﻿ In the given figure, PQ is a chord of a circle with centre O and

## 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.

## CBSE Class 10 Mathematics Solved Question Paper 2015

1.

If the quadratic equation has two roots, then find the value of p.

12206 Views

2.

In Given figure, a tower AB is 20 m high and BC, its shadow on the ground, is m long. Find the sun's altitude.

2000 Views

3.

The different dice are tossed together. Find the probability that the product of the two number on the top of the dice is 6.

2773 Views

# 4.In the given figure, PQ is a chord of a circle with centre O and PT is tangent. If ∠QPT = 60o, find ∠ PRQ.

PQ is the chord of the circle and PT is tangent.

We know that the tangent to a circle is perpendicular to the radius through the point of contact.

∴ ∠ OPT = 90o

Now, Given

∠ QPT = 60o

∴ ∠ OPQ = ∠OPT - ∠QPT

⇒ ∠ OPQ = 90o - 60o = 30o

In Δ OPQ,

OP= OR (Radii of the same circle)

∠ OQP = ∠ OPQ = 30o (in a triangle, equal sides have equal angles opposite to them.)

Now,

∠ OQP + ∠OPQ + ∠POQ = 180o [Angle sum property]

⇒ 30o + 30o + ∠POQ = 180o

⇒ ∠POQ = 180o - 60o = 120o

⇒ Reflex ∠POQ = 360o -120o = 240o

We know that the angle subtended by an arc of a circle at the centre is twice the angle subtended by it any point on the remaining part of the circle.

Therefore,

Reflex ∠POQ = 2 ∠PRQ

⇒ 240o = 2 ∠PRQ

⇒ ∠PRQ = 240 / 2 = 120o

Hence, the measure of angle PRQ is 120o.

3511 Views

5.

In the given figure, two tangents RQ and RP are drawn from an external point R to the circle with centre O. If ∠PRQ = 120o, then prove that OR = PR + RQ.

2137 Views

6.

In the given figure, a triangle ABC is drawn to circumscribe of radius 3 cm, such that the segments RD and DC are respectively of length 6 cm and 9 cm. If the area of ΔABC is 54 cm2, then find lengths of sides AB and AC.

2947 Views

7.

Solve the following quadratic equation for x,

4x2 + 4bx - (a2 - b2) = 0

2298 Views

8.

In an AP, if S5 + S7 = 167 and S10 = 235, then find the AP,  Where Sn denotes the sum of its first n terms.

4564 Views

9.

The points A (4, 7), B (p, 3) and C (7, 3) are the vertices a right triangle, right-angled at B find the value of p.

2708 Views

10.

Find the relation between x and y if the points A (x, y), B (-5, 7) and C (-4, 5) are collinear.

1320 Views