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Welcome to ICOME Quiz Corner

Q1. In a room there are 10 tubelights, having a seperate switch . The number of ways to light the room with different amounts of illumination is

Solution.
Different illumination (amounts) means one tubelight or two tubelights or all 10 tubelights can illuminate the room . There are 2 option in a switch (on or off)

= 210 is the all possible option to on-off in which one arrangement is there when all tubelights are in off mode .
So, required answer is 210 - 1
Solution

Q2. nc8 = nc4 find n .

Solution
ncx = ncy
n = x + y or x = y
n = 12
Solution

Q3. In how many way a group of 5 memebers can be developed from 6 males and 5 females consisting of 3 males and 2 females .

Solution.
3 males out of 6 can be selected 6c3 and 2 females can be selected 5c2

The required solution is 6c3 . 5c2 = 200 ways .
Solution

Q4. how many chords can be drawn through 25 points on a circle .

Solution.
A chord joined by two points

25c2 =
25!/2! x 3!
=
25 x 24 x 23!/2 x 23!


= 25 x 12 = 300
Solution

Q5. How many triangles can be formed by joining the points (vertices) of a hexagon .

Solution.
Hexagon consists six points, a triangle can be formed using 3- points (vertices) . This can be done in 6c3 ways . Number of triangles are 6c3.
Solution

Q6. If 5 parallel lines in plane are intersected to 9 parallel lines . Find the number of parallelograms formed .

Solution.
In parallelogram there are two pairs of parallel lines .so, find 2 parallel lines out 5 parallel lines in 5c2 ways and select 2 parallel lines out of 9 parallel lines in 9c2 ways .

Hence, the number of parallelograms = = 5c2 . 9c2
Solution

Q7. In how many ways can a student choose 6 courses out of 9 courses, If 2 courses are compulsory for every student .

Solution.
Since 2 courses are compulsory . students will choose 4 courses out of 7 courses in 7c4 ways .
Solution

Q8. There are 12 points in a plane , in which 4 points are collinear, find how many straight lines can be drawn .

Solution.
Number of line formed by 12 points 12c2 number of straight lines from 4 collinear points 4c2 . All four collinear points develop a straight line .

The required answer is 12c2 - 4c2 + 1
Solution

Q9. If c0 + c1 + c2 + c3 + ----- + cn = 256 , then find the n c2 .

Solution.
c0 + c1 + c2 + c3 + ----- + cn = 2n

2n = 256 ⇒ 2n = 28 ⇒ n = 8

= 8c2 = 28
Solution

Q10. 8cr = 56

8pr = 336

find r .

Solution.
As we know that ncr . r! = npr
r! =
npr /ncr
=
336/56
= 6

r! = 6

r = 3
Solution