CBSE Class 10 Mathematics Basic Sample Paper 7 2027 Solutions

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SAMPLE PAPER 07 Sample Paper 07 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 90 Cbse Class 10th Mathematics - Basic SP ( ) ( ) ar BDE ar ABC T T ( ) ( ) BD BC 4 3 2 4 3 2 = ( ) BC BC 2 1 2 2 = ^ h BC BC 4 2 2 = 1 4 = : 4 1 = Thus (d) is correct option. 4. If the sum of the areas of two circles with radii R1 and R2 is equal to the area of a circle of radius R , then (a)…
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SAMPLE PAPER 07 Thus (b) is correct option. 7. If m and n are the zeroes of the polynomial x x 3 11 4 2 + −, then value of n m m n + will be (a) 145 12 (b) 145 12 - (c) 12 145 - (d) 12 145 AAns :  We have n m m n + mn m n 2 2 = + ( ) mn m n mn 2 2 = + − ...(1) Sum of zeroes m n + 3 11 =− Product…
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page 92 Cbse Class 10th Mathematics - Basic SP Now, 2 3 2 5 3 2 # # + + k = & k 5 16 = 12. The base radii of a cone and a cylinder are equal. If their curved surface areas are also equal, then the ratio of the slant height of the cone to the height of the cylinder is (a) 2 : 1 (b) 1 : 2 (c) 1 : 3…
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SAMPLE PAPER 07 AAns :  There are 6 possible outcome for a die. ( ) n S 6 = Favourable outcome are 1 and 2 i.e. two outcome. ( ) n E 2 = P (number less than 3), ( ) P E ( ) ( ) n S n E = 6 2 = 3 1 = 18. If p and q are the zeroes of polynomial f x x x 2 7 3 2 = − + ^ h , the value of p q 2 2 + will…
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page 94 Cbse Class 10th Mathematics - Basic SP Section - B Section B consists of 5 questions of 2 marks each. 21. A circle is inscribed in a ABC T touching AB, BC and AC at P , Q and R respectively. If cm AB 10 = cm AR 7 = and cm CR 5 = , then find the length of BC AAns :  [Board 2020 OD Basic] As…
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SAMPLE PAPER 07 4 181 n 1 = − . 45 25 n 1 = − . 46 25 n = Since 46.25 is not an whole number, thus 184 is not a term of given AP. O The ninth term of an AP is 32 - and the sum of its eleventh and thirteenth term is 94 - . Find the common difference of the AP AAns :  Let the first term be a and…
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page 96 Cbse Class 10th Mathematics - Basic SP In ABD T , tan60c BD AB = 3 BD 50 = BD 3 50 = Now in BDC T , tan30c BD CD = 3 1 h 3 50 = h 50 3 = h 3 50 = h 3 50 = . 16 67 = Hence, the height of the building is 16.67 m. 28. Solve graphically : x y 2 3 13 0 − + = ; x y 3 2 12 0 − + = AAns :  We have…
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SAMPLE PAPER 07 30. If tangents PA and PB drawn from an external point P to a circle with centre O are inclined to each other at an angle of 80c, then find POA + . AAns :  As per given information we have drawn the figure below. Since PA and PB are the tangents, PO will be angle bisector of P +…
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page 98 Cbse Class 10th Mathematics - Basic SP = Top area of cylinder + + CSA of cylinder + CSA of conical cavity r rh rl 2 2 π π π = + + ( ) r r h l 2 π = + + ( ) 8 3 2 15 17 # # π = + + 8 55 # # π = 440π = TSA of reaming solid is 440π . O A solid right-circular cone of height 60 cm and radius 30…
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SAMPLE PAPER 07 p q 3 45 − + − 0 = p q 3 - 45 =− ...(2) Subtracting equation (2) from (1) we have p 35 =− Substituting the value of p in equation (1) we have q 4 35 - - ^ h 80 =− q 140 - - 80 =− q - 140 80 = − or q - 60 = q 60 =− Hence, p 35 =− and q 60 =− . O If α and β are the zeroes of…
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page 100 Cbse Class 10th Mathematics - Basic SP Thus FE GB FC GD = Since DEFG is square, we obtain, FG BG FC FG = Therefore FG2 BG FC # = Hence Proved 35. If sin cos 3 θ θ + = , then prove that . tan cot 1 θ θ + = AAns :  We have sin cos θ θ + 3 = Squaring both the sides, we get ( ) sin cos 2 θ θ…
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SAMPLE PAPER 07 (i) From the given digram we can easily get that position of the pole C (5, 4). (ii) Coordinates of B are (6, 6). Distance from origin 6 0 6 0 2 2 = − + − ^ ^ h h 36 36 = + 6 2 = units (iii) If ABCD is a parallelogram, the diagonals bisects each other. Here AC and BD are diagonals.…
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page 102 Cbse Class 10th Mathematics - Basic SP 3. Carbon Monoxide 4. Sulfur dioxide 5. Nitrogen dioxide The higher the AQI value, the greater the level of air pollution and the greater the health concerns. Following frequency distribution shows the Air Quality Index of different localities of…
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