Note :-
Rahul Tuition Centre has provided the answer key of the CBSE Class 10 Social Science board exam 2021-22, Conducted on 30 November 2021.
This answer key is for your knowledge and is not final. It is expected that the CBSE will published the answer key after the declaration of board result.
Every care has been taken in answering, there might be some issues in some questions & answers.
Students are advised to discuss with their school teachers regarding the same before reaching final conclusion. Rahul Tuition Centre is not responsible for any claim.
- SUBJECT- English Core
- Term- I
- Time allowed- 90 minutes
- Maximum Marks- 40
- SECTION-A
SECTION-A
a) 3
b) 4
c) 5
d) 6
Ans. (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
Ans. (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
Ans. (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
Ans. (c) –√3Q
5. In figure, DE || BC, AD= 2 cm and BD= 3 cm, then ar(△ABC): ar(△ADE) is equal toa) 4 : 25
b) 2 : 3
c) 9 : 4
d) 25 : 4
Ans. (d) 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
Ans. (d) 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
Ans. (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
Ans. (a) –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
Ans. (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
Ans. (c) 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
Ans. (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
Ans. (b) 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
Ans. (b) 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
Ans. (a) 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
Ans. (c) 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
Ans. (a) 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
Ans. (c) 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]
Ans. (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
Ans. (b) –1, 7
Q20. Given that sec θ = √2, value of 1+tanθ/sinθ is
a) 2√2
b) √2
c) 3√2
d) 2
Ans. (a) 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
d) 2
Ans. (d) 625
Q22. Which of the following cannot be the probability of an event?
(a) 0.01
(b) 3%
c) 16/17
d) 17/16
Ans. (d) 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
Ans. (b) 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
Ans. (b) 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
Ans. (c) 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
Ans. (b) 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
Ans. (a) 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
Ans. (c) 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
Ans. (c) 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
Ans. (b) 7
Q31. If n is a natural number, then 2(5n + 6n) always ends with
a) 1
b) 4
c) 3
d) 2
Ans. (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
Ans. (d) 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
Ans. (b) 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
Ans. (d) 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
Ans. (d) 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
Ans. (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) 56/7 cm
b) 7/56 cm
c) 25/7 cm
d) 24/7 cm
Ans. (d) 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°
Ans. (a) 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
Ans. (b) 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)
Ans. (c) 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
Ans. (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
Ans. (c) x + 4y = 22
Q43. What are the fixed charges for a book?
a) Rs9
b) Rs10
c) Rs13
d) Rs15
Ans. (d) Rs15
Q44. What are the additional charges for each subsequent day for a book ?
a) Rs 6
b) Rs 5
c) Rs 4
d) Rs 3
Ans. (b) Rs 5
Q45. What is the total amount paid by both, if both of them have kept the book for 2 more days?
a) Rs 35
b) Rs 52
c) Rs 50
d) Rs 58
Ans. (c) Rs 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 :
a) Similar by AA criterion
b) Similar by SAS criterion
c) Similar by RHS criterion
d) Not similar
Ans. (b) 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
Ans. (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
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
Ans. (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.
Ans. (c) The medians have a ratio 1 : 4.
Answer Key (Full)
Answer 1: (b)
Answer 2: (d)
Answer 3: (a)
Answer 4: (c)
Answer 5 (d)
Answer 6: (d)
Answer 7: (c)
Answer 8: (a)
Answer 9: (b)
Answer 10: (c)
Answer 11: (c)
Answer 12: (b)
Answer 13: (b)
Answer 14: (a)
Answer 15: (c)
Answer 16: (b)
Answer 17: (c)
Answer 18: (a)
Answer 19: (b)
Answer 20: (a)
Answer 21: (d)
Answer 22: (d)
Answer 23: (b)
Answer 24: (b)
Answer 25: (c)
Answer 26: (b)
Answer 27: (a)
Answer 28: (c)
Answer 29: (c)
Answer 30: (b)
Answer 31: (d)
Answer 32: (d)
Answer 33: (b)
Answer 34: (d)
Answer 35: (d)
Answer 36: (c)
Answer 37: (d)
Answer 38: (a)
Answer 39: (b)
Answer 40: (c)
Answer 41: (d)
Answer 42: (c)
Answer 43: (b)
Answer 44: (d)
Answer 45: (c)
Answer 46: (b)
Answer 48: (d)
Answer 49: (b)
Answer 50: (c)
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