CBSE Class 10 Mathematics Basic Sample Paper 13 2027 Solutions

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SAMPLE PAPER 13 Sample Paper 13 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,…
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page 174 Cbse Class 10th Mathematics - Basic SP In ABC 3 , we have sin30c AC AB = 2 1 AC AB = 2 1 AB 20 = & AB m 10 = Hence, the height of the pole is 10 m. Thus (b) is correct option. 3. For the following distribution Marks Number of Students Marks Number of students Below 10 3 Below 40 57 Below…
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SAMPLE PAPER 13 ( ) P E ( ) ( ) n S n E = 9 5 = Thus (c) is correct option. 7. The value of c for which the pair of equations cx y 2 − = and x y 6 2 3 − = will have is (a) 3 (b) 3 - (c) 12 - (d) no value AAns :  [Board Term-1 SQP 2014] The given lines are, cx y - 2 = and x y 6 2 - 3 = Condition…
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page 176 Cbse Class 10th Mathematics - Basic SP ( ) P E ( ) ( ) n S n E = 14 5 = Thus (b) is correct option. 10. The perimeters of two similar triangles are 25 cm and 15 cm respectively. If one side of the first triangle is 9 cm, then the corresponding side of second triangle is ............... .…
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SAMPLE PAPER 13 15. If sin cos sin cos x y 3 3 q q q q + = and sin cos x y q q = , than x y 2 2 + is equal to (a) 0 (b) 1/2 (c) 1 (d) 3/2 AAns :  We have, sin cos x y 3 3 q q + sin cos q q = sin sin cos cos x y 2 2 q q q q + ^ ^ h h sin cos q q = sin sin sin cos x x 2 2 q q q q + ^ ^ h h sin cos q…
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page 178 Cbse Class 10th Mathematics - Basic SP CP2 CB BP 2 2 = + and AQ2 AB BQ 2 2 = + CP AQ 2 2 + CB BP AB BQ 2 2 2 2 = + + + CB AB BP BQ 2 2 2 2 = + + + AC PQ 2 2 = + Thus (c) is correct option. 19. Assertion : PA and PB are two tangents to a circle with centre O. Such that AOB 110 + = c, then…
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SAMPLE PAPER 13 2 9 30 =− + 2 9 30 = − + 2 51 25 2 1 = = Hence, 21st term of given AP is 25 2 1 . 22. If , A 5 2 ^ h, , B 2 2 - ^ h and , C t 2 - ^ h are the vertices of a right angled triangle with B 90º + = , then find the value of .t AAns :  [Board Term-2 Delhi 2015] As per question, triangle…
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page 180 Cbse Class 10th Mathematics - Basic SP Now , , a b c 3 3 14 17 3 21 24 = = + = = + = Thus a , , . b c 3 17 24 = = = 25. In Figure, common tangents AB and CD to the two circle with centres O1 and O2 intersect at . E Prove that . AB CD = AAns :  Since EA and EC are tangents from point E to…
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SAMPLE PAPER 13 Let OPQ + be θ , then TPQ + 90c θ = − Since, TP TQ = , due to opposite angles of equal sides we have TQP + 90c θ = − From angle sum property of a triangle we can write, TPQ TQP PTQ + + + + + 180c = PTQ 90 90 c c + θ θ − + − + 180c = PTQ + 180 180 2 c c θ = − + PTQ + 2θ = Hence, PTQ…
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page 182 Cbse Class 10th Mathematics - Basic SP surface area of the article. AAns :  [Board 2018] Total surface Area of article = CSA of cylinder + CSA of 2 hemispheres CSA of cylinder rh 2π = . 2 7 22 3 5 10 # # # = cm 220 2 = Curved surface area of two hemispherical scoops r 2 2 2 # π = . . 4 7…
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SAMPLE PAPER 13 Let OR be x then using Pythagoras theorem we have x x 2 2 + 42 2 = ^ h & x 21 2 = m Area of segment of circle with centre angle 90c ( ) 360 90 7 22 21 2 2 # # c c = 4 1 7 22 21 21 2 # # # # = 11 3 21 693 # # = = Area of triangle ROQ 3 , ( ) 2 1 21 2 2 # = 21 21 441 # = = Area of the…
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page 184 Cbse Class 10th Mathematics - Basic SP AAns :  [Board Term-1 2015] We have redrawn the given figure as below. We have AB AD + BC CD = + AD BC CD AB = + − AD h d x = + − In right , ACD T we have AD2 AC DC 2 2 = + h d x 2 + − ^ h x h d 2 2 = + + ^ h h d x x h 2 2 + − − + ^ ^ h h d2 = h d x…
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SAMPLE PAPER 13 x x 2 2 2 + + . After distribution, some amount is left. (i) How many families are there in the village? (ii) If an amount of <1911 is left after distribution, what is value of x ? (iii) How much amount does each family receive? (iv) What is the amount of fund allocated? AAns : …
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page 186 Cbse Class 10th Mathematics - Basic SP The Covid-19 pandemic has stalled economic activity at an unprecedented scale globally, raising the spectre of job losses and salary cuts. Most of companies decided to bring down the salary by upto 50 %. The following table shows the salaries (in…
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