Using quadratic formula, solve the following quadratic equation for x: 
p²x²+(p²-q²)x-q²=0

3

(a)

Find the roots of the following quadratic equation (if they exist) by the method of completing square \(5x^{2} - 6x-2 = 0\) .

3

(a)

Find the numbers of terms in A.P.: 5, 12, 19, 28, ....., 159.

3

(a)

In the given figure, TBP and TCQ are tangents to the circle whose centre isO.Also \(\angle PBA=60^0\ and \ \angle ACQ=70^0.\)Determine \(\angle BAC\ and \ \angle BTC.\)

3

(a)

In the given figure, if AB = AC, then prove that BC = 2CE.

3

(a)

Draw a line segment AB of length 7 cm. Taking A as centre, draw a circle of radius 3 cm and taking B as centre, draw another circle of radius 2 cm. Construct tangents to each circle from the centre of the other circle

3

(a)

A box contain 100red cards, 200 yellow cards and 50blue cards.If a card is drawn at random from the box, the find the probability that it will be:
(i)A blue card
(ii)Not a yellow card
(iii)Neither yellow nor a blue card.

3

(a)

A number x is chosen from the numbers 1,2,3 and a number y is selected from the numbers 1,4,9. Find the probability that xy=10.

3

(a)

Two dice are thrown simultaneously. Find the probability of getting a multiple of 2 on one die and a multiple of 3 on the other die.

3

(a)

A chemist has one solution which is 50% acid and a second which is 25% acid. How much of each should be mixed to make 10 litre of 40% acid solution.

3

(a)

State which pairs of triangles in the given figure are similar? Also, state the similarity criterion used.

3

(a)

In a trapezium ABCD, diagonals AC and BD intersect at O. If AB = 3CD, then find ratio of areas of triangles COD and AOB.

3

(a)

In \(\triangle PQR\), right-angles at Q, PQ = 3 cm and PR = 6 cm. Determine \(\angle QPR\) and \(\angle PRQ\).

3

(a)

The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of the top of the tower from the foot of the hill is 30°. If the tower is 50 m high, find the height of the hill.

3

(a)

Prove that \(\sum { \left( { x }_{ i }-\bar { x } \right) =0 } \)

3

(a)