CBSE Class 10 Mathematics Basic Sample Paper 30 2027 Solutions

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page 406 Cbse Class 10th Mathematics - Basic SP Sample Paper 30 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 30 Thus (c) is correct option. 4. The point P on x -axis equidistant from the points ( , ) A 1 0 - and ( , ) B 5 0 is (a) (2, 0) (b) (0, 2) (c) (3, 0) (d) ( , ) 3 5 - AAns :  [Board 2020 OD Standard] Let the position of the point P on x -axis be ( , ), x 0 then PA2 PB2 = ( ) ( ) x 1 0…
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page 408 Cbse Class 10th Mathematics - Basic SP Area of circle, r2 π 32 π = cm 9 2 π = Thus (d) is correct option. 9. If sin 2 1 α = and cos 2 1 β = , then the value of α β + ^ h is (a) 0c (b) 30c (c) 60c (d) 90c AAns :  Given, sinα 2 1 = sin 30 = c & α 30 = c and cosβ 2 1 = cos 60 = c & β 60 = c…
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SAMPLE PAPER 30 (a) and 4 24 (b) and 5 30 (c) and 6 36 (d) and 3 24 AAns :  [Board Term-1 Delhi 2016] Let the present age of father x = years and the present age of son y = years Four years hence, it has relation by given condition ( ) x 4 + ( ) y 4 4 = + x y 4 - 12 = ...(1) As the father’s age is…
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page 410 Cbse Class 10th Mathematics - Basic SP Taking first and second ratios, we get 12 5 EF 7 = EF 5 7 12 & # = . 16 8 = cm Taking first and third ratios, we get 12 5 BC 15 = BC 12 5 15 & # = .6 25 = cm Now, sum of the remaining sides of triangle, EF BC + . . 16 8 6 25 = + . 23 05 = cm Thus (a)…
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SAMPLE PAPER 30 Section - B Section B consists of 5 questions of 2 marks each. 21. In figure, O is the centre of a circle. PT are tangents to the circle from an external point P . If , TPQ 70c + = find TRQ + . AAns :  [Board Term-2 Foreign 2015] We redraw the given figure by joining O to T and Q…
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page 412 Cbse Class 10th Mathematics - Basic SP We have sec cos sec 30 45 60 1 º º º + 2 1 3 2 2 1 = + 2 1 2 3 2 1 # = + 4 6 2 1 4 6 2 = + = + 24. a and b are two positive integers such that the least prime factor of a is 3 and the least prime factor of b is 5. Then calculate the least prime factor…
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SAMPLE PAPER 30 36 2 2 3 3 2 3 2 2 # # # # = = HCF(16, 36) 2 2 # = 4 = LCM (16, 36) 2 3 4 2 # = 16 9 # = 144 = Check : HCF ( , ) a b × LCM ( , ) a b a b # = or, 4 144 × × 16 36 = 576 576 = Thus LHS = RHS 28. Find the area of minor segment of a circle of radius 14 cm, when its centre angle is 60c.…
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page 414 Cbse Class 10th Mathematics - Basic SP 300-350 2 325 2 4 f 25 = i / f u 7 =− i i / Mean, M a f f u h # = + i i i / / 225 25 7 50 # = + − ^ h 225 14 = − 211 = Hence, mean of daily expenditure on food is <211. 30. If the distance of , P x y ^ h from , A 6 2 ^ h and , B 2 6 - ^ h are equal,…
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SAMPLE PAPER 30 15 = km/hr 15000 = m/hr In an hour length of water 15000 = m Volume of water flowing from pipe in 1 hr, r h 2 π 7 22 100 7 15000 2 # # = b l m3 Let t be time taken to fill the tank. Now total volume of water flowing in time t , r ht 2 π t 7 22 100 7 15000 2 # # = b l Volume of water…
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page 416 Cbse Class 10th Mathematics - Basic SP Clearly two obtained lines intersect at point , . A 3 5 ^ h Hence, x 3 = and y 5 = ABC is the triangular shaded region formed by the obtained lines with the y-axis. 34. From the top of a 7 m high building the angle of elevation of the top of a tower…
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SAMPLE PAPER 30 Let ABCD be the parallelogram. AB , CD AD BC = = (1) Since length of tangents from an external point to a circle are equal, At A, AP AS = (2) At B BP BQ = (3) At C CR CQ = (4) At D DR DS = (5) Adding above 4 equation we have AP PB CR DR + + + AS BQ CQ DS = + + + or, AB CD + AD BC =…
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page 418 Cbse Class 10th Mathematics - Basic SP AB 2 O 21 Total 50 Total possible outcomes in all case is 50 because there are total 50 sample and out of which we have to select one. Thus ( ) n S 50 = (i) Person has type O blood, Let E1 be the event that the selected person has type O blood.…
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SAMPLE PAPER 30 38. Two poles, 30 feet and 50 feet tall, are 40 feet apart and perpendicular to the ground. The poles are supported by wires attached from the top of each pole to the bottom of the other, as in the figure. A coupling is placed at C where the two wires cross. (i) What is the…
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