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CBSE Class 10 Mathematics Basic Sample Paper 29 2027 Solutions

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SAMPLE PAPER 29 Sample Paper 29 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 divided into 5 Sections A, B,… — Page 1 of 13

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page 394 Cbse Class 10th Mathematics - Basic SP m m m m 3 3 2 2 = + − − 0 = Thus x m =− is a zero of given polynomial. Now substituting x m 3 = + in given polynomial we have ( ) p x ( ) ( ) ( ) m m m m 3 3 3 3 2 = + − + − + ( )[ ] m m m 3 3 3 = + + − − ( )[ ] m 3 0 = + 0 = Thus x m 3 = + is also a… — Page 2 of 13

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SAMPLE PAPER 29 9. If one zero of the quadratic polynomial x x k 3 2 + + is 2, then the value of k is (a) 10 (b) 10 - (c) 7 - (d) 2 - AAns : [Board 2020 Delhi Standard] We have ( ) p x x x k 3 2 = + + If 2 is a zero of ( ) p x , then we have ( ) p 2 0 = ( ) ( ) k 2 3 2 2 + + 0 = k 4 6 + + 0 = k… — Page 3 of 13

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page 396 Cbse Class 10th Mathematics - Basic SP 2 1 BD 6 = & BD m 12 = Thus length of wire is 12 m. Thus (a) is correct option. 14. Distance of point ( , ) P 3 4 from x -axis is (a) 3 units (b) 4 units (c) 5 units (d) 1 units AAns : [Board 2020 Delhi Basic] Point ( , ) P 3 4 is 4 units from the x… — Page 4 of 13

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SAMPLE PAPER 29 AAns : We have R 2 π r r 1 2 2 2 π π = + R 2 r r 1 2 2 2 = + d d 2 2 1 2 2 2 = + b b l l 2 16 2 12 2 2 = + b b l l ( ) ( ) 8 6 100 2 2 = + = R 100 10 = = Thus (a) is correct option. 18. If the radius of the sphere is increased by 100%, the volume of the corresponding sphere is… — Page 5 of 13

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page 398 Cbse Class 10th Mathematics - Basic SP Let the given points are ( , ) A 0 0 , ( , ) B 3 3 and ( , ). C 3 λ Since, ABC T is an equilateral triangle, therefore AB AC = ( ) ( ) 3 0 3 0 2 2 − + − ( ) ( ) 3 0 0 2 2 λ = − + − 9 3 + 9 2 λ = + 2 λ 3 = & λ 3 ! = 23. Write a rational number between… — Page 6 of 13

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SAMPLE PAPER 29 Section - C Section C consists of 6 questions of 3 marks each. 26. If triangle ABC is similar to triangle DEF such that AB DE 2 = and BC 8 = cm then find . EF AAns : As per given condition we have drawn the figure below. Here we have AB 2 DE = and BC 8 = cm Since ABC T ~ DEF T ,… — Page 7 of 13

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page 400 Cbse Class 10th Mathematics - Basic SP Length of the rope is 21 cm. Shaded portion AEFA indicates the area in which the horse can graze. Clearly it is the area of a quadrant of a circle of radius, r 21 = m. Area of quadrant, r 4 1 2 π ( ) 4 1 7 22 21 2 # # = 4 1 7 22 21 21 # # # = . m 346… — Page 8 of 13

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SAMPLE PAPER 29 BGG, GGG}. So, the total number of outcomes, ( ) n S 23 = 8 = At-least two of them are boys means all those cases in which we have either 2 or 3 boys. Thus favourable outcome are {BBB, BBG, BGB, GBB} Number of favourable outcome, ( ) n E 4 = The probability of having at least two… — Page 9 of 13

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page 402 Cbse Class 10th Mathematics - Basic SP and line (2) x y 2 5 1 + + 0 = or, y x 5 1 2 = − − x 2 -3 y -1 1 Plotting the above points and drawing lines joining them, we get the following graph. Clearly, the two lines intersect at point ,2 1 - ^ h. Hence x 2 = and y 1 =− O Let amount… — Page 10 of 13

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SAMPLE PAPER 29 AAns : [Board Term-1 2015] Since BC and OX bisect each other, BXCO is a parallelogram. Therefore || BE XC and || BX CF . In , ABX T by BPT we get, FB AF OX AO = ..(1) In , AXC T EC AE OX AO = ...(2) From (1) and (2) we get FB AF EC AE = By converse of BPT we have EF || BC From (1)… — Page 11 of 13

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page 404 Cbse Class 10th Mathematics - Basic SP 2000 x x 4 20 2 = + 500 x x 5 2 = + x x 5 500 2 + − 0 = (ii) We have x x 5 500 2 + − 0 = x x x 25 20 500 2 + − − 0 = ( ) ( ) x x x 25 20 25 + − + 0 = ( )( ) x x 25 20 + − 0 = x , 20 25 = − Since x 25 =− is not possible, we get x 20 = (iii) Rias car… — Page 12 of 13

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SAMPLE PAPER 29 AAns : Let w be the width of lake. We draw a diagram of the situation as shown below. Here d1 and d2 are the ground distance from balloon to the sides of lake. Now tan45c d 300 = 1 1 d 300 = 1 d1 300 = m Now tan30c d 300 = 2 3 1 d 300 = 2 d2 300 3 = m d2 . 300 1 732 # = . 519 6 =… — Page 13 of 13

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