CBSE Class 10 Mathematics Basic Sample Paper 12 2027 Solutions

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SAMPLE PAPER 12 Sample Paper 12 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 160 Cbse Class 10th Mathematics - Basic SP 3. If a regular hexagon is inscribed in a circle of radius ,r then its perimeter is (a) r 3 (b) r 6 (c) r 9 (d) r 12 AAns :  Side of the regular hexagon inscribed in a circle of radius r is also r , the perimeter is r 6 . Thus (b) is correct option.…
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SAMPLE PAPER 12 AAns :  Isosceles triangle is a triangle in which two side of equal length. Thus two isosceles triangles may not be similar. Hence statement given in option (a) is false. Thus (a) is correct option. 9. The coordinates of a point A on y-axis, at a distance of 4 units from x -axis…
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page 162 Cbse Class 10th Mathematics - Basic SP AAns :  As per given in question we have drawn figure below. In ACB T with C 60c + = , we get cos 60c . AC 2 5 = 2 1 . AC 2 5 = AC . 2 2 5 5 # = = m Thus (a) is correct option. 14. In the figure, PQ is parallel to . MN If PM KP 13 4 = and . KN 20 4 =…
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SAMPLE PAPER 12 a c 0 > Both c and a are of same sign. Thus (c) is correct option. 18. Two coins are tossed simultaneously. The probability of getting at most one head is (a) 4 1 (b) 2 1 (c) 3 2 (d) 4 3 AAns :  All possible outcomes are {HH, HT, TH, TT}. Thus ( ) n S 4 = Favourable outcomes are…
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page 164 Cbse Class 10th Mathematics - Basic SP 22. Prove that in two concentric circles, the chord of the larger circle, which touches the smaller circle is bisected at the point of contact. AAns :  [Board Term-2, 2012] As per the given question we draw the figure as below. Since OP is radius and…
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SAMPLE PAPER 12 ( )( ) n n 12 10 + − 0 = & n 10 = or n 12 =− Neglecting n 12 =− because n can’t be negative we get n 10 = . Hence, 10 terms must be taken to get the sum 120. 25. Find, 100 is a term of the AP , , ,...... 25 28 31 or not. AAns :  [Board Term-2 2012] Let the first term of an AP be a,…
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page 166 Cbse Class 10th Mathematics - Basic SP Area of triangle OQP T , ∆ ( )( ) OQ QP 2 1 = 12 5 30 2 1 # # = = Area of quadrilateral PQOR, POQ 2 # T 2 30 60 # = = cm2 27. The top of two poles of height 16 m and 10 m are connected by a length l meter. If wire makes an angle of 30c with the…
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SAMPLE PAPER 12 Two obtained lines intersect at point ( , ) P 4 2 - . Hence, Solution of the given equation is x 4 = , y 2 =− 30. A solid is in the shape of a cone mounted on a hemisphere of same base radius. If the curved surface areas of the hemispherical part and the conical part are equal, then…
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page 168 Cbse Class 10th Mathematics - Basic SP Total Cost 33 500 # = , Rs 16 500 = 31. Solve for x : , , , x x x x 1 2 3 2 2 1 0 3 2 2 ! + − = − . AAns :  We have x x 1 2 3 2 + − x 2 1 = − ( ) x x x x 2 3 2 3 2 − − + x 2 1 = − ( ) x x x 2 3 4 3 - - x 2 1 = − x x 2 4 3 - - ^ ^h h x x 2 3 2 = − x x…
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SAMPLE PAPER 12 AAns :  We have p x ^ h a a x x 61 6 2 2 = + + + ^ h Since β and 1 β are the zeroes of polynomial, p x ^ h Sum of zeroes, 1 β β + a a 61 2 =− + or, 1 2 β β + a a 61 2 = + − ...(1) Product of zeroes 1 b b a a a 6 2 = + or, 1 a 1 6 = + a 1 + 6 = a 5 = Substituting this value of a in…
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page 170 Cbse Class 10th Mathematics - Basic SP 8 1 3 4 2 1 24 1 = + + + 24 3 32 12 1 = + + + 24 48 2 = = Section - E Section E consists of 3 case study based questions of 4 marks each. 36. Satellite Images : Satellite images are images of Earth collected by imaging satellites operated by…
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SAMPLE PAPER 12 37. 100 Metres Race : The 100 metres is a sprint race in track and field competitions. The shortest common outdoor running distance, it is one of the most popular and prestigious events in the sport of athletics. It has been contested at the summer Olympics since 1896 for men and…
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page 172 Cbse Class 10th Mathematics - Basic SP AAns :  (i) We have ( ) V x x x x 11 24 = + + 2 3 ( ) x x x 11 24 2 = + + ( )( ) x x x 3 8 = + + If x represent height, the dimension of base will be x 3 + and x 8 + . (ii) Here we have to find ( ) V 3 using the remainder theorem. We divide ( ) V x x…
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