CBSE Class 10 Mathematics Basic Sample Paper 6 2027 Solutions

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SAMPLE PAPER 06 Sample Paper 06 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 76 Cbse Class 10th Mathematics - Basic SP Now, D b ac 4 2 = − 3 4 5 1 2 = − − ^ ^ ^ h h h 9 20 = − 0 < Hence, roots of the equation are not real. Thus (c) is correct option. 4. What are the values of x and y for the following system of linear equations ? x y 2 - 2 = x y 3 + 15 = (a) 4 and 5…
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SAMPLE PAPER 06 8. If x y 2 23 + = and x y 4 19 − = , the value of ( ) y x 5 2 - and 2 x y - ^ h will be (a) 7 5 - and 31 (b) 31 and 7 5 - (c) 37 and 7 2 (d) 7 2 and 37 AAns :  We have x y 2 + 23 = ...(1) x y 4 - 19 = ...(2) Adding equation (1) and (2), we have x 6 42 = & x 7 = Substituting the…
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page 78 Cbse Class 10th Mathematics - Basic SP 13. ? cosec cot 1 1 2 α α + + = (a) cosα (b) tanα (c) cosecα (d) sinα AAns :  se cos cot 1 1 2 α α + + se cos cosec 1 1 1 2 α α = + + − ( )( ) cosec cosec cosec 1 1 1 1 α α α = + + + − cosec 1 1 α = + − cosecα = Hence Proved Thus (c) is correct…
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SAMPLE PAPER 06 18. If the circumference of a circle and the perimeter of a square are equal, then (a) Area of the circle Area of the square = (b) Area of the circle Area of the square > (c) Area of the circle Area of the square < (d) Nothing definite can be said about the relation between the…
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page 80 Cbse Class 10th Mathematics - Basic SP Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). Thus (a) is correct option. Section - B Section B consists of 5 questions of 2 marks each. 21. If the distance between the points ( , ) A p 4 and ( ,…
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SAMPLE PAPER 06 AAns :  In GEQ T and GFS T , Due to vertical opposite angle, EGQ + FGS + = Due to alternate angle, EQG + FSG + = Thus by AA similarity we have GEQ T ~GFS FS EQ GS GQ = EQ GS # GQ FS # = O In , CAB T we have A + B + = ...(1) By isosceles triangle property we have AC CB = But, we…
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page 82 Cbse Class 10th Mathematics - Basic SP Thus PAO T ~ QBO T OB OA QB PA = .4 5 6 QB 4 = QB . 6 4 4 5 # = 3 = cm Thus QB 3 = cm 28. If a circle touches the side BC of a triangle ABC at P and extended sides AB and AC at Q and R , respectively, prove that ( ) AQ BC CA AB 2 1 = + + AAns :  As…
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SAMPLE PAPER 06 Number of students 12 26 34 40 50 O Find the mean of the following distribution : Height (in cm) Less than 75 Less than 100 Less than 125 Less than 150 Less than 175 Less than 200 No. of students 5 11 14 18 21 28 Height (in cm) Less than 225 Less than 250 Less than 275 Less than 300…
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page 84 Cbse Class 10th Mathematics - Basic SP Section - D Section D consists of 4 questions of 5 marks each. 32. Water is flowing at the rate of 15 km/hr through a cylindrical pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time the level of water in pond rise…
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SAMPLE PAPER 06 x x x 50 40 2000 2 − + − 0 = ( ) ( ) x x x 50 40 50 − + − 0 = ( )( ) x x 50 40 − + 0 = , x 50 40 = − But negative speed can not be possible. Thus, the speed of fast train is 50 km/hr, and the speed of slow train is 50 10 40 − = km. 34. From a point T outside a circle of centre O,…
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page 86 Cbse Class 10th Mathematics - Basic SP i.e., AOC BOC + + + 90c = or AOB + 90c = Hence Proved 35. Find the ratio in which the point , P 4 3 12 5 ^ h divides the line segment joining the point A , 2 1 2 3 ^ h and ,2 5 - ^ h. AAns :  [Board Term-2 Delhi 2015] Let P divides AB in the ratio :k…
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SAMPLE PAPER 06 Favourable outcome, ( ) n E3 2 2 π = in2. Probability, ( ) P E3 ( ) ( ) n S n E4 = 8 2 16 1 2 2 p p = = (iv) The probability that you score exactly 4 points, Let E4 be the event that she hit the circular band in the radius of 4 inch to 6 inch. Favourable outcome will be area of this…
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page 88 Cbse Class 10th Mathematics - Basic SP (i) The 18-wheeler takes 8 sec, (ii) The truck takes 6 sec, (iii) The car takes 4 sec. AAns :  Let d be the distance between his hidden position on road and a road sign We draw a diagram of the situation as shown below. Now tan60c d 50 = 3 d 50 = d 50…
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