Permutations and Combinations Test

Result

Permutations and Combinations Test - 28

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Weekly Quiz Competition

Question 1
4 / -1

Six points in a plane be joined in all possible ways by indefinite straight lines, and if no two of them be coincident or parallel, and no three pass through the same point (with the exception of the original 6 points). The number of distinct points of intersection is equal to

A
105

B
45

C
51

D
None of these
Question 2
4 / -1

A parallellogram is cut by two sets of m lines parallel to its sides. The number of parallelograms thus formed is

A
(^mC₂)²

B
(^m+1C₂)²

C
(^m+2C₂)²

D
None of these
Question 3
4 / -1

The greatest possible number of points of intersection of 8 straight lines and 4 circle is

A
32

B
64

C
76

D
104

Solution
Question 4
4 / -1

Out of 10 points in a plane 6 are in a straight line. The number of triangles formed by joining these points are

A
100

B
150

C
120

D
None of these

Solution
Question 5
4 / -1

A

B

C

D
None of these

Solution
Question 6
4 / -1

How many numbers lying between 10 and 1000 can be formed from the digits 1,2,3,4,5,6,7,8,9 (repetition is allowed)

A
1024

B
810

C
2346

D
None of these
Question 7
4 / -1

If ⁵⁶P_r+6 : ⁵⁴P_r+3 = 30800 : 1, then r =

A
31

B
41

C
51

D
None of these

Solution
Question 8
4 / -1

The number of ways in which the letters of the word ARRANGE can be arranged such that both R do not come together is

A
360

B
900

C
1260

D
1620

Solution
Question 9
4 / -1

In a certain test there are n questions. In the test 2^{n - i} students gave wrong answers to at least i questions, where i = 1,2,......n.If the total number of wrong answers given is 2047 , then n is equal to

A
10

B
11

C
12

D
13

Solution
Question 10
4 / -1

The number of times the digit 3 will be written when listing the integers from 1 to 1000 is

A
269

B
300

C
271

D
302