27 questions · CET 2025–2026 · Easy 25 · Medium 2 · Hard 0. Newest paper first. Full papers
Answer: B official key
Approach: Square near a round number: (a − b)² = a² − 2ab + b².
Solution:
1397² = (1400 − 3)²
= 1400² − 2 × 1400 × 3 + 3²
= 1,960,000 − 8,400 + 9
= 1,951,609.
Cetking shortcut: Last digit 7² → 9 and last two digits 97² → 09 kill C and D; size ≈ 1.95 million kills A and E.
Answer: B
Solve the following mathematical expression and select the correct answer:
Answer: B official key
Approach: Rewrite as squares and use a² − b² = (a + b)(a − b).
Solution:
53 × 2 × 106 = 4 × 53² and 47 × 2 × 94 = 4 × 47².
Expression = 4(53² − 47²) = 4 × (53 + 47)(53 − 47)
= 4 × 100 × 6 = 2400.
(Direct check: 11236 − 8836 = 2400.)
Cetking shortcut: Spot 106 = 2 × 53 and 94 = 2 × 47 → 4(a² − b²) in one line.
Answer: B
Answer: B official key
Approach: Evaluate the percentages, then isolate x.
Solution:
88% of 370 = 325.6.
24% of 210 = 50.4.
325.6 + 50.4 − x = 118 → 376 − x = 118 → x = 258.
Cetking shortcut: The decimals .6 and .4 add to a whole number — 376 − 118 = 258.
Answer: B
Find the value of the following equation:
30% of 40% of (2/5) of 2500
Answer: D official key
Approach: Fraction-of chain: multiply step by step.
Solution:
2/5 of 2500 = 1000.
40% of 1000 = 400.
30% of 400 = 120.
Cetking shortcut: 0.3 × 0.4 × 0.4 × 2500 = 0.048 × 2500 = 120.
Answer: D
Arrange the following fractions in descending order:
(97/101), (48/50), (89/93), (76/79)
Answer: D official key
Approach: Compare fractions close to 1 by their gap from 1: smaller gap = larger fraction.
Solution:
1 − 97/101 = 4/101 ≈ 0.0396
1 − 48/50 = 2/50 = 0.04
1 − 89/93 = 4/93 ≈ 0.0430
1 − 76/79 = 3/79 ≈ 0.0380
Smallest gap → largest: 76/79 > 97/101 > 48/50 > 89/93.
Why the other options are wrong:
A, B, C, E put 48/50 or 97/101 ahead of 76/79, which has the smallest gap from 1.
Cetking shortcut: For a/b just below 1, compare (b − a)/b — the 'complement' method avoids long division.
Answer: D
Find the value of the following equation:
1.43 + 6 (1/4) − 3 (1/5) + 0.88 − (2.5 × 0.32)
Answer: B official key
Approach: Convert mixed fractions to decimals and simplify (BODMAS).
Solution:
6 1/4 = 6.25; 3 1/5 = 3.2; 2.5 × 0.32 = 0.8.
1.43 + 6.25 − 3.2 + 0.88 − 0.8
= 7.68 − 3.2 + 0.88 − 0.8 = 4.48 + 0.08 = 4.56.
Cetking shortcut: Group: (1.43 + 0.88) + (6.25 − 3.2 − 0.8) = 2.31 + 2.25 = 4.56.
Answer: B
Find the value of
999 (1/7) + 999 (2/7) + 999 (3/7) + 999 (4/7) + 999 (5/7) + 999 (6/7)
Answer: C official key
Approach: Split each mixed number into whole and fraction parts.
Solution:
Whole parts: 999 × 6 = 5994.
Fractions: (1 + 2 + 3 + 4 + 5 + 6)/7 = 21/7 = 3.
Total = 5994 + 3 = 5997.
Cetking shortcut: Fraction pairs 1/7 + 6/7, 2/7 + 5/7, 3/7 + 4/7 each make 1 → 3.
Answer: C
What will come in place of question mark (?) in the given expression ?
(39.3 × 53.4) + (26.7 × 5.9) = ?
Answer: C official key
Approach: Direct multiplication of decimals, then addition.
Solution:
39.3 × 53.4 = 2098.62.
26.7 × 5.9 = 157.53.
Sum = 2098.62 + 157.53 = 2256.15.
Why the other options are wrong:
Cetking shortcut: 39.3 × 53.4 = 40 × 53.4 − 0.7 × 53.4 = 2136 − 37.38 = 2098.62; 26.7 × 5.9 = 26.7 × 6 − 2.67 = 157.53; total 2256.15.
Answer: C
Answer: B official key
Approach: Recognise the identity a² + b² + 2ab = (a + b)².
Solution:
a = 0.2, b = 0.3.
0.2 × 0.2 + 0.3 × 0.3 + 2 × 0.2 × 0.3 = (0.2 + 0.3)².
= (0.5)² = 0.25.
Check: 0.04 + 0.09 + 0.12 = 0.25.
Why the other options are wrong:
A (0.025) – decimal placed wrongly.
C (0.5) – forgets to square a + b.
D (0.05), E (0.6) – arithmetic slips.
Cetking shortcut: Spot a² + b² + 2ab at a glance → (a + b)²; no multiplication needed.
Answer: B
Answer: D official key
Approach: Compare fractions by decimals or by 'gap from 1'.
Solution:
7/6 = 1.17 (greater than 1).
7/9 = 0.778, 4/5 = 0.800, 5/7 = 0.714, 9/11 = 0.818.
Smallest = 5/7 = 0.714.
Why the other options are wrong:
A (7/6) – more than 1, the largest.
B (7/9 = 0.778), C (4/5 = 0.8), E (9/11 = 0.818) – all above 0.714.
Cetking shortcut: For fractions of the form (n − k)/n, compare the gap k/n: 5/7 is short by 2/7 ≈ 0.29, the biggest gap → smallest fraction.
Answer: D
Answer: B official key
Approach: Telescoping product: (1 − 1/n) = (n − 1)/n.
Solution:
Product = (2/3)(3/4)(4/5)…(99/100).
Every numerator cancels the previous denominator.
Only the first numerator (2) and last denominator (100) remain → 2/100 (= 1/50).
Why the other options are wrong:
Cetking shortcut: First numerator over last denominator.
Answer: B
DIRECTION for the question: Solve the following question and mark the best possible option.
Answer: A official key
Approach: Write 999 as 1000 − 1 and distribute.
Solution: 587 × 999 = 587 × (1000 − 1)
= 587000 − 587
= 586413
Cetking shortcut: Last three digits of N × 999 (N < 1000) are 1000 − N = 413; leading part is N − 1 = 586 → 586413. Only option A ends in 413.
Answer: A
DIRECTION for the question: Solve the following question and mark the best possible option.
Answer: E official key
Approach: BODMAS — division and multiplication left to right.
Solution: 400 ÷ 0.1 = 4000 (dividing by 0.1 = multiplying by 10).
4000 × 0.2 = 800.
Why the other options are wrong:
A/B/C: decimal-place slips.
D (8000): uses × 2 instead of × 0.2.
Answer: E
DIRECTION for the question: Solve the following question and mark the best possible option.
Answer: B official key
Approach: Use 5376 ÷ 168 = 32 and adjust decimals.
Solution: 168 × 32 = 5376 ⇒ 5376 ÷ 168 = 32.
5.376 = 5376 ÷ 1000 and 16.8 = 168 ÷ 10.
5.376 ÷ 16.8 = (5376 ÷ 168) × (10 ÷ 1000) = 32 ÷ 100 = 0.32.
Cetking shortcut: Estimate: 5.4 ÷ 17 ≈ 0.3 → only 0.32 fits.
Answer: B
Solve :
777.97 X 999.79
Answer: C official key
Approach: Write 999.79 as 1000 − 0.21 and multiply.
Solution:
777.97 × 1000 = 777970
777.97 × 0.21 = 163.3737
777970 − 163.3737 = 777806.6263 ≈ 777806.63
Cetking shortcut: The answer must be just under 777970 by about 160 → only 777806.63 lies in that range (777706.53 is 100 too low).
Answer: C
Simplify:
((3⁴ × 2³ − 5³)/7) + √256 − (2/5) × (25/4) + 0.75 × 8
Answer: D official key
Approach: BODMAS — evaluate powers and roots, then division/multiplication, then addition/subtraction.
Solution:
3⁴ × 2³ = 81 × 8 = 648; 648 − 5³ = 648 − 125 = 523
523/7 = 74.714
√256 = 16
(2/5) × (25/4) = 50/20 = 2.5
0.75 × 8 = 6
Total = 74.714 + 16 − 2.5 + 6 = 94.214 ≈ 94.21
Cetking shortcut: Only 523/7 is non-terminating; the rest add to 16 − 2.5 + 6 = 19.5, so answer = 74.71 + 19.5 = 94.21.
Answer: D
Answer: A
Approach: BODMAS — innermost brackets first.
Solution:
23 − 20 = 3 ⇒ 42 × 3 = 126.
5 × 80 − 100 = 300 ⇒ 2 × 300 = 600.
Inside: 126 + 2 − 600 + 16 − 4 = −460.
26 + (−460) = −434.
Why the other options are wrong:
B 434: sign error.
C −443, D −453, E 435: arithmetic slips.
Cetking shortcut: Sign check: −600 dominates ⇒ answer must be negative, leaving only A, C, D.
Answer: A
Answer: A
Approach: Identity (a + b)³ = a³ + b³ + 3ab(a + b) with a = 0.081, b = 0.009.
Solution:
3ab = 3 × 0.081 × 0.009 = 0.002187 and a + b = 0.09.
So 0.081³ + 0.009³ + 0.002187 × 0.09 = a³ + b³ + 3ab(a + b) = (a + b)³.
(0.09)³ = 0.000729.
Why the other options are wrong:
B, C, D, E: same digits 729 with the decimal misplaced — (0.09)³ has 6 decimal places.
Cetking shortcut: Spot 0.002187 = 3 × 0.081 × 0.009 and 0.09 = 0.081 + 0.009 ⇒ cube of 0.09.
Answer: A
Answer: A
Approach: Scaling: every term is 3 times an odd number, so each square is 9 times.
Solution:
3² + 9² + 15² + 21² + 27² = 3²(1² + 3² + 5² + 7² + 9²)
= 9 × 165 = 1485.
Why the other options are wrong:
D 495: multiplies by 3 instead of 9.
C 990: multiplies by 6.
B, E: slips.
Cetking shortcut: Factor out 3² = 9 ⇒ 9 × 165 = 1485.
Answer: A
Answer: A
Approach: Last-digit check, then a rough size check.
Solution:
Units digit: 7 × 3 = 21 ⇒ product ends in 1 ⇒ only A (…511) qualifies.
Size check: 968427 × 3493 ≈ 9.68 × 10⁵ × 3.49 × 10³ ≈ 3.38 × 10⁹ ✓.
Exact: 968427 × 3493 = 3382715511.
Why the other options are wrong:
B …523, C …879, D …965, E …673: wrong units digit.
Cetking shortcut: Units digit 7 × 3 → 1 eliminates every option except A.
Answer: A
Answer: B
Approach: Take the common factor 8796 out.
Solution: 8796 × 223 + 8796 × 77 = 8796 × (223 + 77) = 8796 × 300.
8796 × 3 = 26,388 → × 100 = 2,638,800.
Cetking shortcut: Last digits: 6 × 300 ends in 800; only B (2638800) ends in 800 with the right size — E ends 700.
Answer: B
Answer: C
Approach: Left-to-right division then multiplication, then isolate ?.
Solution: 786 ÷ 24 = 32.75.
32.75 × ? = 6.55 → ? = 6.55 ÷ 32.75 = 0.2.
Check: 32.75 × 0.2 = 6.55 ✔
Cetking shortcut: 6.55 is one-fifth of 32.75 (32.75 ÷ 5 = 6.55) → ? = 1/5 = 0.2.
Answer: C
Answer: C
Approach: Use 52416 ÷ 168 = 312 (equivalent to the given fact) and adjust decimals.
Solution: Given 52416 ÷ 312 = 168 ⇔ 52416 ÷ 168 = 312.
52.416 ÷ 0.0168 = (52416 × 10⁻³) ÷ (168 × 10⁻⁴) = 312 × 10 = 3120.
Answer: C
Answer: B
Approach: Undo the fractions to find the number, then take the new fraction.
Solution:
(1/3) × (1/4) × x = 15 → x/12 = 15 → x = 180.
(3/10) × 180 = 54.
Cetking shortcut: 3/10 of x = (3/10) × 12 × 15 = 3.6 × 15 = 54.
Answer: B
Answer: A
Approach: Distributive law — take the common factor out.
Solution:
8796 × 223 + 8796 × 77 = 8796 × (223 + 77) = 8796 × 300 = 26,38,800.
Cetking shortcut: Answer must end in 00 (×300) and be ≈ 8800 × 300 = 26.4 lakh → only 2638800 fits.
Answer: A
Answer: B
Approach: Difference of the two fractions × number = 770.
Solution:
7/8 − 7/18 = 7(18 − 8)/144 = 70/144 = 35/72.
(35/72)x = 770 → x = 770 × 72/35 = 22 × 72 = 1584.
Cetking shortcut: 770/35 = 22 → x = 22 × 72.
Answer: B
If :
X stands for addition ;
÷ stands for subtraction ;
- stands for division,
+ means multiplication
Then,
Answer: C
Approach: Decode symbols, then BODMAS.
Solution:
X → +, ÷ → −, − → ÷, + → ×
20 X 8 ÷ 8 − 4 + 2 becomes 20 + 8 − 8 ÷ 4 × 2
8 ÷ 4 × 2 = 2 × 2 = 4
20 + 8 − 4 = 24
Cetking shortcut: Write the decoded expression on paper before calculating — most errors come from decoding in your head.
Answer: C
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