CBSE Term 1 Class 10 Maths (Standard), Board Exam 2021-22: Question Paper and Answer Key

Class 10th CBSE Term 1, Maths (Standard) Board Exam Question Paper and Answers Key 2021-22 Table

SUBJECT- English Core
Term- I
Time allowed- 90 minutes
Maximum Marks- 40

SECTION-A

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

a) 3 b) 4 c) 5 d) 6

The correct answer is: 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

The correct answer is: 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

The correct answer is: -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

The correct answer is: -√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

The correct answer is: 25 : 4

Q6. If cot(θ) = 1/√3, the value of sec ² θ+ cosec ² θ is

a) 1 b) 40/9 c) 38/9 d) 5 ⅓

The correct answer is: 5 ⅓

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

The correct answer is: 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

The correct answer is: -2

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

a) 17 m/min b) 19 m/min c) 23 m/min d) 13 m/min

The correct answer is: 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

The correct answer is: 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

The correct answer is: -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

The correct answer is: 9

Q13. In △ABC and ADEF, ∠F = ∠C, ∠B = ∠E and AB = ½ 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

The correct answer is: Similar, but not congruent

Q14. In △ABC right angled at B, sinA = 7/25, then the value of cosC is

a) 7/25 b) 24/25 c) 7/24 d) 24/7

The correct answer is: 7/25

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

The correct answer is: 132 cm

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

a) 9/13 b) 35/53 c) 10/13 d) 19/26

The correct answer is: 9/13

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) 05:00 pm d) 5:30 pm

The correct answer is: 05:00 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]

The correct answer is: 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

The correct answer is: -1, 7

Q20. Given that sec θ = √2, value of 1+tanθ/sinθ is

a) 2√2 b) √2 c) 3√2 d) 2

The correct answer is: 2√2

Section-B

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

a) 575 b) 450 c) 750 d) 625

The correct answer is: 625

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

(a) 0.01 (b) 3% c) 16/17 d) 17/16

The correct answer is: 17/16

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 power 4 b) 10 power 5 c) 10 power 6 d) 10 power 3

The correct answer is: 10 power 5

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

a) 1 b) ½ c) √2/2 d) √2

The correct answer is: 1/2

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

The correct answer is: 3:4

Q26. If x – 1 is a factor of the polynomial p(x) = x3 + ax2 + 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

The correct answer is: a = 9, b = –5

Q27. If a and b are two coprime numbers, then a3 and b3 are

a) Coprime b) Not coprime c) Even d) Odd

The correct answer is: Coprime

Q28. The area of a square that can be inscribed in a circle of area 1408 cm2 is

a) 321 cm2 b) 642 cm2 c) 128 cm2 d) 256 cm2

The correct answer is: 128 cm2

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

The correct answer is: right angled triangle

Q30. If α, β are the zeros of the quadratic polynomial p(x) = x2 – (k + 6) x + 2(2k – 1), then the value of k, if α+ β=1/2 α, is

a) –7 b) 7 c) –3 d) 3

The correct answer is: 7

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

a) 1 b) 4 c) 3 d) 2

The correct answer is: 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

The correct answer is: 3 : 5

Q33. If a cotθ + b cosecθ = p and b cotθ + a cosecθ = q, then p2 – q2 =

a) a2 – b2 b) b2 – a2 c) a2 + b2 d) b – a

The correct answer is: b2 – a2

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

The correct answer is: 7 : 22

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

(a) 11 (c) 13 (b) 1 (d) 25

The correct answer is: 25

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

a) 300 b) 400 c) 500 d) 600

The correct answer is: 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) 56/7 cm b) 7/56 cm c) 25/7 cm d) 24/7 cm

The correct answer is: 24/7 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°

The correct answer is: 107°

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

(a) p2 + 1/2p b) p2-1/2p c) p2-1/p2+1 d) p2 + 1/p2 - 1

The correct answer is: p2-1/2p

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)

The correct answer is: A (±3 3, 0), B(0, 3)

SECTION – C

Q.No. 41-45 are based on Case Study–I, you have to answer any (4) four questions. Q. No. 46-50 are based on Case Study-II, you have to answer any (4) four questions.

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

The correct answer is: 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

The correct answer is: x + 4y = 22

Q43. What are the fixed charges for a book?

a) Rs9 b) Rs10 c) Rs13 d) Rs15

The correct answer is: Rs15

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

a) Rs6 b) Rs5 c) Rs4 d) Rs3

The correct answer is: Rs5

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

a) Rs35 b) Rs52 c) Rs50 d) Rs58

The correct answer is: Rs50

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

The correct answer is: Similar by SAS 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

The correct answer is: 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

The correct answer is: CD = 4 AB

Q49. If in △s AOD and BOC, AO = AD = OD, then BC BO OC

a) △AOD ~ △BOC b) △AOD ~ △BCO c) △ADO ~ △BCO d) △ODA ~ △OBC

The correct answer is: △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.