Following is the distribution of I.Q. of 100 students. Find the median I.Q. I.Q.:          55-64  65-74  75-84  85-94  95-104  105-114  115-124  125-134  135-144 No. of Students:     1      2       9      22     33      22        8          2          1

Prove that the following points are the vertices of an isosceles right-angled triangle : (i) A(-8, -9), B(0, -3) and C(-6, 5) (ii) A(1,-1), B(-2,2) and C(-2, -1)

Q.8Which ofthe following is anilpotent matrix(1)0 1(2) | sin theta(2) sin0cose!4i(3)

Following frequency distribution given the weights of 38 students of a class: Weight in Kg: 31-35 36-40 41-45 46-50 51-55 56-60 61-65 66-70 71-75 No. of students9 5 14 3 1 2 2 1 1 Find the probability that weight of a student in the class is: (i)at most 60 kg (ii)at least 36 kg (iii)not more than 50kg. Also define two events in this context, one having probability 0 and the other having probability 1.

Following frequency distribution given the weights of 38 students of a class: Weight in Kg: 31-35 36-40, 41-45, 46-50, 51-55, 56-60 61-65, 66-70 71-75 No. of students 9 5 14 3 1 2 2 1 1 Find the probability that weight of a student in the class is: (i)at most 60 kg (ii)at least 36 kg (iii)not more than 50kg. Also define two events in this context, one having probability 0 and the other having probability 1.

Find the median of Q(i) 10, 32, 17, 19, 21, 22, 9, 35 (ii) 55, 60, 35, 51, 29, 63, 72, 91, 85, 82

If the x-coordinate of a point P on the join of Q(22,1)a n dR(5,1,-2)i s4, then find its z- coordinate.

If the x-coordinate of a point P on the join of Q(22,1)a n dR(5,1,-2)i s4, then find its z- coordinate.

The marks obtained by 100 students of a school are given below. {:("Marks",0-5,5-10,10-15,15-20,20-25,25-30,30-35,35-40),("No . of Students"," "4," "6," "10," "10," "25," "22," "18," "5):} Find out Q_(1),Q_(3),D_(6)and P_(95) .