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CBSE Class 10 Mathematics Solved Question Paper 2017

Short 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?

Let the height of the tower be x and y the length of the shadow on the ground be x:y.

The angle of elevation of the sun from the ground is θ.
We have, x:y =√3:1
Now, In ∆ABC
$tan space straight theta space equals fraction numerator space Height space over denominator Base end fraction tan space straight theta space equals space AB over BC space tan space straight theta space equals fraction numerator square root of 3 over denominator 1 end fraction therefore space tan space straight theta space space equals space 60 degree$

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

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

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

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

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

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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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