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CBSE Class 10 Mathematics Solved Question Paper 2017

Short Answer Type

The probability of selecting a rotten apple randomly from a heap of 900 apples is 0.18. What is the number of rotten apples in the heap?

If a tower 30 m high, casts a shadow 10 3m long on the ground, then what is the angle of elevation of the sun?

If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is 60°, then find the length of OP.

What is the common difference of an A.P. in which a₂₁- a₇= 84?

A circle touches all the four sides of a quadrilateral ABCD. Prove that

AB + CD = BC + DA

Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord.

7.
A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, -5) is the mid-point of PQ, then find the coordinates of P and Q.

Since a line is intersecting Y-axis at P and X- axis at Q,

Coordinates of P = (0,y) and coordinates of Q = (x,0)

Let R be the midpoint of PQ.

$Then, co - ordinates of R = (\frac{0 + x}{2}, \frac{y + 0}{2}) = (2, - 5) \Rightarrow (\frac{x}{2}, \frac{y}{2}) = (2, - 5) \Rightarrow \frac{x}{2} = 2 and \frac{y}{2} = - 5 \Rightarrow x = 4 and y = - 10 Hence, co - ordinates of P are (0, - 10) and co - ordinates of Q are (4, 0) .$