ। −774.67 + 1742.52 − 873.43 − y = − 7472.78#
SI · 19 Aug 2021 · Shift 1
17557.207557.20
27567.207567.20
37576.207576.20
47657.207657.20
41.If (2 + 1/(1 + 4/5)) / (2 + 1/(1 + 1/(1 + 1/4))) = x, then what is the value of x?ਜੇ (2 + 1/(1 + 4/5)) / (2 + 1/(1 + 1/(1 + 1/4))) = x ਹੈ, ਤਾਂ x ਦਾ ਮੁੱਲ ਕੀ ਹੈ?#
43.0.5 × 0.5 + 0.5 − 0.5 is equal to which of the following?0.5 × 0.5 + 0.5 − 0.5 ਕਿਸ ਦੇ ਬਰਾਬਰ ਹੈ?#
SI · 24 Aug 2021 · Shift 1
10.250.25
20.6250.625
30.50.5
40.050.05
44.Raghu consumes 0.75 litre of milk every day, and Rani consumes 1/4 litre of milk every day. If the price of milk is ₹42.25 per litre, then find the total amount (in ₹) spent by the two of them on milk in 15 weeks.ਰਘੂ ਹਰ ਰੋਜ਼ 0.75 ਲੀਟਰ ਦੁੱਧ ਦੀ ਖਪਤ ਕਰਦਾ ਹੈ, ਅਤੇ ਰਾਣੀ ਹਰ ਰੋਜ਼ 1/4 ਲੀਟਰ ਦੁੱਧ ਦੀ ਖਪਤ ਕਰਦੀ ਹੈ। ਜੇ ਪ੍ਰਤੀ ਲੀਟਰ ਦੁੱਧ ਦਾ ਮੁੱਲ ₹42.25 ਹੈ, ਤਾਂ ਦੋਵਾਂ ਦੁਆਰਾ 15 ਹਫ਼ਤਿਆਂ ਵਿੱਚ ਦੁੱਧ 'ਤੇ ਖਰਚ ਕੀਤੀ ਕੁੱਲ ਰਾਸ਼ੀ (₹ ਵਿੱਚ) ਪਤਾ ਕਰੋ।#
SI · 24 Aug 2021 · Shift 1
15,536.255,536.25
24,436.254,436.25
35,226.255,226.25
44,226.254,226.25
45.Find the value of '?' in the equation given below. (0.33 + 0.333) ÷ (0.33 + 0.033) = ?ਹੇਠਾਂ ਦਿੱਤੀ ਸਮੀਕਰਨ ਵਿੱਚ '?' ਦਾ ਮੁੱਲ ਪਤਾ ਕਰੋ। (0.33 + 0.333) ÷ (0.33 + 0.033) = ?#
Work from the innermost bracket outwards, doing division before subtraction inside each bracket. 20 ÷ 10 = 2, so (32 − 2) = 30; then {44 − 30} = 14. Next (7 × 8 ÷ 2) = 56 ÷ 2 = 28. Now [28 ÷ 14] = 2, and finally 15 − 2 = 13. Option 1 (17) is what you get by treating the last step as 15 + 2. Answer: option 2.
