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

Download the PDF Sample Papers Free for off line practice and view the Solutions online.
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 Multiple Choice QuestionsShort Answer Type

1.

The ratio of the height of a tower and the length of its shadow on the ground is √3:1. What is the angle of elevation of the sun?

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2.

Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of the hemisphere? 

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3.

If the distance between the points (4, k) and (1, 0) is 5, then what can be the possible values of k?

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4.

Find the roots of the quadratic equation square root of 2 straight x squared space plus 7 straight x space plus 5 square root of 2 space equals space 0


square root of 2 straight x squared space plus 7 straight x space plus 5 square root of 2 space equals space 0
or
rightwards double arrow square root of 2 straight x squared space plus 5 straight x space plus 2 straight x space plus 5 square root of 2 space equals space 0
rightwards double arrow straight x left parenthesis square root of 2 straight x space plus 5 right parenthesis space plus square root of 2 left parenthesis square root of 2 straight x end root plus 5 right parenthesis space equals space 0
rightwards double arrow space left parenthesis square root of 2 straight x end root space plus 5 right parenthesis left parenthesis straight x plus square root of 2 right parenthesis space equals space 0
rightwards double arrow left parenthesis square root of 2 straight x end root space plus 5 right parenthesis space left parenthesis straight x plus square root of 2 right parenthesis space equals space 0
rightwards double arrow space straight x space plus space square root of 2 space equals space 0
square root of 2 straight x end root space plus 5 space equals space 0
rightwards double arrow space straight x space equals negative square root of 2
straight x space equals negative space fraction numerator 5 over denominator square root of 2 end fraction space equals negative space fraction numerator 5 square root of 2 over denominator 2 end fraction space
Hence space roots space are space minus square root of 2 comma space minus fraction numerator 5 square root of 2 over denominator 2 end fraction space
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5.

Find how many integers between 200 and 500 are divisible by 8.

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6.

Prove that tangents drawn at the ends of a diameter of a circle are parallel to each other.

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7.

Find the value of k for which the equation x2 + k(2x + k − 1) + 2 = 0 has real and equal roots. 

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8.

Draw a line segment of length 8 cm and divide it internally in the ratio 4: 5.
Steps of construction.

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9.

In the given figure, PA and PB are tangents to the circle from an external point P. CD is another tangent touching the circle at Q. If PA = 12 cm, QC = QD = 3 cm, then find PC + PD.

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10.

A number is chosen at random from the number –3, –2, –1, 0, 1, 2, 3. What will be the probability that square of this number is less then or equal to 1? 

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