If x = 2+32-3 , then what is the value of x2+x-9 ? 0 3?2 3?3 5?3

2. If the mean of m observations out of n observations is n and the mean of remaining observations is m, then what is the mean of all n observations?
Options
A. 2m ?m^2/n
B. 2m ?m/n
C. 2m
D. 2m ?m

Correct Answer: 2m ?m^2/n

Explanation:

Mean of m observations is n

Mean of n-m observations is m

So total = nm+ (n-m)m

Total observations = n

Mean = Total / Total observations = (2mn-m^2)/n = 2m ?m^2/n

3. Two equal circles intersect such that each passes through the centre of the other. If the length of the common chord of the circles is 10?3 cm, then what is the diameter of the circle?
Options
A. 10 cm
B. 15 cm
C. 20 cm
D. 30 cm

Correct Answer: 20 cm

Explanation:

Let there be 2 circles with centre O1 and OAB is the common chord

Since both passes through the center of each other as shown in figure

So O1O is the radius of both

Let O1O = r = AO1= AO

AX = AB / 2 = 5?3 cm (since OX perpendicular to chord bisects it)

AOO1 forms an equilateral triangle with on side = radius = r

Sin 60 = ?3/2 = AX / AO = 5?3/r

So r = 10 cm

So diameter = 20 cm

4. A 12 m long wire is cut into two pieces, one of which is bent into a circle and the other into a square enclosing the circle. What is the radius of the circle?
Options
A. 12/?+4
B. 6/?+4
C. 3/?+4
D. 6/?+2?2

Correct Answer: 6/?+4

Explanation:

As it is clear that 2r = a where a is the side of the square and

R is the radius of circle

It is given that 2?r + 4a = 12

a = 12/(?+4)