CBSE Class 10 Mathematics Basic Sample Paper 27 2027 Solutions

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page 364 Cbse Class 10th Mathematics - Basic SP Sample Paper 27 Class - 10th Exam - 2026 - 27 Mathematics - Basic Time : 3 Hours Max. Marks : 80 General Instructions : Read the following instructions carefully and follow them: 1. This question paper contains 38 questions. 2. This Question Paper is…
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SAMPLE PAPER 27 OP 12 2 2 + 132 = OP2 13 12 2 2 = − 169 144 = − 25 = Thus OP 5 = cm Thus (b) is correct option. 3. If the point ( , ) P k 0 divides the line segment joining the points ( , ) A 2 2 - and ( , ) B 7 4 - in the ratio 1 : 2, then the value of k is (a) 1 (b) 2 (c) 2 - (d) 1 - AAns : …
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page 366 Cbse Class 10th Mathematics - Basic SP 8. Ratio of volumes of two cylinders with equal height is (a) : H h (b) : R r (c) : R r 2 2 (d) None of these AAns :  [Board Term-2 Foreign 2017] : R h r h 2 2 p p : R r 2 2 = Thus (c) is correct option. 9. The point which divides the line segment…
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SAMPLE PAPER 27 Given, 82 x x x x x 5 27 31 89 107 156 = + + + + + + + + + ^ ^ ^ ^ ^ h h h h h 82 5 # x 410 5 = + 410 410 - x 5 = & x 0 = Required mean is, x x x x x x 5 130 126 68 50 1 = + + + + + + + + + x 5 375 5 = + 5 375 0 = + 5 375 = 75 = Thus (a) is correct option. 14. Aruna has only < 1 and…
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page 368 Cbse Class 10th Mathematics - Basic SP AAns :  (b) 20 Here, a 5 =−, d ( ) 2 5 5 = − −− 2 5 = nth term, an ( ) a n d 1 = + − a11 ( ) 5 11 1 2 5 # =− + − b l a11 5 25 =− + 20 = Thus (b) is correct option. 19. Assertion : In a circle of radius 6 cm, the angle of a sector 60c. Then the area…
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SAMPLE PAPER 27 Here angle AOB + and APB + are supplementary angle. Thus AOB + APB 180c + = − 180 70 110 c c c = − = OA and OB are radius of circle and equal in length, thus angle OAB + and OBA + are also equal. Thus in triangle OAB ∆ we have OBA OAB AOB + + + + + 180c = OAB OBA + + + AOB 180c + =…
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page 370 Cbse Class 10th Mathematics - Basic SP We have Sn n2 = ...(1) Substituting n by n 1 - we get Sn 1 - ( ) n 1 2 = − Now nth term, an S S n n 1 = − − ( ) n n 1 2 2 = − − ( ) n n n 2 1 2 2 = − − + n 2 1 = − Now, 10th term of AP, a10 2 10 1 19 # = − = Hence, the 10th term of AP is 19. Section -…
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SAMPLE PAPER 27 28. Solve for x and y : x y 2 3 2 + 1 =− x y 3 - 3 = AAns :  [Board Term-1 2015] We have x y 2 3 2 + 1 =− x y 3 4 + 6 =− ...(1) and x y 1 3 - 3 = x y 3 - 9 = ...(2) Subtracting equation (2) from equation (1), we have y 5 15 =− & y 1 =− Substituting y 3 =− in eq. (1), we get x 3 4 3…
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page 372 Cbse Class 10th Mathematics - Basic SP 31. A 7 m long flagstaff is fixed on the top of a tower standing on the horizontal plane. From point on the ground, the angles of elevation of the top and bottom of the flagstaff are 60º and 45º respectively. Find the height of the tower correct to…
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SAMPLE PAPER 27 Hence, p 35 =− and q 60 =− . 33. In fig., two circular flower beds have been shown on two sides of a square lawn ABCD of side 56 m. If the centre of each circular flower bed is the point of intersection O of the diagonals of the square lawn, find the sum of the areas of the lawn and…
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page 374 Cbse Class 10th Mathematics - Basic SP We have drawn diagonal AC and BD. AO OC AC 2 1 = = and BO OD BD 2 1 = = AC BD = Since diagonal of rhombus bisect each other at right angle, AOB + 90º = AB2 OA OB 2 2 = + AC BD 2 2 2 2 = + b b l l AC BD 4 4 2 2 = + or AB 4 2 AC BD 2 2 = + Hence proved…
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SAMPLE PAPER 27 Speed (in km/h) 20- 30 30- 40 40- 50 50- 60 60- 70 70- 80 80- 90 90- 100 Number of Vehicles 1 3 7 16 35 29 7 2 Based on the above information, answer the following questions. (i) Find the number of vehicles whose speed is more than 70 km/h and find the number of vehicles whose speed…
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page 376 Cbse Class 10th Mathematics - Basic SP (iii) If B is taken as origin, what are the co-ordinate of P ? (iv) What is distance between P and Q if origin is taken A? AAns :  (i) In following figure we have shown the co- ordinate taking A as origin. (ii) In following figure we have shown the…
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SAMPLE PAPER 27 (i) If its height is y , then what polynomial represents the length of a side of the square base ? (ii) If area of base is 576 metre, what is the side of base? (iii) What is the height of pyramid at above area of base ? What is the ratio of length of side to the height ? O (iv) What…
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