Check whether the following are quadratic equations: x² – 2x = (–2) (3 – x)

2

(a)

Check whether the following are quadratic equations: (2x – 1)(x – 3) = (x + 5)(x – 1)

2

(a)

Find the roots of the following quadratic equation, if they exist, by the method of completing the square: 2x²+x+4=0

2

(a)

Out of a group of children, \({7\over 2}\) times the square root of the number are creative, the two remaining ones are visionary. What is the total number of children ? How many persons in the group are creative?
Write one-one characteristics each of creativity and vision.

2

(a)

Solve for x : \(\sqrt { 6x+7 } -(2x-7)=0\)

2

(a)

Which term of the AP 14, 11, 8, ....... is -1?

2

(a)

Find the sum of 2n terms of the series 1² - 2² + 3² - 4² + 5² - 6² +.......

2

(a)

Fill in the blanks a = -18.9, d = 2.5, n = ...., a_n=3.6

2

(a)

Prove that the angle between two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.

2

(a)

In figure O is the centre of a circle.PT and PQ are tangents to the circle from an external point P. If \(\angle TPQ=70^0, find\ \angle TRQ\)

2

(a)

Two circles touch internally at a point P and from a point T the common tangent at P, tangent segments TQ, TR are drawn to the two circles. Prove that TQ = TR.

2

(a)

A circle is inscribed in a triangle ABC having sides AB = 8 cm, BC = 10 cm and CA = 12 cm as shon in fig. Find AD, BE and CF. 

2

(a)

PA and PB are the tangents to a circle which circumscribes an equilateral \(\Delta\)ABQ. If \(\angle PAB=60°\), as shown in the figure, prove that QP bisects AB at right angle.

2

(a)

A statue, 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60\(\unicode{xb0} \) and from the same point the angle of elevation of the top of the pedestal is 45\(\unicode{xb0} \). Find the height of the pedestal.

2

(a)

A spherical balloon of radius 'r' subtends an angle \(\theta\) at the eye of an observer.If the angle of elevation of is \(\phi \), find the height of the centre of the balloon.

2

(a)

A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see Fig.), and these are equally likely outcomes. What is the probability that it will point at
(i) 8 ?
(ii) an odd number?
(iii) a number greater than 2?
(iv) a number less than 9?

2

(a)

A bag contains 24 balls out of which x are white. If one ball is drawn at random the probability of drawing a white ball is y. 12 more white balls are added to the bag. Now if a ball is drawn from the bag, the probability of drawing the white ball is \(\frac{5}{3}y\). Find the value of x.

2

(a)

 A jar contains 24 marbles, some are green and others are blue.If a marble is drawn at random from the jar, the probability that it is green is \(2\over3\).Find the number of blue marbles.

2

(a)