The much-awaited CBSE Board Exam Paper class 10 for term-1 have begun on 30th November 2021. These board exams are being held offline from 11:30 AM to 1:00 PM at the centres allotted to the students. According to the new pattern, the students are given 90 minutes overall to complete the question paper and mark their responses in the OMR sheet. The papers consist of 50 questions out of which the students are required to answer only 40. There is no negative marking and each question carries 1 mark. There are three sections: Section A and B had 20 questions each, out of which 16 each have to be answered respectively while in section C, 8 questions out of 10 have to be answered.
In this blog post, we have provided the questions and answer key for 2021 CBSE Maths Board Exam Paper class 10 Term-1 (Basic: Set 4; 430/1/4). Grab a pen, go through the questions, compare your responses with the answer key given below and calculate your marks.
Section A
Q1. If xy = 180 and HCF (x, y) = 3, then LCM (x, y) is:
(a) 177
(b) 183
(c) 60
(d) 63
Correct Answer: (c) 60
Q2. The prime factorisation of 156 is:
(a) 2² x 3 x 13
(b) 2² × 3² × 13
(c) 6² x 2²
(d) 2³ × 3 × 13
Correct Answer: (a) 2² x 3 x 13
Q3. The decimal expansion of the rational number
(a) 1
(b) 2
(c) 3
(d) 5
Correct Answer: (b) 2
Q4. The number of quadratic polynomials having zeroes -2 and 5 is :
(a) 1
(b) 2
(c) 3
(d) more than 3
Correct Answer: (d) more than 3
Q5. If 1 is one of the zeroes of the polynomial p(x) = ax² – bx + 1, then:
(a) a + 1 = b
(b) a – b = 0
(c) a – b – 1 = 0
(d) a + b = 1
Correct Answer: (a) a + 1 = b
Q6. The quadratic polynomial whose zeroes are 2 and 3 is :
(a) x² + 5x + 6
(b) x² + 5x – 6
(c) x² – 5x + 6
(d) x² – 5x – 6
Correct Answer: (c) x² – 5x + 6
Q7. The pair of equations y = 0 and y = -7 has :
(a) one solution
(b) two solutions
(c) no solutions
(d) infinitely many solutions
Correct Answer: (c) no solutions
Q8. One equation of a pair of dependent linear equations is -5x + 7y = 2. The second equation can be :
(a) 10x + 14y + 4 = 0
(b) -10x – 14y + 4 = 0
(c) -15x + 21y + 6 = 0
(d) 10x – 14y = -4
Correct Answer: (d) 10x – 14y = – 4
Q9. If ax + by = a² – b² and bx + ay = 0, then the value of (x + y) is:
(a) a² – b²
(b) b – a
(c) a – b
(d) a² + b²
Correct Answer: (c) a – b
Q10. The distance between the points A(0, 6) and B(0, -2) is:
(a) 6 units
(b) 8 units
(c) 4 units
(d) 2 units
Correct Answer: (b) 8 units
Q11. If in two △s DEF and PQR, ∠D = ∠Q and ∠R = ∠E, then which of the following is not true?
(a)
(b)
(c)
(d)
Correct Answer: (b)
Q12. Two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 25. Then, the ratio of their corresponding sides is:
(a) 4:5
(b) 5:4
(c) 3:6
(d) 5:7
Correct Answer: (a) 4:5
Q13. In the given figure, DE || BC. If AD = x, DB = (x – 2), AE = (x + 2) and EC = (x – 1), then the value of x is:
(a) 2
(b) 4
(c) 8
(d)16
Correct Answer: (b) 4
Q14. If tan Ө = √3, then sec Ө is:
(a)
(b) 2
(c)
(d)
Correct Answer: (b) 2
Q15. The value of
(a) 0
(b) cos Ө
(c) -sin Ө
(d) 1
Correct Answer: (d) 1
Q16. If Ө = 45°, then sec Ө cot Ө – cosec Ө tan Ө is:
(a) 0
(b) 1
(c) 2
(d) 3
Correct Answer: (a) 0
Q17. Which of the following cannot be the probability of an event?
(a)
(b) 0.1
(c) 3%
(d)
Correct Answer: (d)
Q18. If the probability of an event is m, then the probability of its complementary event is :
(a) m – 1
(b) m
(c) 1 – m
(d)
Correct Answer: (c) 1 – m
Q19. A dice is thrown once. The probability of getting an even prime number is:
(a)
(b)
(c)
(d) 0
Correct Answer: (c)
Q20. A letter is drawn at random from the letters of the word MIRROR. Which are the letters that have equal probabilities of being drawn?
(a) I and O
(b) M, I, R
(c) M, I, O
(d) M, I, O, R
Correct Answer: (c) M, I, O
Section B
Q21. The HCF of 30, 72 and 432 is:
(a) 2
(b) 3
(c) 6
(d) 4
Correct Answer: (c) 6
Q22. What condition is to be satisfied by q so that a rational number
(a) q = 2m 3n, m, n are non-negative integers
(b) q = 2m + 3n , m, n are non-negative integers
(c) q = 2m 5n , m, n are non-negative integers
(d) q= 2m + 5n , m, n are non-negative integers
Correct Answer: (c) q = 2m 5n , m, n are non-negative integers
Q23. The smallest number by which
(a)
(b)
(c)
(d)
Correct Answer: (c)
Q24. Three bells ring at intervals of 4, 7 and 14 minutes. If all three ring at 6 a.m., when will they ring after that together again?
(a) 6:04 a.m.
(b) 6:07 a.m.
(c) 6:14 a.m.
(d) 6:28 a.m.
Correct Answer: (d) 6:28 a.m.
Q25. If (-2) is a zero of the polynomial p(x) = x² + ax + 2b and a + b = 4, then :
(a) a = 1, b = 3
(b) a = 3, b = 1
(c) a = -1, b = 5
(d) a = 5, b = -1
Correct Answer: (b) a = 3, b = 1
Q26. The graph of the polynomial y = p(x) is given in the figure. The number of zeroes of p(x) is :
(a) 2
(b) 4
(c) 3
(d) 1
Correct Answer: (b) 4
Q27. The parabola representing a quadratic polynomial p(x) = ax² + bx + c opens upward, when :
(a) a > 0
(b) b >0
(c) c > 0
(d) a < 0
Correct Answer: (a) a > 0
Q28. The number of solutions of the following pair of linear equations: x + 3y – 4 = 0; 2x + 6y = 7 is
(a) one
(b) two
(c) infinitely many
(d) zero
Correct Answer: (d) zero
Q29. If x = a, y = b is the solution of the system of equations 3x – y = 8 and x+y = 4, then the values of a and b are respectively:
(a) 3 and 1
(b) 3 and 5
(c) 5 and 3
(d) -1 and -3
Correct Answer: (a) 3 and 1
Q30. The area of the triangle formed by the lines 2x + 3y = 12, x – y – 1 = 0 and x = 0 (as shown in the figure) is:
(a) 7 sq units
(b) 5 sq units
(c) 6.5 sq units
(d) 6 sq units
Correct Answer: 7.5 sq units (not given in the options)
Q31. If the greater of the two supplementary angles exceeds the smaller by 18°, then the greater angle is of measure:
(a) 81°
(b) 54°
(c) 36°
(d) 99°
Correct Answer: (d) 99°
Q32. In a △ABC, ∠A = 90°, AB = 5 cm and AC = 12 cm. If AD ⊥ BC, then AD is equal to :
(a)
(b)
(c)
(d)
Correct Answer: (b)
Q33. If △ABC~△DEF such that DE = 3 cm, EF = 2 cm, DF = 2.5 cm and BC = 4 cm, then the perimeter of △ABC is:
(a) 18 cm
(b) 20 cm
(c) 12 cm
(d) 15 cm
Correct Answer: (d) 15 cm
Q34. If the lengths of the diagonals of a rhombus are 16 cm and 12 cm, then the length of the side of the rhombus is:
(a) 4 cm
(b) 2 cm
(c) 10 cm
(d)14 cm
Correct Answer: (c) 10 cm
Q35. The length of the altitude of an equilateral triangle of side 8 cm is:
(a)
(b)
(c)
(d)
Correct Answer: (b)
Q36. The perimeter of a △ABC with vertices A(0, 4), B(0, 0) and C(3, 0) is:
(a) 5 units
(b) 11 units
(c) 12 units
(d) (7 + √5) units
Correct Answer: (c) 12 units
Q37. If tan A =
(a)
(b)
(c)
(d)
Correct Answer: (a)
Q38. If sin (A + B) = cos (A – B) = 1, then :
(a) A = B = 0°
(b) A = B = 45°
(c) A = 60°, B = 30°
(d) A = 90°, B = 60°
Correct Answer: (b) A = B = 45°
Q39. If cosec Ө – cot Ө =
(a) 1
(b) 2
(c) 3
(d) 4
Correct Answer: (c) 3
Q40. In a single throw of a pair of dice, the probability of getting the sum a perfect square is :
(a)
(b)
(c)
(d)
Correct Answer: (b)
Section C
Case Study 1: Q41-45
A rough co-ordinate map of Lahiri’s locality is shown below:
Q41. The coordinates of the grocery store are:
(a) (11, 8)
(b) (7, 2)
(c) (2, 7)
(d) (8, 6)
Correct Answer: (b) (7, 2)
Q42. The distance between the hotel and the post office is :
(a) 5 units
(b) √5 units
(c) √17 units
(d) 17 units
Correct Answer: (c) √17 units
Q43. If a point (x, y) is equidistant from both the laundry and the post office, then :
(a) x = y = 4
(b) x + y = 7
(c) x + y = -7
(d) x – y = 7
Correct Answer: (b) x + y = 7
Q44. Anuradha goes first to the laundry from the post office, and then from there to the grocery store. The total distance travelled by her is:
(a) 34 units
(b) 28 units
(c) (√4 + √6) units
(d) (√8 + √26) units
Correct Answer: (d) (√8 + √26) units
Q45. The co-ordinates of the reflection of the post office on the y-axis are:
(a) (-4, -5)
(b) (4,-5)
(c) (-4, 5)
(d) (0,5)
Correct Answer: (c) (-4, 5)
Case Study 2: Q46 – Q50
Pookalam is the flower bed or flower pattern designed during Onam in Kerala. It is similar to ‘Rangoli’ in North India and ‘Kolam’ in Tamil Nadu. During the festival of Onam, your school is planning to conduct a Pookalam competition. Your friend who is a partner in competition, suggests two designs given below:
Design-I: The design is made with a circle of radius 32 cm leaving an equilateral triangle ABC in the middle as shown in the figure.
Design-II: The Pookalam is made with 9 circular designs, each of radius 7 cm, enclosed in a square.
Q46. The length of the side of △ABC is :
(a)
(b)
(c) 48 cm
(d) 64 cm
Correct Answer: (b)
Q47. The length of the altitude of △ABC is:
(a) 8 cm
(b) 12 cm
(c) 48 cm
(d) 52 cm
Correct Answer: (c) 48 cm
Q48. The area of the square ABCD is :
(a) 1264 sq cm
(b) 1764 sq cm
(c) 1830 sq cm
(d) 1944 sq cm
Correct Answer: (b) 1764 sq cm
Q49. The area of each circular region is :
(a) 124 sq cm
(b) 132 sq cm
(c) 144 sq cm
(d) 154 sq cm
Correct Answer: (d) 154 sq cm
Q50. The area of the remaining portion of the square ABCD (besides the 9 circles) is :
(a) 378 sq cm
(b) 260 sq cm
(c) 340 sq cm
(d) 278 sq cm
Correct Answer: (a) 378 sq cm
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 Basic 430/2/4 Answer Key will be updated soon.
Answer key for CBSE Board Exam Paper Class 10 Math Standard 030/1/4 and 030/2/4 to be published soon.
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To start your preparation for CBSE Board Exam Paper Class 10 Term-2 click here.
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