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CBSE Mathematics Basic Question Paper 2026
Class 10 · Code 430/5/1 · Date: 17-02-2026
80Maximum Marks
3 HrsDuration
38Total Questions
5Sections (A–E)
430/5/1Paper Code
📌 General Instructions
- This question paper has 5 Sections A–E. All questions are compulsory.
- Section A consists of 20 MCQs of 1 mark each.
- Section B consists of 5 questions of 2 marks each.
- Section C consists of 6 questions of 3 marks each.
- Section D consists of 4 questions of 5 marks each.
- Section E consists of 3 Case Study questions of 4 marks each.
- Internal choice is provided in some questions. Attempt only one option.
Q11 MarkMCQ
7 × 11 × 13 + 5 is
- (A) a prime number
- (B) an odd number
- (C) a composite number
- (D) a multiple of 5
Q21 MarkMCQ
The roots of the quadratic equation x² + 9 = 0 are
- (A) real and equal
- (B) not real
- (C) real and negative of each other
- (D) rational numbers
Q31 MarkMCQ
The distance between the points (–2, 5) and (5, –2) is
- (A) 7√2
- (B) 14
- (C) 2√7
- (D) 7
Q41 MarkMCQ
A cylinder of radius r is surmounted on a hemisphere of same radius. If total height of the object is 13 cm, then its inner surface area is
- (A) 2πr(r + 13)
- (B) 13πr
- (C) 2π(13 + r)²
- (D) 26πr
Q51 MarkMCQ
Which of the following statements is not always true?
- (A) Two circles are similar.
- (B) Two isosceles right triangles are similar.
- (C) Two rectangles are similar.
- (D) Two equilateral triangles are similar.
Q61 MarkMCQ
If value of cot θ is √5, then sin θ equals
- (A) 1/√6
- (B) √6
- (C) √5/6
- (D) 1/2
Q71 MarkMCQ
A chord QR subtends an angle of 105° at the centre O of the circle. The measure of angle ∠RQP is
- (A) 75°/2
- (B) 105°/2
- (C) 75°
- (D) 15°
Q81 MarkMCQ
The probability of getting sum greater than 10, when two dice are rolled together, is
- (A) 1/9
- (B) 1/18
- (C) 1/12
- (D) 1
Q91 MarkMCQ
The graph of a polynomial p(x) is shown. The curve crosses the x-axis at 4 distinct points. The number of zeroes of the polynomial p(x) is
- (A) 5
- (B) 1
- (C) 0
- (D) 4
Q101 MarkMCQ
nth term of the A.P.: −1/3, 4/3, 3, ... is
- (A) (5n − 9)/3
- (B) (5n − 6)/3
- (C) (3n − 4)/3
- (D) (3n + 2)/3
Q111 MarkMCQ
In the given figure, DE ∥ BC. If AD : AB = 1 : 3 and AE = 2.5 cm then AC equals
- (A) 7.5 cm
- (B) 5 cm
- (C) 10 cm
- (D) 2.5 cm
Q121 MarkMCQ
The value of k for which sum of the zeroes of the polynomial p(x) = 3x² − kx + 6 is 2, is
- (A) 2
- (B) −6
- (C) −2
- (D) 6
Q131 MarkMCQ
A bag contains some red and some white balls. If the probability of getting a red ball is 2/7, then the probability of getting a white ball is
- (A) 1/14
- (B) 5/7
- (C) 1/7
- (D) 2/7
Q141 MarkMCQ
If −26, x, 2 are in A.P., then the value of x is
- (A) 14
- (B) −13
- (C) −12
- (D) −14
Q151 MarkMCQ
PQ is a tangent to a circle at a point P on the circle. The number of tangents which can be drawn to the circle parallel to PQ is
- (A) 2
- (B) 1
- (C) many
- (D) zero
Q161 MarkMCQ
A card is drawn from a well-shuffled deck of 52 playing cards. The probability of getting a queen of spade is
- (A) 1/26
- (B) 1/52
- (C) 0
- (D) 1/4
Q171 MarkMCQ
The length of a pendulum is 70 cm and it describes an arc of length 88 cm when it swings. The angle subtended by the arc at the centre is
- (A) 36°
- (B) 70°
- (C) 72°
- (D) 80°
Q181 MarkMCQ
The total surface area of a solid cone of radius 7 cm and slant height 25 cm, is
- (A) 724 cm²
- (B) 704 cm²
- (C) 550 cm²
- (D) 616 cm²
Directions: (A) Both A and R are true and R is the correct explanation of A. (B) Both A and R are true but R is NOT the correct explanation of A. (C) A is true, R is false. (D) A is false, R is true.
Q191 Mark
Assertion (A): For an acute angle θ, cos θ is always less than 1.
Reason (R): In a right-angled triangle, hypotenuse is the longest side and cos θ = Base/Hypotenuse.
Reason (R): In a right-angled triangle, hypotenuse is the longest side and cos θ = Base/Hypotenuse.
- (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 Mark
Assertion (A): Median of a data is the value of N/2, where N represents sum of all frequencies.
Reason (R): Median divides the whole distribution in two equal parts.
Reason (R): Median divides the whole distribution in two equal parts.
- (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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Q21(a)2 Marks
If sec A = √2 and tan B = √3, then find the value of 2 sin A cos B.
OR
Q21(b)2 Marks
Evaluate: (4cos³60° + cosec 30°) / tan²30°
Q222 Marks
Find the H.C.F. and L.C.M of 1530 and 2040.
Q232 Marks
If A(a, 0), B(1, 1) and C(0, b) form a triangle, right angled at B, then establish a relation between a and b.
Q24(a)2 Marks
Find the probability that a number selected at random from 30, 31, 32, …, 60 is (i) a prime number (ii) a multiple of 6.
OR
Q24(b)2 Marks
Slips of letters of the word 'BACKGROUND' are put in a bowl. Find the probability that a picked slip's letter is (i) a vowel (ii) present in the word 'BALL'.
Q252 Marks
In the given figure, AB ∥ DC. If OB = 3OD and CD = 1.8 cm, then find the length AB.
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Q263 MarksProof
Prove that √2 is an irrational number.
Q273 Marks
Points P(6, 0), Q(2, 8) and R(−2, 4) are vertices of △PQR. MN ∥ QR such that PM/MQ = 1/3. Using distance formula and section formula, show that MN/QR = 1/4.
Q28(a)3 Marks
In an A.P., it is given that a = 2, d = 8 and Sₙ = 90. Find the value of n.
OR
Q28(b)3 Marks
How many 4-digit numbers are divisible by 7?
Q293 MarksProof
Prove that: √[(1−sin A)/(1+sin A)] = 1/(sec A + tan A)
Q30(a)3 Marks
If α, β are zeroes of p(x) = 5x² − 7x − 3, form a quadratic polynomial whose zeroes are 2/α and 2/β.
OR
Q30(b)3 Marks
Find the zeroes of p(x) = 3x² + 7x − 20 and verify the relationship between zeroes and coefficients.
Q313 Marks
Chord AB of a circle subtends an angle of 120° at centre O. Find the length of arc AB if radius = 21 cm.
Q32(a)5 Marks
In △ABC, ∠A = 90° and AD ⊥ BC. Prove: (i) △DBA ~ △DAC (ii) DA² = DB × DC (iii) Find area of △ABC when DB = 9 cm, DC = 16 cm.
OR
Q32(b)5 Marks
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, prove that the other two sides are divided in the same ratio. (Basic Proportionality Theorem)
Q335 Marks
Two poles of equal heights stand on either side of an 80 m wide road. From a point between them, the angles of elevation of the tops are 60° and 30°. Find the height of the poles and the distances of the point from the poles.
Q34(a)5 Marks
ABCD is a rectangle of dimensions 80 cm × 60 cm. Another rectangle PQRS is drawn inside ABCD leaving equal width x cm along all edges. If area of PQRS is half of area of ABCD, find x.
OR
Q34(b)5 Marks
A train covers 90 km at uniform speed. Had the speed been 15 km/h more, it would have taken 30 minutes less. Find the original speed.
Q355 Marks
Find the mean and mode of the following data:
Class: 10–20, 20–30, 30–40, 40–50, 50–60, 60–70, 70–80
Frequency: 5, 4, 10, 13, 12, 10, 6
Class: 10–20, 20–30, 30–40, 40–50, 50–60, 60–70, 70–80
Frequency: 5, 4, 10, 13, 12, 10, 6
Q364 MarksCase Study
Case Study: Fitness Machines
Seema spends 15 min on exercise bicycle and 30 min on double cross walker, burning 435 calories. When she spends 30 min on bicycle and 40 min on walker, she burns 690 calories. Let x = calories burned/min on bicycle, y = calories burned/min on walker.
(i) Represent the situation as linear equations. (ii) Show equations have unique solution. (iii)(a) Solve using elimination method. OR (iii)(b) Solve using substitution method.
Seema spends 15 min on exercise bicycle and 30 min on double cross walker, burning 435 calories. When she spends 30 min on bicycle and 40 min on walker, she burns 690 calories. Let x = calories burned/min on bicycle, y = calories burned/min on walker.
(i) Represent the situation as linear equations. (ii) Show equations have unique solution. (iii)(a) Solve using elimination method. OR (iii)(b) Solve using substitution method.
Q374 MarksCase Study
Case Study: Mushroom (Amanita muscaria)
The mushroom has a hemispherical cap (radius = 3 cm) and a cylindrical stem (height = 2 cm, diameter = 1.4 cm).
(i) Total height of one mushroom. (ii) Volume of the stem. (iii)(a) Volume of 7 mushrooms. OR (iii)(b) Total surface area of 7 mushrooms.
The mushroom has a hemispherical cap (radius = 3 cm) and a cylindrical stem (height = 2 cm, diameter = 1.4 cm).
(i) Total height of one mushroom. (ii) Volume of the stem. (iii)(a) Volume of 7 mushrooms. OR (iii)(b) Total surface area of 7 mushrooms.
Q384 MarksCase Study
Case Study: Circular Museum Hall
A circular museum has outer radius 14 m and inner circle radius 7 m. A statue lies in sector OAB, fenced along OA, AP, PB and BO where P is on the outer circle.
(i) Find m∠AOP. (ii) Prove △OAP ≅ △OBP. (iii)(a) Find length of fencing. (√3 = 1.73) OR (iii)(b) Find area of quadrilateral OAPB.
A circular museum has outer radius 14 m and inner circle radius 7 m. A statue lies in sector OAB, fenced along OA, AP, PB and BO where P is on the outer circle.
(i) Find m∠AOP. (ii) Prove △OAP ≅ △OBP. (iii)(a) Find length of fencing. (√3 = 1.73) OR (iii)(b) Find area of quadrilateral OAPB.
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Section A — Quick MCQ Answer Key
All 20 MCQ answers at a glance with key reason
| Q No. | Answer | Key Reason |
|---|---|---|
| Q1 | C | 7×11×13+5 = odd+odd = even composite |
| Q2 | B | D = 0−36 = −36 < 0, roots not real |
| Q3 | A | √(49+49) = √(2×49) = 7√2 |
| Q4 | D | 2πr(h₁+r) = 2πr(13−r+r) = 26πr |
| Q5 | C | Two rectangles need not be similar (sides may not be proportional) |
| Q6 | A | cot θ = √5 → hypotenuse = √6 → sin θ = 1/√6 |
| Q7 | B | ∠RQP = 90° − 75°/2 = 105°/2 |
| Q8 | C | Favourable: (5,6),(6,5),(6,6) = 3/36 = 1/12 |
| Q9 | D | Graph crosses x-axis 4 times → 4 zeroes |
| Q10 | B | a = −1/3, d = 5/3 → aₙ = −1/3+(n−1)5/3 = (5n−6)/3 |
| Q11 | A | AD/AB = AE/AC → 1/3 = 2.5/AC → AC = 7.5 cm |
| Q12 | D | Sum = k/3 = 2 → k = 6 |
| Q13 | B | P(white) = 1 − 2/7 = 5/7 |
| Q14 | C | x+26 = 2−x → 2x = −24 → x = −12 |
| Q15 | B | Exactly 1 tangent parallel (at diametrically opposite point) |
| Q16 | B | Only one queen of spades in 52 cards → 1/52 |
| Q17 | C | 88 = (θ/360)×2×(22/7)×70 → θ = 72° |
| Q18 | B | TSA = πr(l+r) = (22/7)×7×32 = 704 cm² |
| Q19 | A | Both A and R true; R correctly explains A (base < hypotenuse → cos < 1) |
| Q20 | D | A false (median is not N/2, that's the position); R true (median divides equally) |
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Frequently Asked Questions
Common searches about CBSE Class 10 Math Basic Board Paper 2026
Where can I find CBSE Class 10 Maths Basic Answer Key 2026? ▼
The complete CBSE Class 10 Mathematics Basic Answer Key 2026 with all 38 questions and step-by-step solutions for all sections (A to E) is available free right here on SkillYog at www.skillyog.com. All answers are verified for 100% accuracy against the official CBSE marking scheme.
What is the paper pattern of CBSE Class 10 Maths Basic 2026? ▼
The paper has 38 questions in 5 sections. Section A: 20 MCQs (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. Duration: 3 hours.
What is the answer to Q1 in CBSE Maths Basic 2026? ▼
The answer to Q1 (7×11×13+5) is Option C — a composite number. 7×11×13 = 1001 (odd). Odd + 5 (odd) = 1006 (even). All even numbers greater than 2 are composite. Hence the result is an even composite number.
What is the answer to Q35 (Mean and Mode) in Maths Basic 2026? ▼
Mean = 47.83 (using step deviation method with a = 45, h = 10, Σfᵢuᵢ = 17, Σfᵢ = 60). Mode = 47.5 (modal class = 40–50, using formula with f₁=13, f₀=10, f₂=12, ℓ=40, h=10).
What is the difference between Maths Basic and Maths Standard? ▼
CBSE Class 10 Mathematics Basic (Code 241/430) is designed for students who do not wish to pursue Mathematics at higher secondary level. Maths Standard (Code 041/30) is for students aiming for streams like Science and Commerce that require Mathematics in Class 11–12. Standard paper has more complex questions and harder problem-solving.
What is the answer to Q34 (Train Speed problem) in Maths Basic 2026? ▼
The original speed of the train is 45 km/h. Using the equation 90/x − 90/(x+15) = 1/2, we get x² + 15x − 2700 = 0, which factors to (x+60)(x−45) = 0. Since speed cannot be negative, x = 45 km/h.
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