CBSE Class 10 Mathematics Basic Sample Paper 23 2027 Solutions

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page 310 Cbse Class 10th Mathematics - Basic SP Sample Paper 23 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…
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SAMPLE PAPER 23 We have p x ^ h ax bx c 2 = + + Let α and 1 α be the zeroes of p x ^ h, then Product of zeroes, a c 1 1 # α α = = or a c 1 = So, required condition is, c a = Thus (d) is correct option. 4. If 1 - is a zero of the polynomial , p x kx x k 4 2 = − + ^ h the value of k is (a) –4 (b) –2…
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page 312 Cbse Class 10th Mathematics - Basic SP Thus (a) is correct option. 9. If xi’s are the mid-points of the class intervals of grouped data, fi’s are the corresponding frequencies and x is the mean, then ( ) f x x i i - / is equal to (a) 0 (b) 1 - (c) 1 (d) 2 AAns :  [Board Term-1 Foreign…
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SAMPLE PAPER 23 ( ) x 2 1 9 21 6 − + 0 = ( ) x 2 1 12 6 − + 0 = x 6 12 = & x 2 = Thus (a) is correct option. 14. If the sum of the circumferences of two circles with radii R1 and R2 is equal to the circumference of a circle of radius R, then (a) R R R 1 2 + = (b) R R R > 1 2 + (c) R R R > 1 2 + (d)…
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page 314 Cbse Class 10th Mathematics - Basic SP Thus (b) is correct option. 20. Assertion : The values of x are a 2 - ,a for a quadratic equation x ax a 2 0 2 2 + − = . Reason : For quadratic equation ax bx c 0 2 + + = x a b b ac 2 4 2 ! = − − (a) Both assertion (A) and reason (R) are true and…
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SAMPLE PAPER 23 O A bag contains 3 red, 4 green and 5 white candles, one candle is drawn at random from the bag, find the probability that candle is not red. AAns :  Total number of possible outcomes are . 3 4 5 12 + + = ( ) n S 12 = When candles not red, there are 9 possibilities, n E ^ h 9 = P…
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page 316 Cbse Class 10th Mathematics - Basic SP and YX QR 14 7 2 1 = = Thus ZY QP ZX PR YX QR = = By SSS criterion we have PQR T ~ ZYX T Thus X + R + = 180 60 70 50 º º º ° = − + = ^ h Thus X + 50º = Section - C Section C consists of 6 questions of 3 marks each. 26. If in a triangle ABC right…
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SAMPLE PAPER 23 Adding equation (1) and (2) we have AB AC 2 2 + AD BD 2 2 2 = + ^ h (BD DC = ) AD BC 2 2 2 1 2 2 = + b l ( BD BC 2 1 = ) AD BC 2 2 1 2 2 = + Hence Proves O In the given figure, find the value of x in terms of ,a b and .c AAns :  [Board Term-1 2012] In triangles LMK and , PNK K + is…
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page 318 Cbse Class 10th Mathematics - Basic SP The smallest number that is divisible by two numbers is obtained by finding the LCM of these numbers Here, the given numbers are 306 and 657. 306 6 51 # = 3 2 3 17 # # # = 657 9 73 # = 3 3 73 # # = LCM(306, 657) 2 3 3 17 73 # # # # = 22338 = Hence,…
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SAMPLE PAPER 23 a x b x c b x a x c − − + − − ^ ^ ^ ^ h h h h c x a x b 2 = − − ^ ^h h ax abx acx abc bx bax bcx abc 2 2 − − + + − − + cx cxb cxa abc 2 2 2 2 2 = − − + ax bx cx abx acx bax bcx cbx acx 2 2 2 2 2 2 + − − − − − + + 0 = x a b c abx acx bcx 2 2 2 + − − + + ^ h 0 = x a b c x ab ac bc 2 2…
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page 320 Cbse Class 10th Mathematics - Basic SP 50-60 3 f f 29 2 + + 1 60-70 2 f f 31 2 + + 1 N f 40 = = / Now, f f 31 2 + + 1 40 = f f + 1 2 9 = f2 f 9 = − 1 ...(1) Since median is 32.5, which lies in 30-40, median class is 30-40. Here l 30 = , N 2 2 40 = 20 = , f 12 = and F f 14 = + 1 Now, Median…
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SAMPLE PAPER 23 Earth is excavated to make a railway tunnel. The tunnel is a cylinder of radius 7 m and length 450 m. A level surface is laid inside the tunnel to carry the railway lines. Figure given below shows the circular cross - section of the tunnel. The level surface is represented by AB,…
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page 322 Cbse Class 10th Mathematics - Basic SP Varsha is a licensed architect and design very innovative house. She has made a house layout for her client which is given below. In the layout, the design and measurements has been made such that area of two bedrooms and kitchen together is 95 sq.m.…
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SAMPLE PAPER 23 0 x x x 11 24 100 = + + − 3 2 There is only one positive solution to this equation, because there is one change of sign. By hit and trial we find the x 2 = is the only positive solution. x x x x x x x x x x x x x x 2 11 24 100 2 13 50 13 24 100 13 26 50 100 50 100 0 3 2 3 2 2 2 2 −…
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