10th Maths Quarterly Exam 2024 Question Paper & Answer Key | Ariyalur District

10th Maths Quarterly Exam 2024 Answer Key - Ariyalur District

Solutions

PART-I (14x1=14)

Answer all the questions

1. Let n(A)=m and n(B)=n then the total number of non empty relations that can be defined from A to B is c) 2^mn-1
2. f(x)+f(1-x)=2 then f(1/2)=........ a) 1
3. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is d) 2520
4. Find the sum of n terms of the series is 2+2+2+... to n terms. b) 2n
5. If (x-6) is the HCF of pair of polynomials x²-2x-24 and x²-kx-6 then find the value of k. b) 5
6. The solution of (2x-1)²-9 is equal to a) -1, 2
7. 7^4k ≡ ____ (Mod 100) d) 1
8. If in triangle ABC and EDF, AB/DE = BC/FD then they will be similar when c) ∠B = ∠D
9. When proving that a quadrilateral is a trapezium, it is necessary to show a) Two sides are parallel (one pair of opposite sides)
10. If ΔABC is an isosceles triangle with ∠C = 90° and AC= 5 cm then AB is a) 5√2 cm
11. Find the slope of the equation is 2y= x+8 a) ½
12. The straight line given by the equation x=11 is d) parallel to the y axis
13. If sinθ = cosθ then 2tan²θ + sin²θ - 1 is equal to a) 3/2
14. If sinθ + cosθ = a and secθ + cosecθ = b then the value of b(a²-1) is equal to b) 2a

PART-II (10x2=20)

Answer any 10 questions. Question No. 28 is compulsory

15. A x B = {(3,2) (3, 4) (5,2) (5,4)}, then find A and B.
    Answer: A = {3, 5}, B = {2, 4}
16. Show that the function f: N → N defined by f(m)=m²+m+3 is one-one function.
    Answer: For f(m₁) = f(m₂), we get (m₁-m₂)(m₁+m₂+1) = 0. Since m₁, m₂ ∈ N, m₁+m₂+1 ≠ 0. Thus m₁=m₂. Hence, f is one-one.
17. Find the 3^rd term and 4^th term of a sequence if a_n = n² if n is odd; n²/2 if n is even.
    Answer: a₃ = 3² = 9; a₄ = 4²/2 = 8
18. Find the sum of the series. 1+4+9+16+......+2225
    Note: The question has a typo, as 2225 is not a perfect square. Assuming the series is 1² + 2² + ... + n², the last term must be a perfect square.
19. Simplify: (x²-16) / (x²+8x+16)
    Answer: (x-4)/(x+4)
20. Find the LCM of the expressions are (p²-3p+2), (p²-4).
    Answer: (p-1)(p-2)(p+2) or (p-1)(p²-4)
21. If the difference between a number and its reciprocal is 24/5, find the numbers.
    Answer: The numbers are 5 or -1/5.
22. The length of the tangent to a circle from a point p, which is 25cm away from the centre is 24 cm. what is the radius of the circle.
    Answer: 7 cm
23. In ΔABC, if DE || BC, AD=x, DB=x-2, AE=x+2 and EC=x-1 then find the length of the sides AB and AC.
    Answer: x=4. AB = 6, AC = 9.
24. Find the value of 'a' if the line through (-2, 3) and (8, 15) is perpendicular to y = ax+2.
    Answer: a = -5/6
25. Find the slope of a line joining the points are (14, 10) and (14, -6).
    Answer: Undefined
26. Prove that √(1+sinθ)/(1-sinθ) = secθ+tanθ.
    Answer: Proof involves multiplying numerator and denominator by (1+sinθ) inside the root.
27. Prove that secθ/sinθ - sinθ/cosθ = cotθ.
    Answer: Proof involves taking LCM and using the identity cos²θ = 1-sin²θ.
28. f(x)=3x-2, g(x)=2x+k and if fog=gof then find the value of k.
    Answer: k = -1

PART-III (10x5=50)

Answer any 10 questions. Question No. 42 is compulsory

29. A function f is defined by f(x) = 2x-3. Find i) (f(0)+f(1))/2 ii) x such that f(x)=0 iii) x such that f(x)=x iv) x such that f(x)=f(1-x).
    Answer: i) -2, ii) x=3/2, iii) x=3, iv) x=1/2
30. If f(x)=2x+3, g(x)=1-2x and h(x)=3x prove that fo(goh)=(fog)oh.
    Answer: Both LHS and RHS simplify to 5-12x. Hence proved.
31. Find the sum of all natural numbers between 100 and 1000 which are divisible by 11.
    Answer: 44550
32. Find the sum of series is 10³+11³+12³+...+20³.
    Answer: 42075
33. Find the GCD of the polynomials x³+x²-5x+3 and x³+3x²-x-3.
    Answer: (x-1)(x+3) or x²+2x-3
34. Find the square root of the expression 289x⁴ - 612x³ + 970x² - 684x + 361.
    Answer: |17x² - 18x + 19|
35. If vertices of a quadrilateral are at A(-4, -2), B(-3,k), C(3, -2) and D(2,3) and its area is 28 sq.units. Find the value of k.
    Answer: k = -5 or k = 11
36. Find the equation of the perpendicular bisector of the line joining the points A(-4, 2) and B(6,-4).
    Answer: 5x - 3y - 8 = 0
37. State and prove Thales theorem.
    Answer: Statement: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio. (Proof as per textbook).
38. An insect 8 m away initially from the foot of a lamp post which is 6m tall, crawls towards it moving through a distance. The distance from the top of the lamp post is equal to the distance it has moved. How far is the insect away from the foot of the lamp post?
    Answer: 1.75 m
39. Prove that √(1+cosθ)/(1-cosθ) + √(1-cosθ)/(1+cosθ) = 2cosecθ.
    Answer: Proof involves taking LCM and simplifying.
40. A straight line AB cuts the co-ordinate axes at A and B. If the mid-point of AB is (2,-3) find the equation of AB.
    Answer: 3x - 2y - 12 = 0
41. Let f: A→B be a function defined by f(x) = x/2 - 1 where A={2,4,6,10,12}, B={0,1,2,4,5,9} represented f by i) set of ordered pairs ii) a table iii) an arrow diagram iv) a graph.
    i) {(2,0), (4,1), (6,2), (10,4), (12,5)} ii) Table, arrow diagram, and graph to be drawn based on the ordered pairs.
42. The ratio of 6^th and 8^th term of an A.P is 7: 9. Find the ratio of 9^th term to 13^th term.
    Answer: 5:7

PART-IV (2x8=16)

Answer the following

43. a) Construct a triangle similar to a given triangle ABC with its sides equal to 6/5 of the corresponding sides of the triangle ABC (scale factor 6/5). (OR)
    b) Construct a triangle PQR such that QR=5 cm, ∠P=30° and the altitude from P to QR is of length 4.2 cm.
    Answer: Geometric constructions to be performed as per standard procedures.
44. a) Graph the quadratic equation x²-8x+16=0 and state the nature of their solution. (OR)
    b) A school announces that for a certain competition, the cash price will be distributed for all the participants equally as shown below.
    No of participants (x): 2, 4, 6, 8, 10
    Amount for each participant in (y): 180, 90, 60, 45, 36
    i) Find the constant of variation.
    ii) Graph the above data and hence, find how much will each participant get if the number of participants are 12.
    a) The graph is a parabola y=(x-4)² which touches the x-axis at (4,0). Nature of solution: Real and equal roots.
    b) i) It is an inverse variation. The constant of variation, k = xy = 360.
    ii) From the graph or by calculation (y=360/12), if there are 12 participants, each will get Rs. 30.

Original Question Paper Images

SSLC Quarterly Exam 2024 English Key Answer - Villupuram District | Samacheer Kalvi Guide

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VILLUPURAM DISTRICT

KEY TO SSLC QUARTERLY EXAMINATION 2024

ENGLISH

PART I (14x1=14)

Answer all the questions

Choose the appropriate synonyms for the italicised words.

1. a) chewed	1
2. a) instinctively	1
3. d) natively	1

Choose the appropriate antonym for the italicised words.

4. c) joyfully	1
5. d) slowly	1
6. a) disliked	1

7. b) furniture	1
8. b) -ure	1
9. c) Educational Management and Information System	1
10. a) once in a blue moon	1
11. c) match	1
12. a) on	1
13. c) works / d) will work	1
14. b) Though	1

PART II (20 Marks)

Section - I 3x2=6

Answer any THREE of the following questions in a sentence or two.

15. No, the mother bird did not offer any food to the young bird. (2)

16. Slamming of the doors woke up the mother. (2)

17. INSV stand for Indian Naval Ship Vessel. (2)

18. Next to grocery shop opposite to temple. (2)

Section II 3x2=6

Read the following sets of poetic lines and answer any THREE of the following.

19.

a) The distant, unclear or forgotten past/ past memories (1)

b) No (1)

20.

a) Walk with a smile and song/ Be positive / Be optimistic (1)

b) Walk with a smile and song/ Be positive / Be optimistic (1)

21.

a) No (1)

b) strong in her faith / firm in her belief (1)

22.

a) Ants are industrious / planners/ save for the future (1)

b) Ants to Cricket (1)

Section III 3x2=6

Answer any THREE of the following.

23. A watch was given to me by my uncle on my birthday. / A watch was given to me on my birthday by my uncle. I was given a watch by my uncle on my birthday. / I was given a watch on my birthday by my uncle. (2)

24. Muthu said, "Are tickets available for the match?" (2)

25. "Be not so amazed, daughter Miranda," said Prospero. (2)

26.

a) "Make me a cup of tea, will you?" (2)

b) "You should speak politely to the elders."

27.

a) "If you apply for a loan, you will get it immediately." (2)

b) "Storytelling is an art which involves planning, research, and skill."

Section IV 1x2=2

Answer the following question.

28. Any relevant instructions may be given full marks. (2)

PART III (50 Marks)

Section I 2x5=10

Answer any TWO of the following in utmost ten lines.

29. Character Sketch of Sasanka Sanyal:

• Proud and Dignified: Insists on paying for his tea
• Emotionally Scarred: Haunted by the loss of his wife and son
• Intelligent and Talented: Recites Tagore's poem, highlighting his literary talent
• Remorseful Yet Forgiving: Initially resents Aditya for taking his medal but ultimately forgives him upon its return.
• Principled and Self-Reliant: Rejects money from Aditya, valuing dignity and the return of his medal over charity.
• Lonely and Isolated: Lives a solitary life, surprised that anyone visits him, emphasizing his emotional detachment.
• Emotionally Complex: Exhibits a mix of bitterness and warmth in his interactions, reflecting deep feelings about the past. brief character sketch of Sasanka Sanyal.

(Mentioning any five characteristics with justification can be awarded 5 marks)

30. Description of the funny incident that caused the confusion in the house:

Imagination - November 17, 1915 - chaos ensues - Mother throws shoe - neighbour's window - Grandfather shoots patrolman - mysterious footsteps - dining room - suspecting burglars - Herman scared - police called - Bodwell confused - frantic ransacking - zither found - Grandfather believes in deserters - mayhem - gun fired - breakfast jokes - thirsty for water.

(Narrating funny incidents with error-free sentences can be awarded full marks.)

31. Description of the struggles undergone by the young seagull to overcome its fear of flying:

Fearful seagull - alone on ledge - siblings fly away - anxiety about flying - parents encourage - hunger drives decision - desperate attempt - falls off ledge - discovers ability to fly - joy of soaring - family reunion - struggles with landing - floats on water - first flight success.

(Answers that include error-free sentences capturing the above key points may be awarded full marks.)

32. The selection and training process which the crew underwent:

Selection process - 30 applicants - 6 women chosen - survival skills assessed - mentored by Commander Dilip Donde - three years of training - theoretical courses - navigation and weather prediction - hands-on training - emergency management - basic sail training in Mumbai and Kochi - previous voyages on INSV Mhadei - teamwork emphasized - resource management skills developed.

(Responses that present error-free sentences incorporating the key points listed above may be eligible for full marks)

Section II 2x5=10

Answer any TWO of the following in utmost ten lines.

33. The kind of behaviour does the poet want the readers to possess from 'Grumble Family'

• Positivity - embrace a joyful outlook
• Gratitude - appreciate life's gifts
• Acceptance - tolerate imperfections
• Humour - find laughter in challenges
• Optimism - focus on solutions, not problems

(Responses that capture error-free sentences reflecting these key behaviours may be awarded full marks.)

34. Portrayal of Today's Woman

• Innate beauty - symbolizes strength
• Resilience - faces challenges with courage
• Nurturer - cares for loved ones
• Strong beliefs - persistent and determined
• Empowerment - embodies confidence and pride

(Responses that include error-free sentences reflecting these key points may be awarded full marks.)

35. Read the following poetic lines and answer the questions given below:

i) fear - cheer, whole - toll

ii) abba

iii) Metaphor

iv) from-future, what – with- whole

36. Paraphrase the following stanza:

Reference: These lines are from the poem 'The Ant and the cricket' from Aesop Fables. The poem emphasizes the importance of preparation and responsibility over carefree living.

Paraphrase: A foolish young cricket, who enjoyed singing during the warm, sunny days of summer and spring, began to complain when he discovered that his cupboard was empty and that winter had arrived.

Conclusion: Through the cricket's experience, the poem conveys a vital lesson about the consequences of neglecting responsibilities and the value of preparing for the future.

Reference – 1 Mark
Paraphrase – 3 Marks
Conclusion – 1 Mark

Section III 1x5=5

Answer any ONE of the following.

37. Rearrange the following sentences in coherent order:

1. Somu sent the Krishnan family a strange, pink bird named Zigzag.
2. After Visu left, the bird snored loudly, causing chaos.
3. Zigzag refused to speak and made a mess with fruit and nuts.
4. Dr. Krishnan took Zigzag to his clinic, where the bird calmed the environment.
5. Dr. Krishnan realized Zigzag was a valuable asset, trained to help patients.

38. Read the following passage and answer the questions that follow.

(a) Another name for this Japanese folktale is "The Story of the Aged Mother".

(b) The cruel proclamation was an order from the despotic leader to put all aged people to death.

(c) The aged mother helped her son find his way back by secretly leaving a trail of twigs as they climbed the mountain.

(d) The impossible command issued by the governor was to make a rope of ashes.

(e) The result of the farmer revealing the truth to the governor was the abolition of the cruel law.

Section IV 4x5=20

Answer any four of the following:

39. Advertisement

Outline	1
Title	1
Picture	1
Caption	1
Address	1

40. Letter Writing

From – To	1
Date, Salutation	1
Body of the Letter	2
Subscription and superscription	1

41. Notice Writing

Name of the institution and programme	1
Date and Venue	1
Content	2
Name and Designation	1

42. Look at the following picture and describe what you think is happening in it in about five sentences.

Any five relevant sentences without mistakes.

43. Notes:

Title	1
Words/phrases with all important points. (With / without hyphen) / Sub heading with points.	4

(Or)

Summary:

Title	1
Rough copy	2
Fair copy (Based on rough copy, fair copy should have been prepared without grammatical and syntactical errors)	2

Section V

Identify and correct the errors 1x5=5

45. Identify and correct the errors in the following sentences:

(a) She is good at playing the piano.

(b) Each of the boys has completed their homework.

(c) He went to the market yesterday.

(d) She is the tallest girl in the class.

(e) We are planning a trip to Paris next summer.

46. Quote from memory:

Strong is she in her faith and beliefs.
"Persistence is the key to everything,"
says she. Despite the sighs and groans and moans,
She's strong in her faith, firm in her belief!
She's a lioness; don't mess with her.

PART IV (16 Marks)

46. Write a paragraph of about 150 words by developing any ONE the following hints. (8)

a) Supplementary – Summary of the story

Title	1
Own summary without mistakes	6
Moral	1

(or)

b) Supplementary – Summary of the story

Title	1
Own summary without mistakes	6
Moral	1

47.

a) Answers

The main sources of plastic pollution include single-use plastics, packaging, and discarded fishing gear. (2)

Plastic waste impacts marine life by causing entanglement in plastic debris, ingestion of plastic particles, and other detrimental effects on their health. (2)

Some countries have implemented bans on plastic bags and straws, and others promote biodegradable alternatives. (2)

To effectively combat plastic pollution, collective action is required at both individual and governmental levels. (2)

(or)

b) Answers

The speaker's favourite activity is swinging. (2)

From the swing, the speaker can see rivers, trees, cattle, and the countryside. (2)

The speaker feels that swinging is the “pleasantest thing" a child can do, indicating great enjoyment and happiness. (2)

The speaker looks at the garden green and the roof so brown from the swing. (2)