CBSE Board Exam Paper Class 10 Maths Term-1 2021 was held on 4th December 2021. There were four sets released by the CBSE Board: 2 for Standard and 2 for Basic with their unique codes. The exam was held offline, and applicants were expected to fill out OMR sheets. Students who took the CBSE Board Exam Paper Class 10 exam can access the questions and answer keys for **Standard Set 4 – code 030/1/4 **in this blog post. Links for the answer key to the other 3 sets are given below.

### Section A – 2021 Class 10 Board Exam Paper

**Q1. The exponent of 5 in the prime factorization of 3750 is**

(a) 3

(b) 4

(c) 5

(d) 6

**Correct Answer: (b) 4**

**Q2. The graph of a polynomial P(x) cuts the x-axis at 3 points and touches it at 2 other points. The number of zeroes of P(x) is**

(a) 1

(b) 2

(c) 3

(d) 5

**Correct Answer: (d) 5**

**Q3. The values of x and y satisfying the two equations 32x + 33y = 34, 33x + 32y = 31 respectively are:**

(a) -1, 2

(b) -1, 4

(c) 1, -2

(d) -1, -4

**Correct Answer: (a) -1, 2**

**Q4. If A(3, √3), B(0, 0), and C(3, k) are the three vertices of an equilateral triangle ABC, then the value of k is**

(a) 2

(b) -3

(c) -√3

(d) -√2

**Correct Answer: (c) -√3**

**Q5. In figure, DE || BC, AD = 2 cm and BD = 3 cm, then ar(△ABC): ar(△ADE) is equal to**

(a) 4 : 25

(b) 2 : 3

(c) 9 : 4

(d) 25 : 4

**Correct Answer: (d) 25 : 4**

**Q6. If cot(θ) = **

, the value of sec^{2}θ + cosec^{2}θ is(a) 1

(b) ` `

(c) ` `

(d) ` `

**Correct Answer: (d) **

**Q7. The area of a quadrant of a** **circle where the circumference of circle is 176 m, is**

(a) 2464 m square

(b) 1232 m square

(c) 616 m square

(d) 308 m square

**Correct Answer: (c) 616 m square**

**Q8. For an event E, P(E) + P(Ē) = x, then the value of x³ – 3 is**

(a) -2

(b) 2

(c) 1

(d) -1

**Correct Answer: (a) -2**

**Q9. What is the greatest possible speed at which a girl can walk 95 m and 171 m in an exact number of minutes?**

(a) 17 m/min

(b) 19 m/min

(c) 23 m/min

(d) 13 m/min

**Correct Answer: (b) 19 m/min**

**Q10. In figure, the graph of a polynomial P(x) is shown. The number** **of zeroes of P(x) is**

(a) 1

(b) 2

(c) 3

(d) 4

**Correct Answer: 3**

**Q11. Two lines are given to be parallel. The equation of one of the lines is 3x – 2y = 5. The equation of the second line can be**

(a) 9x + 8y = 7

(b) -12x – 8y = 7

(c) -12x + 8y = 7

(d) 12x + 8y = 7

**Correct Answer: (c) -12x + 8y = 7**

**Q12. Three vertices of a parallelogram ABCD are A(1, 4), B(-2, 3) and C(5,8). The ordinate of the fourth vertex D is**

(a) 8

(b) 9

(c) 7

(d) 6

**Correct Answer: (b) 9**

**Q13. In △ABC and △DEF, ∠F = ∠C, ∠B = ∠E and AB = DE. Then, the two triangles are**

(a) Congruent, but not similar

(b) Similar, but not congruent

(c) Neither congruent nor similar

(d) Congruent as well as similar

**Correct Answer: (b) Similar, but not congruent**

**Q14. In △ABC right angled at B, sin A = , then the value of cos C is**

(a) ` `

(b) ` `

(c) ` `

(d) ` `

**Correct Answer: (a) **

**Q15. The minute hand of a clock is 84 cm long. The distance covered by the tip of the minute hand from 10:10 am to 10:25 am is**

(a) 44 cm

(b) 88 cm

(c) 132 cm

(d) 176 cm

**Correct Answer: (c) 132 cm**

**Q16.** T**he probability that the drawn card from a pack of 52 cards is neither** **an ace nor a spade is**

(a) ` `

(b) ` `

(c) ` `

(d) ` `

**Correct Answer: (a) **

**Q17. Three alarm clocks ring their alarms at regular intervals of 20 min, 25 min and 30 min respectively. If they first beep together at 12 noon, at what time will they beep again for the first time?**

(a) 4:00 pm

(b) 4:30 pm

(c) 5:00 pm

(d) 5:30 pm

**Correct Answer: (c) 5:00 pm**

**Q18. A quadratic polynomial, the product and sum of whose zeroes are 5 and 8 respectively is-**

(a) k [x² – 8x + 5]

(b) k [x² + 8x + 5]

(c) k [x² – 5x + 8]

(d) k [x²+ 5x + 8]

**Correct Answer: (a) k [x²- 8x + 5] **

**Q19. Points A (-1, y) and B(5, 7) lie on a circle with centre 0 (2, -3y). The values of y are**

(a) 1, -7

(b) -1, 7

(c) 2, 7

(d) -2, -7

**Correct Answer: (b) -1, 7**

**Q20. Given that sec θ = √2, value of **

is(a) 2√2

(b) √2

(c) 3√2

(d) 2

**Correct Answer: (a) 2√2**

### Section-B | 2021 CBSE Class 10 Board Exam Paper

**Q21. The greatest number which when divides 1251, 9377 and 15628 leaves remainder 1, 2 and 3 respectively is**

(a) 575

(b) 450

(c) 750

(d) 625

**Correct Answer: (d) 625**

**Q22. Which of the following cannot be the probability of an** **event?**

(a) 0.01

(b) 3%

(c) ` `

(d) ` `

**Correct Answer: (d) **

**Q23. The diameter of a car wheel is 42 cm. The number of complete revolutions it will make in moving 132 km is**

(a) 10^{4}

(b) 10^{5}

(c) 10^{6}

(d) 10^{3}

**Correct Answer: (b) 10 ^{5} **

**Q24. If θ is an acute angle and tan θ + cot θ = 2, then the value of sin³θ + cos³θ is**

(a) 1

(b) ` `

(c) ` `

(d) √2

**Correct Answer: (c) **

**Q25.** **The ratio in which the** **line 3x + y – 9 = 0 divides the line segment joining the points (1, 3) and (2, 7) is**

(a) 3 : 2

(b) 2 : 3

(c) 3 : 4

(d) 4 : 3

**Correct Answer: (c) 3 : 4**

**Q26. If x – 1 is a factor of the polynomial p(x) = x ^{3} + ax^{2} + 2b and a + b = 4, then**

(a) a = 5, b = –1

(b) a = 9, b = –5

(c) a = 7, b = –3

(d) a = 3, b = 1

**Correct Answer: (b) a = 9, b = –5**

**Q27. If a and b are two coprime numbers, then a^{3} and b^{3} are**

(a) Coprime

(b) Not coprime

(c) Even

(d) Odd

**Correct Answer: (a) Coprime**

**Q28. The area of a square that can be inscribed in a circle of area cm^{2} is**

(a) 321 cm^{2}

(b) 642 cm^{2}

(c) 128 cm^{2}

(d) 256 cm^{2}

**Correct Answer: (c) 128 cm ^{2}**

**Q29. If A (4, –2), B(7, – 2) and C(7, 9) are the vertices of a △ABC, then △ABC is**

(a) equilateral triangle

(b) isosceles triangle

(c) right-angled triangle

(d) isosceles right-angled triangle

**Correct Answer: (c) right-angled triangle**

**Q30. If α, β are the zeros of the quadratic polynomial p(x) = x^{2} – (k + 6)x + 2(2k – 1), then the value of k, if α+ β = αβ , is**

(a) –7

(b) 7

(c) –3

(d) 3

**Correct Answer: (b) 7**

**Q31. If n is a natural number, then 2(5^{n} + 6^{n}) always ends with**

(a) 1

(b) 4

(c) 3

(d) 2

**Correct Answer: (d) 2**

**Q32. The line segment joining the points P(–3, 2) and Q(5, 7) is divided by the y-axis in the ratio**

(a) 3 : 1

(b) 3 : 4

(c) 3 : 2

(d) 3 : 5

**Correct Answer: (d) 3 : 5**

**Q33. If a cot θ + b cosec θ = p and b cot θ + a cosec θ = q, then p^{n} – q^{n} =**

(a) a^{2} – b^{2}

(b) b^{2} – a^{2}

(c) a^{2} + b^{2}

(d) b – a

**Correct Answer: (b) b ^{2} – a^{2} **

**Q34. If the perimeter of a circle is half to that of a square, then the ratio of the area of the circle to the area of the square is**

(a) 22 : 7

(b) 11 : 7

(c) 7 : 11

(d) 7 : 22

**Correct Answer: (d) 7 : 22**

**Q35. A dice is** **rolled twice. The probability that 5 will not come up either time is**

(a) ` `

(b) ` `

(c) ` `

(d) ` `

**Correct Answer: (d) **

**Q36. The LCM of two numbers is 2400. Which of the following CANNOT be their HCF?**

(a) 300

(b) 400

(c) 500

(d) 600

**Correct Answer: (c) 500**

**Q37. In fig., PA, QB and RC are each perpendicular to AC. If x = 8 cm and z = 6 cm, then y is equal to**

(a) ` cm`

(b) ` cm`

(c) ` cm`

(d) ` cm`

**Correct Answer: (d) cm **

**Q38. In a △ABC, ∠A = x°, ∠B = (3x – 2)°, ∠C = y°. Also ∠C – ∠B = 9°. The sum of the greatest and the smallest angles of this triangle is**

(a) 107°

(b) 135°

(c) 155°

(d) 145°

**Correct Answer: (a) 107°**

**Q39. If sec θ + tan θ = p, then tan θ is**

(a)

(b)

(c) ` `

(d) ` `

**Correct Answer: (b) **

**Q40. The base BC of an equilateral △ABC lies on the y-axis. The co-ordinates of C are (0, –3). If the origin is the mid-point of the base BC, what are the co-ordinates of A and B?**

(a) A (√3, 0), B(0, 3)

(b) A (±3√3, 0), B(3, 0)

(c) A (±3√3, 0), B(0, 3)

(d) A (–√3, 0), B(3, 0)

**Correct Answer: (c) A (±3√3, 0), B(0, 3) **

### SECTION – C | 2021 CBSE Class 10 Board Exam Paper Answer Key

**Case Study-I**

A book store shopkeeper gives books on rent for reading. He has variety of books in his store related to fiction, stories and quizzes etc. He takes a fixed charge for the first two days and an additional charge for subsequent day. Amruta paid ₹ 22 for a book and kept for 6 days; while Radhika paid ₹ 16 for keeping the book for 4 days.

Assume that the fixed charge be ₹ x and additional charge (per day) be ₹ y.

Based on the above information, answer any four of the following questions :

**Q41. The situation of amount paid by Radhika, is algebraically represented by**

(a) x – 4y = 16

(b) x + 4y = 16

(c) x – 2y = 16

(d) x + 2y = 16

**Correct Answer: (d) x + 2y = 16 **

**Q42. The situation of amount paid by Amruta, is** **algebraically represented by**

(a) x – 2y = 11

(b) x – 2y = 22

(c) x + 4y = 22

(d) x – 4y = 11

**Correct Answer: (c) x + 4y = 22 **

**Q43. What are the fixed charges for a book?**

(a) ₹ 9

(b) ₹ 10

(c) ₹ 13

(d) ₹ 15

**Correct Answer: (b) ₹ 10 **

**Q44. What are the additional charges for each subsequent day for a book?**

(a) ₹ 6

(b) ₹ 5

(c) ₹ 4

(d) ₹ 3

**Correct Answer: (d) ₹ 3**

**Q45. What is the total amount paid by both, if both of them have kept the book for 2 more days?**

(a) ₹ 35

(b) ₹ 52

(c) ₹ 50

(d) ₹ 58

**Correct Answer:** **(c) ₹ 50**

**Case Study – II**

A farmer has a field in the shape of trapezium, whose map with scale 1 cm = 20 m, is given below :

The field is divided into four parts by joining the opposite vertices.

Based on the above information, answer any four of the following questions :

**Q46. The two triangular regions AOB and COD are**

(a) Similar by AA criterion

(b) Similar by SAS criterion

(c) Similar by RHS criterion

(d) Not similar

**Correct Answer: (a) Similar by AA criterion**

**Q47. The ratio of the area of the** **△AOB to the area of △COD, is**

(a) 4 : 1

(b) 1 : 4

(c) 1 : 2

(d) 2 : 1

**Correct Answer: (b) 1 : 4**

**Q48. If the ratio of the perimeter of △AOB to the perimeter of △COD would have been 1 : 4, then**

(a) AB = 2 CD

(b) AB = 4 CD

(c) CD = 2 AB

(d) CD = 4 AB

**Correct Answer: (d) CD = 4 AB **

**Q49. If in △s AOD and BOC, , then**

(a) △AOD ~ △BOC

(b) △AOD ~ △BCO

(c) △ADO ~ △BCO

(d) △ODA ~ △OBC

**Correct Answer: (b) △AOD ~ △BCO**

**Q50. If the ratio of areas of two similar triangles AOB and COD is 1 : 4, then** **which of the following statements is true?**

(a) The ratio of their perimeters is 3 : 4.

(b) The corresponding altitudes have a ratio 1 : 2.

(c) The medians have a ratio 1 : 4.

(d) The angle bisectors have a ratio 1 : 16.

**Correct Answer: (b) The corresponding altitudes have a ratio 1 : 2. **

That’s the end of the paper and the answer key. Hope the exams are going well for you. How much did you score in this one? Do let us know in the comments below. Best Wishes for the rest of your exams!

You might also want to take a look at the video solutions of CBSE Sample Paper solutions 2021-22:

CBSE Board Exam Paper Class 10 Maths Answer key for Basic set 4 code 430/1/4 here

Answer key for CBSE Board Exam Paper Class 10 Math Basic 430/2/4 and 030/2/4 to be published soon.

Check out the syllabus for CBSE Board Exam Paper Class 10 2021-22 here

To start your preparation for CBSE Board Exam Paper Class 10 Term-2 click here.

Looking for previous year question papers class 10 and their answer keys?

Get access to the previous year question papers class 10 for 2018 here

CBSE previous year question papers class 10 (2017) with answer key here

Solutions for previous year question papers class 10 (2016) here

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