Scholarship Exam Sample Question Paper for Class 8 Paper 1 Set A1 is specially designed for Class 8th students preparing for the MSCE scholarship exam. This paper focuses on Paper 1, covering First Language and Mathematics, ensuring comprehensive preparation based on the MSCE scholarship syllabus for Class 8th. Here, students will find a sample question paper with detailed answers and explanations to aid their understanding. It is an excellent resource for practicing and gaining confidence for the Scholarship Exam Class 8th. Use this to familiarize yourself with the pattern of the MSCE scholarship class 8th Paper 1 and excel in your exam preparation.
Instructions for Question No. 01 and 02
Read the dialogue and choose the correct option.
Ranjana: Hi Ananya!
Ananya: Hello Ranjana, How was your visit to the science park, yesterday?
Ranjana: It was amazing. I got to know much about science and technology and how much progress science and technology has done? Mini Robots, use of solar energy, wonders of physics, advancement in the field of automotive.
Ananya: Yes, you are right. Science has really made an impact in our lives.
1. Choose the correct option which is mentioned in the above dialogue.
What has really made an impact in our lives?
(1) Science
(2) Mathematics
(3) Physics
(4) Solar Energy
Answer: (1) Science
Explanation: The dialogue clearly states, “Science has really made an impact in our lives.”
2. Things seen by Ranjana at Science Park:
(1) Advancement in the field of mechanics
(2) Underdevelopment in the field of automotive
(3) Non-development in the field of automotive
(4) Advancement in the field of automotive
Answer: (4) Advancement in the field of automotive
Explanation: The dialogue specifies that Ranjana learned about advancements in the field of automotive.
03. Choose two correct alternatives of adjective clauses in the following sentences.
(1) He thought that he was safe there.
(2) He is the man whom we all respect.
(3) He is the boy who broke the window.
(4) He ran so quickly that he soon overtook me.
Answer: (2) He is the man whom we all respect.
Answer: (3) He is the boy who broke the window.
Explanation: Both sentences contain clauses that function as adjectives modifying nouns.
Instructions for Question No. 04 and 05
Read the letter and choose the correct alternative.
Sohoni Brothers,
Hospital Road,
Agra.
25th February 2024
Subject – The Agra Trade Exhibitions
Dear Sir,
This is to confirm the points agreed in our recent discussions:
- We will be taking a display stand at your exhibition for our range of books.
- The cost of the stall and display area measuring 12 feet by 8 feet on the ground floor of the exhibition hall.
We look forward to receiving final details of the location of our stand/stall before 20th February 2024.
S. B. Sohoni
4. What is missing in the letter?
(1) Subscription or courteous leave taking.
(2) Subject of the letter.
(3) Body of the letter.
(4) Salutation.
Answer: (1) Subscription or courteous leave taking.
Explanation: The letter lacks a formal closing or subscription.
5. What is the display area required by the writer of the letter?
(1) 12 inches by 8 feet.
(2) 12 feet by 8 inches.
(3) 12 feet by 8 cm.
(4) 12 feet by 8 feet.
Answer: (4) 12 feet by 8 feet.
Explanation: The letter clearly mentions the dimensions as 12 feet by 8 feet.
Instructions for Question No. 06 to 08
Read the passage and choose the correct alternatives.
What are the main schools of classical dancing?
The four main schools of classical dancing in India are: Bharata Natyam, Kathakali, Manipuri, and Kathak.
Bharata Natyam is the oldest and most popular dance form of India. Earlier, it was known by various names. Some called it Bharatam, some Natyam, some Desi Attam, and some Sadir.
The districts of Tanjore and Kanchipuram of Tamil Nadu were the focal points in the development of Bharata Natyam. It was danced as a solo performance by devadasis (temple dancers) on all auspicious occasions. Later, kings and rich people lent their patronage to it and it started shedding its purely sacred character.
The dancer is directed by the Natuvanar, who is a musician and, invariably, a teacher. Another musician plays the cymbals. The music for Bharata Natyam is the Carnatic school of music. The mridangam (a drum), played on both sides with the hands, provides the rhythm.
The home of Kathakali is Kerala. Kathakali literally means ‘story-play.’ It combines music, dance, poetry, drama, and mime. Its present form has evolved out of older forms such as Ramanattam and Krishnanattam.
6. The districts of ____ and ____ of Tamil Nadu were the focal points in the development of Bharatanatyam.
(1) Kerala, Krishnanattam
(2) Bhartam, Desi Attam
(3) Tanjore and Kanchipuram
(4) Kerala and Ramanattam
Answer: (3) Tanjore and Kanchipuram
Explanation: The passage clearly states that Tanjore and Kanchipuram were the focal points for Bharatanatyam development.
7. Kathakali’s present form has ____ of older forms.
(1) directed by
(2) evolved out
(3) involve out
(4) played on
Answer: (2) evolved out
Explanation: The passage mentions that Kathakali’s present form has evolved out of older forms like Ramanattam and Krishnanattam.
8. Choose the correct option mentioned in the passage.
What is the oldest and most popular dance form of India?
(1) Kathakali
(2) Manipuri
(3) Bharata Natyam
(4) Kathak
Answer: (3) Bharata Natyam
Explanation: The passage explicitly states that Bharata Natyam is the oldest and most popular dance form of India.
Instructions for Question No. 09, 10, and 11
Read the tour itinerary and choose the correct alternative.
Best of Kerala – 7 nights / 8 days
Cochin, Munnar, Tekkady, Alleppey, Kovalam. Old temples, pristine beaches, scenic backwaters, colonial town, splendid monuments, and varied wildlife are the striking features of Kerala.
City tour by bus, luxury hotels, and all types of food are available.
- Day 1: Arrival in Cochin
- Day 2: Cochin to Munnar
- Day 3: Munnar
- Day 4: Munnar to Tekkady (30 km / 2.5 hours)
- Day 5: Tekkady to Alleppey
- Day 6: Alleppey to Kovalam (160 km / 4.5 hours)
- Day 7: Kovalam to Trivandrum
- Day 8: Departure from Trivandrum
Suitable for young travelers and senior citizens.
9. What is not included in the tour itinerary?
(1) Tickets
(2) Bus tour
(3) All types of food
(4) Luxury hotels
Answer: (1) Tickets
Explanation: The tour itinerary does not mention ticket costs, whereas it includes a bus tour, luxury hotels, and all types of food.
10. Choose the correct alternative mentioned in the passage.
The tour is suitable for –
(1) Women
(2) Children
(3) Senior citizens
(4) Girls
Answer: (3) Senior citizens
Explanation: The passage explicitly mentions the tour is suitable for young travelers and senior citizens.
11. The striking features of Kerala are old temples, ____ beaches, scenic backwaters, colonial towns, splendid monuments, and varied wildlife.
(1) full of fishes
(2) long
(3) sandy
(4) pristine
Answer: (4) pristine
Explanation: The passage describes Kerala’s beaches as “pristine.”
12. Find the meaning of the underlined non-English word.
“Asanas should be practiced in a clean, airy, and well-lit room.”
(1) Jogging
(2) Yoga position
(3) Running
(4) Practice
Answer: (2) Yoga position
Explanation: “Asanas” refers to yoga postures or positions.
13. Choose the correct alternative of the noun phrase.
“A blue crab crawled sideways across the beach.”
(1) Crawled
(2) The beach
(3) A blue crab
(4) Sideways
Answer: (3) A blue crab
Explanation: “A blue crab” is the noun phrase as it includes the noun “crab” with its modifier “blue.”
14. Choose the correct option for the underlined word.
“Rats and mice ran here and there all over Dick and kept him awake.”
(1) Walked slower
(2) Scampered
(3) Overcame
(4) Dismayed
Answer: (2) Scampered
Explanation: The word “ran” here is synonymous with “scampered,” meaning quick, light movements.
15. In the Covid pandemic, WHO gave all instructions on how to take care of ourselves.
(1) World Healthy Org.
(2) World Health Organization
(3) Worldly Health Organization
(4) World Health Organization
Answer: (2) World Health Organization
Explanation: WHO stands for the “World Health Organization.”
16. The sum is difficult. But he ____ work this sum.
(1) Can
(2) Shall
(3) Have
(4) Need
Answer: (1) Can
Explanation: “Can” indicates the ability to work on the sum.
17. Choose the correct option for the figure of speech ‘personification.’
(1) The camel is the ship of the desert.
(2) Words are like leaves, and where they most abound.
(3) Death lays his icy hand on kings.
(4) Many are called, but few are chosen.
Answer: (3) Death lays his icy hand on kings.
Explanation: Personification gives human qualities to non-human entities. Here, “Death” is described as having an “icy hand,” a human attribute.
18. Which type of synthesis is used in the following sentence? Choose the correct option.
“Being tired of play, Atharv sat down to rest.”
(1) By using an infinitive
(2) By using conjunction
(3) By using participle
(4) By using co-ordinator
Answer: (3) By using participle
Explanation: The phrase “Being tired of play” is a participle phrase used to combine two ideas into one sentence.
19. Choose the correct option of the exclamatory sentence.
“The moonlight very sweetly sleeps upon this bank.”
(1) How sweet the sleeps moonlight upon this bank!
(2) What a sweet the moonlight sleeps upon this bank!
(3) What the moonlight a sweet sleeps upon this bank!
(4) How sweet the moonlight sleeps upon this bank!
Answer: (4) How sweet the moonlight sleeps upon this bank!
Explanation: The correct exclamatory sentence begins with “How” and maintains proper word order.
20. Find out the type of conjunction used in the sentence.
“Though he is suffering much pain, yet he does not complain.”
(1) Co-relative conjunction
(2) Co-ordinating conjunction
(3) Compound conjunction
(4) Subordinative conjunction
Answer: (1) Co-relative conjunction
Explanation: The conjunction pair “Though…yet” is a co-relative conjunction used to show contrast.
21. Choose the correct ‘Wh’ question word to get the underlined part as an answer.
“Aniket was fascinated by the beauty of nature since childhood.”
(1) Who
(2) What
(3) How
(4) Where
Answer: (2) What
Explanation: The underlined phrase “the beauty of nature” answers the question “What was Aniket fascinated by?”
22. Choose two correct alternatives to complete the web.
(1) Air
(2) Tempo
(3) Invite
(4) Rhythm
Answer: (1) Air
Answer: (2) Tempo
Explanation: Air and Tempo are terms related to music and fit in the web diagram.
Instructions for Question No. 23 and 24
Read an advertisement and choose the correct alternative.
23. Match the pairs:
| A | B |
|---|---|
| SAMI A30 | Mega Prize |
| SAMI A35 | Bumper Prize |
| SAMI A40 | Super Prize |
(1) 1 – A, 2 – B, 3 – C
(2) 1 – C, 2 – B, 3 – A
(3) 1 – A, 2 – C, 3 – B
(4) 1 – B, 2 – A, 3 – C
Answer: (3) 1 – A, 2 – C, 3 – B
Explanation: Based on the pairs given in the question, option (3) is correct.
24. Find the wrong word that is not mentioned in the advertisement in the following web diagram.
Selected cities for the offer:
Aurangabad, Nagpur, Mumbai, Pune
(1) Aurangabad
(2) Mumbai
(3) Pune
(4) Nagpur
Answer: (3) Pune
Explanation: Pune is not listed in the cities mentioned in the advertisement.
25. Choose two correct alternatives for the following sentence.
“Hrishikesh ____ by my question.”
(1) Is annoying
(2) Had annoyed
(3) Is annoyed
(4) Was annoyed
Answer: (3) Is annoyed
Answer: (4) Was annoyed
Explanation: The verbs “is annoyed” and “was annoyed” correctly complete the sentence in the present and past tense.
26.
Answer: (1)
Explanation: We need to simplify the given expression:
27. The surface area of a sphere is 616 sq.cm. Which of the following is an incorrect alternative related to the sphere with double the radius of that sphere?
(1) Surface area will be 2464 sq.cm.
(2) Surface area will be 1232 sq.cm
(3) Surface area will increase by 1848 sq.cm. than the first sphere.
(4) Surface area will be four times the surface area of the first sphere.
Answer: (2) Surface area will be 1232 sq.cm
Explanation: Doubling the radius of a sphere quadruples the surface area, so 1232 sq.cm is incorrect as it is not consistent with this calculation.
28. Anjurani weighed an object and noted its weight in four different ways as given below. Which two alternatives denote the same weight?
(1) 12 kg. 175 deca gm.
(2) 13 kg. 75 gm.
(3) 121 hecto gm. 75 deca gm
(4) 135 hecto gm. 250 gm.
Answer: (1) 12 kg. 175 deca gm.
Answer: (3) 121 hecto gm. 75 deca gm.
Explanation: Both (1) and (3) represent the same weight in different units.
29. The side of the adjoining square MNOP is 18 cm. Points ‘X’ and ‘Y’ are the midpoints of the sides MP and NO respectively. Find the area of the shaded region.
(1) 324 sq.cm
(2) 162 sq.cm.
(3) 81 sq.cm.
(4) 243 sq.cm.
Answer: (2) 162 sq.cm.
Explanation: The shaded region is a triangle with half the area of the square. The area of the square is 18×18=324 sq.cm. Half of this is 162 sq.cm.
30.
(1) 1
(2) 0
(3) 2y + 4x
(4) 4x – 2y
Answer: (1) 1
Explanation: We are tasked with simplifying:
31. A square-shaped compound of a temple has a side 40 m. On each side of the compound, triangular gardens of side equal to that of the side of the compound are there. What will be the total cost of 5 rounds of wire fencing for protection from their outer edges only, for all the gardens, at the rate of ₹80 per meter of wire?
(1) ₹256000
(2) ₹160000
(3) ₹512000
(4) ₹128000
Answer: (1) ₹256000
Explanation: The perimeter of the compound is 4×40=160 m. For 5 rounds of fencing, the total length required is 5×160=800 m. Cost = 800×80=₹256000.
32. ₹9700 is invested in the bank with simple interest at the rate of 5% p.a. To get the same amount that will be received in 4 years in 2 1/2 years only, by how much should the rate of interest be increased?
(1) 8%
(2) 5%
(3) 3%
(4) 2.5%
Answer: (3) 3
Explanation: The simple interest formula is SI=P×R×T/100. Solving for R, the rate is increased by 3% to achieve the same total amount in 2.5 years.
33. If (x−y)2=49 and (x+y)2=169, then find 4xy=?
(1) 30
(2) 60
(3) 90
(4) 120
Answer: (2) 60
Explanation: Using the identity (x+y)2−(x−y)2=4xy, we substitute the given values: 169−49=4xy⇒4xy=60.
34. All the vertices of a triangle are on the circumference of the circle at equal distances from each other and at a distance of 14 cm from the center of the circle. What will be the length of the median of that triangle?
(1) 7 cm.
(2) 14 cm
(3) 21 cm
(4) 28 cm
Answer: (2) 14 cm.
Explanation: The median of an equilateral triangle inscribed in a circle is equal to the radius of the circle, which is 14 cm.
35. Which of the two alternative expressions from the given are perfect squares?
Answer: (3) (25p2+36q2−30pq)
Answer: (4) (64ab+64a2+16b2)
Explanation: Expanding these expressions shows that they are perfect squares:
- (25p2+36q2−30pq)=(5p−6q)2
- (64ab+64a2+16b2)=(8a+4b)2
36. What will be the eighth odd number after the even number 3x−5?
(1) 3x−22
(2) 3x−13
(3) 3x+10
(4) 3x+3
Answer: (3) 3x+10
Explanation: Each odd number is separated by 2. Starting from 3x−5+2(8), the eighth odd number is 3x+10.
37. While selling an article, if Raghav increased its selling price by ₹384, he would have 5% profit instead of 3% loss. What should be the original price of the article?
(1) ₹19200
(2) ₹12800
(3) ₹7680
(4) ₹4800
Answer: (4) ₹4800
Explanation: The difference of 8% is equal to ₹384. Using the formula: 8% of cost price = ₹384, we find Cost Price=₹4800.
38. Two triangles are formed by diagonal BD of kite ABCD as shown in the figure. Which test from the following is not applicable for proving these two triangles congruent?
(1) SAS
(2) SSS
(3) ASA
(4) Hypotenuse-side
Answer: (4) Hypotenuse-side
Explanation: The hypotenuse-side test is not valid here because these triangles are not right-angled triangles.
39. Rafiq has ₹28,500 with him in the form of some ₹2000 notes and some ₹500 notes only. Which of the following could be the number of ₹500 notes?
(1) 57
(2) 25
(3) 23
(4) 11
Answer: (1) 57
Explanation: Let the number of ₹2000 notes be x and ₹500 notes be y. Solving 2000x+500y=28500 under divisibility constraints gives y=57.
40.
Answer: (2) 16
Explanation: Solving 1/25=k−5/4, we rewrite it as k 5/4=, which gives k=16.
41. The area of a square hall with a height of 4 m 49 sq.m. What will be the total cost (in rupees) of coloring all the walls of that hall at the rate of ₹300 per sq.m.?
(1) ₹11200
(2) ₹74000
(3) ₹33600
(4) ₹42000
Answer: (3) ₹33600
Explanation: Total wall area = Perimeter of the hall Height = 4×7×4=112 sq.m. Cost = 112×300=₹33600.
42. In a transaction, if the selling price is four times the loss, then what is the percentage loss to the seller?
(1) 20
(2) 25
(3) 12.5
(4) 14.3
Answer: (2) 25
Explanation: Let the loss be x, and selling price = 4x. Using the relation CostPrice=SP+Loss, CP=4x+x=5x. Percentage loss = x/5x×100=25%.
43. The conical tent with a height of 21 m has a base circumference of 176 m. How much air (in cubic meters) can be contained in that tent?
(1) 17248
(2) 2464
(3) 7840
(4) 15680
Answer: (3) 7840
44. How many shares of ₹500 each did Pari purchase, if she spent ₹46350 with a 3% commission?
(1) 95
(2) 90
(3) 81
(4) 87
Answer: (3) 81
Explanation: Total cost with commission = ₹500×Shares×1.03=₹46350. Solving gives Shares=81.
45. A side of a square is congruent to the 30 cm diagonal of a second square. Select an incorrect alternative from the given options regarding the relation between the areas of the two squares.
(1) Areas of both the squares are not equal.
(2) The area of the second square is half that of the first square.
(3) The area of the first square is more by 900 sq.cm.900\ \text{sq.cm.} than the other square.
(4) The area of the second square is less by 450 sq.cm. than the area of the first square.
Answer: (4) The area of the second square is less by 450 sq.cm. than the area of the first square.
Explanation: Solving the areas shows the difference between the areas is 900 sq.cm., not 450 sq.cm.
46. In the adjoining circle with center C, ∠PRS=55∘, then ∠PSQ=?
(1) 55∘
(2) 40∘
(3) 45∘
(4) 35∘
Answer: (3) 45∘
Explanation: Using the circle’s properties, the angle subtended at the center is twice that subtended at the circumference.
47. An obtuse angle is formed between the hour hand and minute hand of a clock. Which two alternatives from the following will correctly represent the possible time?
(1) 1:20 hrs
(2) 11:40 hrs
(3) 4:05 hrs
(4) 8:55 hrs
Answer: (2) 11:40 hrs
Answer: (4) 8:55 hrs
Explanation: Both 11:40 and 8:55 form obtuse angles as verified by the positions of the hour and minute hands.
48. The ratio of the lengths of the diagonals of a 20 cm sided rhombus is 3:4. What will be the area in sq.cm of that rhombus?
(1) 768
(2) 384
(3) 192
(4) 96
Answer: (2) 384
Explanation: Using the relation d 2/1+d 2/2=4a2, where a=20 cm, the area = 1/2 d1d2=384 sq.cm.
49. After reading 5/9 part and 68 pages of a book, 92 pages are still remaining. What is the total number of pages in that book?
(1) 360
(2) 280
(3) 153
(4) 117
Answer: (2) 280
Explanation: If 4/9 part of the book equals 68+92=160, the total number of pages is 160/4×9=280.
Directions for Question Nos. 50 and 51
In a school, there are 50 students enrolled in each of Std. V to Std. VIII. Below is a joint bar diagram representing the attendance of the students standard-wise. Observe the graph and answer the questions.
50. By what percentage is the present girls’ attendance more than the present boys’ attendance?
(1) 10
(2) 2
(3) 20
(4) 2.5
Answer: (3) 20
Explanation: If boys’ attendance is 40 and girls’ attendance is 48, the percentage increase is 48−40/40=20%.
51. By considering the attendance of both boys and girls, which standard has the least attendance?
(1) Eighth
(2) Seventh
(3) Fifth
(4) Sixth
Answer: (1) Eighth
Explanation: From the bar diagram, the total attendance of Std. VIII is the lowest compared to other standards.
52. If 25% of 780=M% of 1950, then M=?
(1) 10
(2) 12
(3) 8
(4) 14
Answer: (3) 8
Explanation: Solving 25/100×780=M/100×195, we find M=8.
53. If the LCM of two consecutive even numbers is 312, then what will be the sum of these two numbers?
(1) 48
(2) 46
(3) 52
(4) 50
Answer: (4) 50
Explanation: The two consecutive even numbers are 24 and 26. Their sum is 50.
54. All points shown on the given number line are at equal distances. ∣UR∣−∣QT∣=?
(1) ∣RS∣
(2) ∣TU∣
(3) ∣QR∣
(4) ∣SQ∣
Answer: (3) ∣QR∣
Explanation: From the number line, ∣UR∣−∣QT∣=∣QR∣ as it represents the difference in the lengths directly between points U,R, and Q,T.
55. Five years ago, a mother’s age was twice her daughter’s age. If the ratio of their present ages is 11:6, then what will be the difference in their ages (in years) five years hence?
(1) 20
(2) 25
(3) 30
(4) 35
Answer: (2) 25
Explanation: Let the present ages of the mother and daughter be 11x and 6x respectively. The difference in their ages is 11x−6x=5x. Five years hence, the difference remains the same, 5x=25.
56. If a+b=13 and ab=36, then a2+b2=?
(1) 169
(2) 81
(3) 97
(4) 16
Answer: (3) 97
Explanation: Using the identity a2+b2=(a+b)2−2ab, substitute a+b=13 and ab=36:
(13)2−2(36)=169−72=97.
57. Which of the two options given below are incorrect statements?
(1) All integers are not real numbers.
(2) Some rational numbers are integers.
(3) All rational numbers are integers.
(4) Some integers are not whole numbers.
Answer: (1) All integers are not real numbers.
Answer: (3) All rational numbers are integers.
Explanation: (1) is incorrect because all integers are real numbers. (3) is incorrect because not all rational numbers are integers.
58. The following table shows the subject-wise marks scored by a student in a summative test. Find the average marks.
| Subjects | Marathi | Hindi | Maths | Science | Social Science |
|---|---|---|---|---|---|
| Marks | 32 | 36 | 48 | 44 | 40 |
(1) 40
(2) 38
(3) 42
(4) 36
Answer: (1) 40
Explanation: Total marks = 32+36+48+44+40=200. Average = 200/5=40.
59. In the adjoining figure, line AB∣∣line CD, and ∠RGC=50∘, then find ∠SFA−∠PEA=?
(1) 50∘
(2) 80∘
(3) 100∘
(4) 130∘
Answer: (3) 100∘
Explanation: Using the properties of parallel lines and transversals, ∠SFA=150∘ and ∠PEA=50∘. The difference is 150∘−50∘=100.
60. 4b−2a+5−3b−9+5a−4+3b−2a=?
(1) 4b+9a−4
(2) 2a+4b−8
(3) a−4b−8
(4) a+4b−8
Answer: (4) a+4b−8
Explanation: Combine like terms:
4b−3b+3b=4b, −2a+5a−2a=a, and 5−9−4=−8.
61. What will be the difference in rupees between the simple interest and the compound interest earned on ₹5000 in 2 years at the rate of 5% p.a.
(1) 12.5
(2) 25
(3) 37.5
(4) 50
Answer: (2) 25
Explanation: Using the formulas for SI and CI:
SI=5000×5×2/100=500.
CI=5000×(1+5/100)2−5000=525. Difference = 525−500=25.
62. The average weight of Siya and Nisha is 29 kg. The average weight of Fiza and Siya is 26 kg. If the total weight of Nisha and Fiza is 50 kg., what will be the maximum weight (in kg) among the three girls?
(1) 25
(2) 28
(3) 30
(4) 34
Answer: (3) 30
Explanation: Let Siya’s weight = x, Nisha’s = y, and Fiza’s = z.
x+y=58, x+z=52, y+z=50. Solving these gives x=30, y=28, z=22.
63. A work is completed by some workers in a few days. If the number of workers is made 3/2 times the original number of workers, then how many times will the days required be increased compared to the original to complete the same work?
(1) 3/2
(2) 1 1/2
(3) 1/4
(4) 1/2
Answer: (4) 1/2
Explanation: If workers increase by 3/2, the time decreases proportionally. So, new time = 2/3 of the original, which is 1/2 less.
64. The length of the longest chord of a circle is 7 m. What will be the length of the parallel chord to it, at a distance of 2.1 m?
(1) 2.8 m
(2) 5.6 m
(3) 4.2 m
(4) 3.5 m.
Answer: (2) 5.6 m.
65.
(1) 1
(2) 6
(3) 12
(4) 17
Answer: (3) 12
Explanation: Simplify.
66. In the adjoining figure, EFGH is a rhombus with a diagonal of 28 cm, and the vertices are on the circle with center O. Find the area of the shaded region.
1) 56 sq.cm.
(2) 112 sq.cm.
(3) 105 sq.cm.
(4) 210 sq.cm
Answer: (2) 112 sq.cm
Explanation: The area of the rhombus = 1/2×diagonal1×diagonal2=1/2×28×8=112 sq.cm.
67. Which of the following two alternatives are perfect cube numbers?
(1) 0.02700
(2) −0.000625
(3) −13.310
(4) 0.0729
Answer: (1) 0.0270
Answer: (2) −0.000625
Explanation: Both 0.02700 and −0.000625 are perfect cubes: 0.0270=(0.3)3.
68. By how much is the greatest of the following numbers greater than the smallest of the given numbers?
14/5,2/1,15.7,7/6,5/3
(1) 14/5
(2) 30/1
(3) 15/2
(4) 2/1
Answer: (1) 14/5
Explanation: Convert to decimals:
14/5=2.8,2/1=2,15/7=2.14,7/6=1.16,5/3=1.67. The greatest number (2.8) exceeds the smallest (1.16) by 1.6.
69. ‘Diagonals of the ____ are perpendicular bisectors of each other.’ Choose the correct alternative from the given options to complete the above statement.
(A) Rectangle
(B) Square
(C) Rhombus
(D) Parallelogram
(E) Kite
(1) Only A and B
(2) Only B and C
(3) Only B, C, and E
(4) Only A, B, and E
Answer: (3) Only B, C, and E
Explanation: Squares, rhombuses, and kites have diagonals that are perpendicular bisectors of each other.
70. Observe the two planes X and Y shown in the diagram and select two correct statements from the given options.
(1) Points F,B,C belong to different planes.
(2) A line is formed where two planes intersect.
(3) Points A,G,E are non-collinear points lying in the same plane.
(4) Two planes are parallel to each other.
Answer: (2) A line is formed where two planes intersect.
Answer: (3) Points A,G,E are non-collinear points lying in the same plane.
Explanation: Statement (2) describes the intersection of planes, and (3) shows non-collinear points in the same plane.
71. Spandan purchased two articles each for ₹3750 when an 8% discount was declared. How much should he pay to the seller for this purchase?
(1) ₹7200
(2) ₹3450
(3) ₹6900
(4) ₹8100
Answer: (3) ₹6900
Explanation: Original cost = 3750×2=₹7500. After 8% discount:
(7500−(7500×0.08))=₹6900.
72. In the adjoining figure of △EFG, point H is the midpoint of the segment FGF. If ∠EFH=45∘ and EF=EG=102 cmEF = EG = 10√2, then EH=? cm.
(1) 10√2
(2) 10
(3) 20
(4) 20√2
Answer: (2) 10
Explanation: Since H is the midpoint, EH=EF/√2=10√2/√2=10 cm.
73. [(m+9)(m−5)]−[(m−8)(m+4)]=?
(1) 8m−138m – 13
(2) m−5m – 5
(3) (𝑚 – 4)²
(4) m+77
Answer: (1) 8m−13
Explanation: Expanding the expressions and simplifying gives:
(𝑚² + 4𝑚 – 45) – (𝑚² – 4𝑚 – 32) = 8𝑚 – 13
74. The height of the trapezium PQRS shown in the adjoining figure is 8 cm. Segment ST≅PS, and PQ=SR=17 cm Then find the perimeter of PQRS in cm.
(1) 80
(2) 96
(3) 88
(4) 72
Answer: (3) 88
Explanation: The perimeter of the trapezium is the sum of all sides:
Perimeter=PQ+QR+RS+SP=17+27+17+27=88 cm.
75. What is the compound interest (in rupees) for ₹10,000 for two years and six months, at the rate of 10%
(1) 2650
(2) 3310
(3) 2500
(4) 2705
Answer: (2) 3310
Explanation:
Using the compound interest formula: ,
where P=10,000, r=10%, and n=2.5 years.
CI=10,000(1+10/100)².⁵−10,000=3310 rupees.
