CBSE Class 10 Mathematics Basic Sample Paper 15 2027 Solutions

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SAMPLE PAPER 15 Sample Paper 15 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 202 Cbse Class 10th Mathematics - Basic SP y 3 7 6 = − ^ h 21 6 = − 15 = Hence, fraction is 15 7 . Thus (a) is correct option. 3. If 1 - is a zero of the polynomial ( ) f x x x 7 8 2 = − − , then other zero is (a) 4 (b) 8 (c) 1 (d) –4 AAns :  We have f x ^ h x x 7 8 2 = − − Let other zero be…
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SAMPLE PAPER 15 x a b y b a 2 2 − + + − − ^ ^ h h 8 8 B B x a b y a b 2 2 = − − + − + ^ ^ h h 8 8 B B ( ) ( ) x a b y b a 2 2 − + − − ( ) ( ) x a b y a b 2 2 =− − − + ( ) ( ) x a b y b a 2 2 + + − ( ) ( ) x a b y a b 2 2 = − + + ( ) ( ) x a b a b y b a a b 2 2 + − + + − − − 0 = ( ) ( ) x b y a 2 2…
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page 204 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. 13. The 11th term of an AP 5 - , 2 5 - , 0, 2 5 , ....., is (a) 20 - (b) 20 (c) 30 - (d) 30 AAns :  Here, a 5 =−,…
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SAMPLE PAPER 15 Class 30-40 has the maximum frequency 30, therefore this is model class. Thus (c) is correct option. 17. In figure, MN BC < and : : AM MB 1 2 = , then ( ) ( ) .................... ar ABC ar AMN T T = (a) 3 1 (b) 9 1 (c) 9 8 (d) 9 5 AAns :  Here, AM k = MB k 2 = MN BC < Thus AB AM…
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page 206 Cbse Class 10th Mathematics - Basic SP Section - B Section B consists of 5 questions of 2 marks each. 21. In Figure a quadrilateral ABCD is drawn to circumscribe a circle, with centre , O in such a way that the sides , AB , BC , CD and DA touch the circle at the points , , P Q R and S…
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SAMPLE PAPER 15 Now a38 a d 37 = + a38 d d d 7 37 30 =− + = a18 a d 17 = + d d 7 17 =− + d 10 = a38 d d 30 3 10 # = = a 3 18 # = a38 a 3 18 = Hence Proved O If the number , x x 3 2 1 + + and x 7 - are in AP find the value of x . AAns :  If ,x y and z are three consecutive terms of an AP then we…
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page 208 Cbse Class 10th Mathematics - Basic SP O In , . ABD AB AC T = If the interior circle of ABC T touches the sides , AB BC and CA at , D E and F respectively. Prove that E bisects . BC AAns :  As per question we draw figure shown below. Since length of tangents from an external point to a…
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SAMPLE PAPER 15 Here , , a b n c 3 1 2 2 2 2 = = − =− ^ h For a pair of linear equations to have infinite number of solutions, a a 2 1 b b c c 2 1 2 1 = = m 3 2 1 - n 1 3 2 5 = − = or m 2 2 1 - ^ h 15 = and n 5 1 6 − = ^ h Hence, m ,n 4 17 5 11 = = 31. A hemispherical bowl of internal diameter 36…
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page 210 Cbse Class 10th Mathematics - Basic SP Radius of each circle . 2 3 5 = cm Diameter of smaller shaded semi-circle 7 = cm Radius .3 5 = cm Area of shaded portion = area of largest semi-circle + area of smaller shaded semicircle – area of two unshaded semicircles 2 1 7 22 7 7 2 1 7 22 2 7 2 7…
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SAMPLE PAPER 15 In ABC T AD is the median, therefore BC BD 2 = and in PQR T , PM is the median, QR QM 2 = Given, PQ AB PM AD QR BC = = or, PQ AB PM AD QM BD 2 2 = = In triangles ABD and , PQM PQ AB PM AD QM BD = = By SSS similarity we have ABD T ~ PQM T By CPST we have B + , Q + = In ABC T and ,…
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page 212 Cbse Class 10th Mathematics - Basic SP Section - E Section E consists of 3 case study based questions of 4 marks each. 36. Volume of Solid : A cuboidal solid of base x by x 1 + is shown in figure. Height of original solid is x 2 + . A small cuboidal solid of base x 2 - by x 2 - and height…
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SAMPLE PAPER 15 Three friends Amar, Bandhu and Chakradev lives in societies represented by the points A, B and C respectively. They all work in offices located in a same building represented by the point O. Since they all go to same building everyday, they decided to do carpooling to save money on…
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page 214 Cbse Class 10th Mathematics - Basic SP (ii) What is the mode NAV of mutual funds ? (iii) What is the mean NAV of mutual funds ?] O (iv) What is the median NAV of mutual funds ? AAns :  The given classes are not continuous. So, let us make them continuous and rewrite the table. Class…
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