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CBSE Mathematics Standard Question Paper 2026
Class 10 · Code 30/5/3 · Date: 17-02-2026
80Max Marks
3 HrsDuration
38Questions
5Sections A–E
30/5/3Paper Code
📌 General Instructions
- This question paper has 5 Sections A–E. All questions are compulsory.
- Section A: 20 MCQs of 1 mark each.
- Section B: 5 questions of 2 marks each.
- Section C: 6 questions of 3 marks each.
- Section D: 4 questions of 5 marks each.
- Section E: 3 Case Study questions of 4 marks each.
- Internal choice is provided in some questions. Attempt only one option.
Q11 MarkMCQ
A conical cavity of maximum volume is carved out from a wooden solid hemisphere of radius 10 cm. Curved surface area of the cavity carved out is (use π = 3.14):
- (A) 314√2 cm²
- (B) 314 cm²
- (C) 3140/3 cm²
- (D) 3140√2 cm²
Q21 MarkMCQ
If aₙ represents nth term of the A.P. −15/4, −10/4, −5/4, … then value of a₁₆ − a₁₂ is:
- (A) 4
- (B) 5/4
- (C) 5
- (D) 25/4
Q31 MarkMCQ
Meena calculates that the probability of her winning the first prize in a lottery is 0.08. If total 800 tickets were sold, the number of tickets bought by her is:
- (A) 64
- (B) 640
- (C) 100
- (D) 10
Q41 MarkMCQ
A camping tent in hemispherical shape of radius 1.4 m has a door opening of area 0.50 m². Outer surface area of the tent is:
- (A) 11.78 m²
- (B) 12.32 m²
- (C) 11.82 m²
- (D) 12.86 m²
Q51 MarkMCQ
PQ is tangent to a circle with centre O. If OQ = a, OP = a + 2 and PQ = 2b, then relation between a and b is:
- (A) a² + (a+2)² = (2b)²
- (B) b² = a + 4
- (C) 2a² + 1 = b²
- (D) b² = a + 1
Q61 MarkMCQ
Simplest form of sec A / √(sec²A − 1) is:
- (A) sin A
- (B) tan A
- (C) cosec A
- (D) cos A
Q71 MarkMCQ
The line segment joining the points P(−4, −2) and Q(10, 4) is divided by y-axis in the ratio:
- (A) 2 : 5
- (B) 1 : 2
- (C) 2 : 1
- (D) 5 : 2
Q81 MarkMCQ
A wire is attached from point A on the ground to the top of pole BC making angle of elevation 60°. If AB = 5√3 m, then length of the wire is:
- (A) 10 m
- (B) 10√3 m
- (C) 15 m
- (D) (5/2)√3 m
Q91 MarkMCQ
In the given figure, AB ∥ EF. If AB = 24 cm, EF = 36 cm and DA = 7 cm, then AE equals:
- (A) 2.5 cm
- (B) 10.5 cm
- (C) 3.5 cm
- (D) 14/3 cm
Q101 MarkMCQ
Devansh proved △ABC ~ △PQR using SAS similarity. If he found ∠C = ∠R, then which of the following was proved true?
- (A) AC/PR = AB/PQ
- (B) BC/PR = AC/QR
- (C) AC/PR = BC/PQ
- (D) AC/PR = BC/QR
Q111 MarkMCQ
Step deviation method used: x̄ = a + (Σfᵢuᵢ/Σfᵢ) × h. Given x̄ = 64, h = 5, a = 62.5. The value of ū is:
- (A) 0.5
- (B) 1.5
- (C) 0.3
- (D) 7.5
Q121 MarkMCQ
For an acute angle θ, if sin θ = 1/9, then value of (9cosec θ + 1)/(9cosec θ − 1) is:
- (A) 0
- (B) 80/81
- (C) 1
- (D) 82/80
Q131 MarkMCQ
Which of the following cannot be the probability of an event?
- (A) 39/100
- (B) 0.001/20
- (C) 10/0.2
- (D) 10%
Q141 MarkMCQ
The value of m for which the quadratic equation 3x² − 7x + m = 0 has real and equal roots, is:
- (A) 7
- (B) 49/12
- (C) 49/3
- (D) 4
Q151 MarkMCQ
If the zeroes of a polynomial p(x) are −3 and 8, then p(x) equals:
- (A) x² + 5x − 4
- (B) (x + 3)(−x + 8)
- (C) a(x² + 5x − 24)
- (D) x² − 24
Q161 MarkMCQ
The value of p for which roots of the quadratic equation x² − px + 6 = 0 are rational, is:
- (A) 1
- (B) −5
- (C) 25
- (D) √5
Q171 MarkMCQ
An arc of length 2.2 cm subtends an angle θ at the centre of a circle with radius 2.8 cm. The value of θ is:
- (A) 50°
- (B) 60°
- (C) 45°
- (D) 30°
Q181 MarkMCQ
Two dice are rolled together. The probability of getting an outcome (x, y) where x > y, is:
- (A) 5/12
- (B) 5/6
- (C) 1
- (D) 0
Q19 & Q20 — Assertion-Reason: (A) Both true, R explains A (B) Both true, R doesn't explain A (C) A true, R false (D) A false, R true
Q191 MarkA-R
Assertion (A): H.C.F. (36m², 18m) = 18m, where m is a prime number.
Reason (R): H.C.F. of two numbers is always less than or equal to the smaller number.
Reason (R): H.C.F. of two numbers is always less than or equal to the smaller number.
- (A) Both A and R true; R is correct explanation
- (B) Both true; R not correct explanation
- (C) A true, R false
- (D) A false, R true
Q201 MarkA-R
Assertion (A): The system of linear equations 3x − 5y + 7 = 0 and −6x + 10y + 14 = 0 is inconsistent.
Reason (R): When two linear equations don't have unique solution, they always represent parallel lines.
Reason (R): When two linear equations don't have unique solution, they always represent parallel lines.
- (A) Both A and R true; R is correct explanation
- (B) Both true; R not correct explanation
- (C) A true, R false
- (D) A false, R true
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Q212 Marks
In the given figure, point D divides side BC of △ABC in the ratio 1 : 2. A(1,5), B(−2,1), C(4,2). Find length AD.
Q22(a)2 Marks
Evaluate: (sin³60° − tan30°) / cos²45°
OR
Q22(b)2 Marks
For acute angles A and B, if tan(A + 2B) = √3 and sin(2A + B) = 1/√2, find measures of A and B.
Q232 Marks
A bag contains 25 balls — some yellow, some green. If probability of getting a green ball is 3/5, find the number of yellow balls.
Q242 Marks
In the given figure, AB ∥ DE and AC ∥ DF. Show that △ABC ~ △DEF. If BC = 10 cm, EB = CF = 5 cm and AB = 7 cm, find length DE.
Q252 MarksProof
Prove that 14 − 2√3 is an irrational number, given that √3 is irrational.
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Q26(a)3 Marks
A circle centred at O(2, 1) passes through A(5, 6) and B(−3, K). Find values of K. Hence find length of chord AB.
OR
Q26(b)3 Marks
Prove that point P dividing A(−1, 7) and B(4, −3) in ratio 3:2 lies on line x − 3y = −1. Also find lengths PA and PB.
Q273 Marks
Use graphical method to solve the system of linear equations: x = −3 and 5x − 2y = −5.
Q28(a)3 Marks
In an A.P., 15th term exceeds the 8th term by 21. If sum of first 10 terms is 55, form the A.P.
OR
Q28(b)3 Marks
The sum of first n terms of an A.P. is 2n² + 13n. Find its nth term and hence 10th term.
Q293 Marks
Dimensions of a window are 156 cm × 216 cm. Arjun wants to put grills creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.
Q303 MarksProof
Prove that: tan θ/(1 − cot θ) + cot θ/(1 − tan θ) = 1 + tan θ + cot θ
Q313 Marks
A chord of a circle of radius 14 cm subtends an angle of 60° at the centre. Find the area of the smaller sector and perimeter of the smaller segment.
Q32(a)5 MarksProof
D is the mid-point of side BC of △ABC, CE and BF intersect at O on AD. AD is produced to G such that OD = DG. Prove: (i) OBGC is a parallelogram (ii) EF ∥ BC (iii) △AEF ~ △ABC
OR
Q32(b)5 MarksProof
In parallelogram ABCD, Q is mid-point of CD. Line AR intersects BD at P and BC produced at R. Prove: (i) AQ = QR (ii) AP = 2PQ (iii) PR = 2AP
Q33(a)5 Marks
The mean of the following distribution is 53. Find missing frequency p, then find the mode.
Classes: 0–20, 20–40, 40–60, 60–80, 80–100 | Frequencies: 12, 15, p, 28, 13
Classes: 0–20, 20–40, 40–60, 60–80, 80–100 | Frequencies: 12, 15, p, 28, 13
OR
Q33(b)5 Marks
Compute median: Class Intervals (mid values) 115, 125, 135, 145, 155, 165, 175 with Frequencies 12, 15, 20, 16, 10, 16, 11.
Q345 Marks
PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent at C which lies on OP. If OP = 13 cm, find length AB and PA.
Q355 Marks
Two water taps together can fill a tank in 8⁸⁄₉ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time each tap takes to fill the tank separately.
Q364 MarksCase Study
Case Study: Elevated Water Storage Tank
AB is an elevated water tank and CD is a nearby multistorey building, 54 metres away. From window W, angle of elevation of top of tank is 45° and angle of depression of its foot is 30°. h = height of tank above window level, d = height of window from ground.
(i) Write a relation between d and y (where y = WA distance). (1 mark)
(ii) Determine the value of h. (1 mark)
(iii)(a) Determine height of the water tank. (2 marks) OR (iii)(b) Find x (wire length) and height of window above ground. (2 marks)
(ii) Determine the value of h. (1 mark)
(iii)(a) Determine height of the water tank. (2 marks) OR (iii)(b) Find x (wire length) and height of window above ground. (2 marks)
Q374 MarksCase Study
Case Study: Parabolic Arch — Chenab Railway Bridge
A parabolic arch connects two hills at P(228.5, 0) and Q(−238.5, 0). The parabolic curve is represented by P(x) = −0.0025x² − 0.025x + 136. A is the highest point of the arch (on y-axis).
(i) Write coordinates of point A. (1 mark)
(ii) Find the span of the arch. (1 mark)
(iii)(a) Write zeroes using diagram and verify relationship between sum of zeroes and polynomial. (2 marks) OR (iii)(b) Find p(100) and p(−100). Are they same? (2 marks)
(ii) Find the span of the arch. (1 mark)
(iii)(a) Write zeroes using diagram and verify relationship between sum of zeroes and polynomial. (2 marks) OR (iii)(b) Find p(100) and p(−100). Are they same? (2 marks)
Q384 MarksCase Study
Case Study: Wall Mounted Lamp (Cuboidal with Spherical Bulb)
Lamp is cuboidal, open top and bottom. Dimensions: 24 cm × 12 cm × 17 cm. A spherical bulb of diameter 7 cm is inside.
(i) Find surface area of the bulb. (1 mark)
(ii) Maximum diameter of bulb if at least 1 cm space left from each side. (1 mark)
(iii)(a) Area of fabric if there is a fold of 2 cm on top and bottom edges. (2 marks) OR (iii)(b) Find space available inside the lamp. (2 marks)
(ii) Maximum diameter of bulb if at least 1 cm space left from each side. (1 mark)
(iii)(a) Area of fabric if there is a fold of 2 cm on top and bottom edges. (2 marks) OR (iii)(b) Find space available inside the lamp. (2 marks)
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Section A — Quick MCQ Answer Key
All 20 MCQs with correct answer and key reason
| Q No. | Answer | Key Reason |
|---|---|---|
| Q1 | A | For max cone in hemisphere: h = r = 10 cm, ℓ = 10√2 cm. CSA = πrℓ = 3.14×10×10√2 = 314√2 cm² |
| Q2 | C | d = 5/4, a₁₆ − a₁₂ = 4d = 4 × 5/4 = 5 |
| Q3 | A | 0.08 = n/800 → n = 64 tickets |
| Q4 | C | 2πr² − 0.5 = 2×(22/7)×1.96 − 0.5 = 12.32 − 0.5 = 11.82 m² |
| Q5 | D | PQ⊥OQ: a² + 4b² = (a+2)² → 4b² = 4a+4 → b² = a+1 |
| Q6 | C | secA/√tan²A = secA/tanA = (1/cosA)/(sinA/cosA) = 1/sinA = cosecA |
| Q7 | A | y-axis: x = 0. Section formula: 10k − 4 = 0 → k = 2/5 → ratio 2:5 |
| Q8 | B | cos60° = AB/AC → 1/2 = 5√3/AC → AC = 10√3 m |
| Q9 | C | △DAB ~ △DEF by AA: AB/EF = DA/DE → 24/36 = 7/DE → DE = 10.5, AE = 10.5−7 = 3.5 cm |
| Q10 | D | SAS similarity with ∠C = ∠R: sides including equal angle are AC/PR = BC/QR |
| Q11 | C | 64 = 62.5 + ū × 5 → 1.5 = 5ū → ū = 0.3 |
| Q12 | D | sinθ = 1/9 → cosecθ = 9. (9×9+1)/(9×9−1) = 82/80 |
| Q13 | C | 10/0.2 = 50. Probability must be between 0 and 1; 50 > 1, so not valid |
| Q14 | B | D = 0 for equal roots: 49 − 12m = 0 → m = 49/12 |
| Q15 | B | Zeroes −3 and 8: P(x) = k(x+3)(x−8). For k=−1: (x+3)(−x+8) ✓ |
| Q16 | B | D = p²−24. For rational roots, D must be perfect square. p=−5: D = 25−24 = 1 (perfect square) ✓ |
| Q17 | C | 2.2 = (θ/360°)×2×(22/7)×2.8 → θ = 45° |
| Q18 | A | Favourable outcomes (x>y): 15 pairs. P = 15/36 = 5/12 |
| Q19 | A | HCF(36m², 18m) = 18m ✓ (True). HCF ≤ smaller number ✓ (True). R correctly explains A. |
| Q20 | C | a₁/a₂ = b₁/b₂ ≠ c₁/c₂ → inconsistent (A True). Equations with no unique solution could also be coincident, not always parallel (R False). |
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Frequently Asked Questions
Common searches about CBSE Maths Standard Board Paper 2026
Where can I find CBSE Class 10 Maths Standard Answer Key 2026? ▼
The complete CBSE Class 10 Mathematics Standard Answer Key 2026 with all 38 questions and step-by-step solutions for all 5 sections (A to E) is available free on SkillYog at www.skillyog.com. All answers verified for 100% accuracy.
What is the answer to Q1 (conical cavity in hemisphere) in Maths Standard 2026? ▼
Answer is Option A — 314√2 cm². For a conical cavity of maximum volume carved from a hemisphere of radius 10 cm: height of cone = radius = 10 cm. Slant height ℓ = √(r²+h²) = √(100+100) = 10√2 cm. CSA of cone = πrℓ = 3.14 × 10 × 10√2 = 314√2 cm².
What is the paper pattern of CBSE Class 10 Maths Standard 2026? ▼
Section A: 20 MCQs including 2 Assertion-Reason (1 mark each = 20 marks). Section B: 5 very short answer questions (2 marks each = 10 marks). Section C: 6 short answer questions (3 marks each = 18 marks). Section D: 4 long answer questions (5 marks each = 20 marks). Section E: 3 case study questions (4 marks each = 12 marks). Total: 80 marks, 3 hours.
What is the difference between Maths Basic and Maths Standard? ▼
Maths Standard (Code 041/30) is for students who wish to pursue Mathematics at Class 11 and 12. It has more complex and application-based questions. Maths Basic (Code 241/430) is for students who do not wish to take Mathematics further. Standard paper has harder proofs, more complex problem solving, and higher-order thinking questions like Q32 (parallelogram proof) and Q35 (quadratic word problem).
What is the answer to Q35 (two water taps) in Maths Standard 2026? ▼
Let smaller tap take x hours. Larger tap takes (x−4) hours. Together they fill in 80/9 hours. Setting up: 80/9 × [1/x + 1/(x−4)] = 1, this gives 9x² − 196x + 320 = 0. Solving: x = 20 or x = 16/9 (rejected). Smaller tap = 20 hours, Larger tap = 16 hours.
What is the answer to Q34 (tangents PA and AB) in Maths Standard 2026? ▼
Using the tangent-radius property and similarity of triangles: QP = 12 cm, PA = 26/3 cm, AB = 20/3 cm. The solution uses △OQP ~ △ACP (AA similarity) with ratios 5:12:13, leading to 18x = 12, x = 2/3.
What are the answers to Q37 (Chenab Bridge Case Study) in Maths Standard 2026? ▼
(i) A = (0, 136). (ii) Span = 467 units. (iii)(a) Zeroes are 228.5 and −238.5; Sum = −10 = −b/a = −(−0.025)/0.0025 = −10 ✓. (iii)(b) p(100) = 108.5, p(−100) = 113.5 — they are NOT the same because the polynomial has an odd-degree term.
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