Subject

Mathematics

Class

CBSE Class 10

Pre Boards

Practice to excel and get familiar with the paper pattern and the type of questions. Check you answers with answer keys provided.

Sample Papers

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 Multiple Choice QuestionsLong Answer Type

21. The diagonal of a rectangular field is 16 metres more than the shorter side. If the longer side is 14 metres more than the shorter side, then find the lengths of the sides of the field.
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22.

Find the 60th term of the AP 8, 10,12, ..., if it has a total of 60 terms and hence find the sum of its last 10 terms.

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23. A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?


Let the average speed of train for the first 54 km be x km/h

⇒ Average speed for the next 63 km = ( x + 6) km/h

We know


Time space equals fraction numerator space Distance over denominator Speed end fraction

therefore space Time space taken space by space the space train space to space cover space 54 space km space equals space 54 over straight x space straight h
Also comma space time space taken space by space the space train space to space cover space the space next space 63 space km space equals space fraction numerator 63 over denominator straight x space plus space 6 end fraction space straight h

According space to space the space question comma

54 over straight x space plus space fraction numerator 63 over denominator straight x space plus space 6 end fraction space equals space 63

rightwards double arrow space fraction numerator 54 space left parenthesis straight x space plus space 6 space right parenthesis space plus 63 straight x over denominator straight x space left parenthesis straight x space plus space 6 right parenthesis end fraction space space equals space 3

⇒ 117x + 324 = 3 ( x2 + 6x)

⇒ 117x + 324 = 3x2 + 18x

⇒ 3x2 - 99x -324 = 0 ..(i)

Taking common from the above equation (i)

we have

x2 - 33x - 108 = 0

⇒ x2 - 36x + 3x -108 = 0

⇒ x (x - 36) + 3 (x - 36) = 0

⇒ (x - 36) (x +3 )=0

⇒ x -36 = 0 Or x + 3 =0

x = 36 or x = -3

 The speed of the train cannot be negative. Thus, x = 36

Hence, the speed of the train to cover 54 km or its first speed is 36 km/h.

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24.

Prove that the length of tangents drawn from an external point to a circle is equal.

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25. Prove that the tangent drawn at the midpoint of an arc of a circle is parallel to the chord joining the end points of the arc.
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26.

Construct a ΔABC in which AB = 6 cm, ∠A = 30o and ∠B = 60o. Construct another ΔAB'C' similar to ΔABC with base AB' = 8 cm

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27. At a point A, 20 metres above the level of water in a lake, the angle of elevation of a cloud is 30°. The angle of depression of the reflection of the cloud in the lake, at A is 60°. Find the distance of the cloud from A.
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28. A card is drawn at random from a well-shuffled deck of playing cards.

(i) a card of a spade or an ace.
(ii) a black king
(iii) neither a jack nor a king
(iv) either a king or queen
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29.

Find the values of k so that the area of the triangle with vertices (1,-1), (-4, 2k) and (-k, 5) is 24 sq. units

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30. In Figure, PQRS is a square lawn with side PQ = 42 metres. Two circular flower beds are there on the sides PS and QR with centre at O, the intersection of its diagonals. Find the total area of the two flower beds (shaded parts).


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