CBSE Class 10 Mathematics Basic Sample Paper 2 2027 Solutions

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SAMPLE PAPER 02 Sample Paper 02 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 20 Cbse Class 10th Mathematics - Basic SP 3. A tree casts a shadow 15 m long on the level of ground, when the angle of elevation of the sun is 45c. The height of a tree is (a) 10 m (b) 14 m (c) 8 m (d) 15 m AAns :  Let BC be the tree of height h meter. Let AB be the shadow of tree. In ABC T ,…
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SAMPLE PAPER 02 7. If a number x is chosen at random from the numbers , , , , 2 1 0 1 2 - - . Then, the probability that x 2 2 1 is (a) 5 2 (b) 5 4 (c) 5 1 (d) 5 3 AAns :  Total number of possible outcomes are 5. We observe that x 2 2 1 when x takes anyone of the following three values 1 - , 0 and…
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page 22 Cbse Class 10th Mathematics - Basic SP 12. In the adjoining figure, TP and TQ are the two tangents to a circle with centre O. If , POQ 110c + = then PTQ + is (a) 60c (b) 70c (c) 80c (d) 90c AAns :  Here OP PT = and OQ QT = , In quadrilateral OPTQ, we have POQ OPT PTQ OQT 360c + + + + + + +…
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SAMPLE PAPER 02 14 14 = + 28 = cm Thus (c) is correct option. 16. If x y 25 2 2 + = , xy 12 = , then x is (a) ( , ) 3 4 (b) ( , ) 3 3 - (c) ( , , , ) 3 4 3 4 - - (d) ( , ) 3 3 - AAns :  [Board Term - 2 Foreign 2015] We have x y 2 2 + 25 = and xy 12 = x x 12 2 2 +b l 25 = x x 144 25 4 2 + − 0 = x x…
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page 24 Cbse Class 10th Mathematics - Basic SP (b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). (c) Assertion (A) is true but reason (R) is false. (d) Assertion (A) is false but reason (R) is true. AAns :  Common difference of an AP d a…
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SAMPLE PAPER 02 60 24 16 2 20 # = + − 60 8 40 = + 60 5 = + 65 = 24. Explain why ( ) 7 13 11 11 # # + and ( ) 7 6 5 4 3 2 1 3 # # # # # # + are composite numbers. AAns :  ( ) 7 13 11 11 # # + ( ) 11 7 13 1 # # = + ( ) 11 91 1 # = + 11 92 # = and ( ) 7 6 5 4 3 2 1 3 # # # # # # + ( ) 3 7 6 5 4 2 1 1…
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page 26 Cbse Class 10th Mathematics - Basic SP Section - C Section C consists of 6 questions of 3 marks each. 26. Compute the mode for the following frequency distribution: Size of items (in cm) 0- 4 4- 8 8- 12 12- 16 16- 20 20- 24 24- 28 Frequency 5 7 9 17 12 10 6 AAns :  Class 12-16 has the…
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SAMPLE PAPER 02 Area of shaded region [ ] R r 360 2 2 c π θ − [ ( . ) ] 7 22 7 3 5 360 30 2 2 c c = − ( . )( . ) 7 22 7 3 5 7 3 5 12 1 # = + − . . 7 22 10 5 3 5 12 1 # # # = . cm 9 625 2 = 29. Find the ratio in which ( , ) P m 4 divides the segment joining the points ( , ) A 2 3 and ( , ) B 6 3 - .…
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page 28 Cbse Class 10th Mathematics - Basic SP ( ) ( ) sin cos sin sin cos sin 1 1 θ θ θ θ θ θ = − + + − ( ) sin cos sin sin cos sin sin 1 2 θ θ θ θ θ θ θ = + − + − ( ) ( ) sin cos sin sin cos sin cos 1 1 2 θ θ θ θ θ θ θ = + − + − − ( ) ( ) ( ) sin cos sin sin cos cos 1 1 1 2 θ θ θ θ θ θ = + − + −…
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SAMPLE PAPER 02 Plotting these points on graph, we get two parallel line as shown below. 34. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle. AAns :  A circle centre O is inscribed in a quadrilateral ABCD as shown in…
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page 30 Cbse Class 10th Mathematics - Basic SP 1 x h = & x h = ...(1) In right angled EDB T tan30c ED BE = 3 1 x h 8 = − x h 3 8 = − ^ h ...(2) From (1) and (2), we get h h 3 8 3 = − 8 3 h h 3 = − h 3 1 8 3 3 1 3 1 # = − + + 4 3 3 1 = + ^ h 12 4 3 = + ^ h m Since, x h = , x 12 4 3 = + ^ h Distance…
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SAMPLE PAPER 02 (ii) What is the minimum time after which his shad- ow will become larger than his original height? O What is the distance of Rohan from pole at this point ? (iii) What will be the length of his shadow after 4 seconds? AAns :  (i) As per question statement we make the diagram at…
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page 32 Cbse Class 10th Mathematics - Basic SP There is profit of Rs 24025 thousand if 175 car are produced. O (iv) When 400 cars are produce, ( ) P 400 ( ) ( ) 400 350 400 6600 2 =− + − 26600 =− There is loss of Rs 26600 thousand if 400 cars are produced. 38. Political survey questions are…
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