 # CBSE [Delhi]_X_Mathematics_2015_Set I

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• Q1 Marks:1 • Q2

The tops of two towers of height x and y, standing on level ground, subtend angles of 30° and 60° respectively at the centre of the line joining their feet, then find x:y.

Marks:1  • Q3

A letter of English alphabet is chosen at random. Determine the probability that the chosen letter is a constant.

Marks:1

Number of English alphabet = 26
Number of constants = 21

Probability of choosing a constant = 21/26

• Q4

In Fig. 1, PA and PB are tangents to the circle with centre O such that ∠APB=50o.  Write the measure of∠OAB. Marks:1

Join OC.  • Q5

In Fig. 2, AB is the diameter of a circle with centre O and AT is a tangent. If . Marks:2  • Q6

Solve the following quadratic equation for x:

4x2 – 4a2x + (a4 – b4) = 0

Marks:2 • Q7

From a point T outside a circle of centre O, tangents TP and TQ are drawn to the circle. Prove that OT is the right bisector of line segment PQ.

Marks:2

Given: TP and TQ are tangents to circle and OT intersects chord PQ at R.

To Prove: OT bisects PQ at right angle.  • Q8

Find the middle term of the A.P.
6, 13, 20, …, 216.

Marks:2  • Q9

If A(5, 2), B(2,–2) and C(–2, t) are the vertices of a right angled triangle with angle B = 90°, then find the value of t.

Marks:2

In right angled triangle, ABC, By Pythagoras Theorem,

AC2 = AB2 + BC2

(5 + 2)2 +(2 – t)2 =(5 – 2)2 +(2 +2)2 +(2 + 2)2
+(–2 – t)2

72 + 4 – 4t + t2 = 9 + 16 + 16 + 4 + 4t + t2
53 – 4t = 45 + 4t
53 – 45 = 8t
t = 8/8 = 1  