Welcome to ICOME Quiz Corner
Q1.
Find the maximum number of points of intersection of 20 circles.
(a) 380
(b) 300
(c) 340
(d) 360
Solution.
a
In this case number of circles are 20
20 x 19 = 380
Note: The point of intersection of n circles = 2 x
nC2 = n(n-1)
Solution
Q2.
A examination paper consists two sections A and B, having 4 questions and 3 questions respectively. At least a question
from each is to be attempted in how many ways this can be done ?
(a) 105
(b) 100
(c)120
(d) 90
Solution.
a
(24 - 1). (23 - 1) = 15 x 7 = 105
Note : Attempt atleast one question out of n questions
nC1 + nC2 + nC3 + ----------------------------------+nCn
= 2n - 1
Solution
Q3.
Find x & y, 9C6 + 2(9C5) + 9C4 = yCx .
(a) 11,6
(b) 6,11
(c) 4,5
(d) 5,4
Solution.b
= 9C6 + 9C5 + 9C5 + 9C4
= 10C6 + 10C5 = 11C6
x = 6 , y = 11,
nCr + nCr+1 = n+1Cr+1
Solution
Q4.
In a ▵ABC, sides are AB, BC, and CA having points 4, 5, 6 respectively on them . Find the number of triangles that can be
constructed using these points as vertices .
(a) 421
(b) 198
(c) 240
(d) 364
Solution.a
= 15C3 - (4C3 + 5C3 + 6C3)
= 455 - (4 + 10 + 20) = 421
Note: points which are on any side will be linear. A triangle can't be constructed among the linear points.
Solution
Q5.
Find r, 18Cr-1 = 18C2r + 1
(a) 4
(b) 6
(c) 5
(d) 9
Solution.b
r-1 + 2r + 1 = 18
3r = 18
r = 6
Solution
