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Permutations and Combinations- Case Based Type Questions - Free with solutions


MCQ Practice Test & Solutions: Test: Permutations and Combinations- Case Based Type Questions (10 Questions)

You can prepare effectively for Commerce Mathematics (Maths) Class 11 with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Permutations and Combinations- Case Based Type Questions". These 10 questions have been designed by the experts with the latest curriculum of Commerce 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 20 minutes
  • - Number of Questions: 10

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Test: Permutations and Combinations- Case Based Type Questions - Question 1

There are 12 points in a plane of which 5 are collinear.

Q. How many straight lines can be drawn using all the points?

Detailed Solution: Question 1

Number of straight lines

= 12C25C2 + 1

= 66 – 10 + 1 = 57

Test: Permutations and Combinations- Case Based Type Questions - Question 2

There are 12 points in a plane of which 5 are collinear.

Q. How many chords can be drawn using seven points on the circumference of a circle?

Detailed Solution: Question 2

Number of chords = 7C2 = 21

Test: Permutations and Combinations- Case Based Type Questions - Question 3

There are 12 points in a plane of which 5 are collinear.

Q. How many straight lines can be formed using the collinear points?

Detailed Solution: Question 3

We can draw only one straight line through the 5 collinear points.

Test: Permutations and Combinations- Case Based Type Questions - Question 4

There are 12 points in a plane of which 5 are collinear.

Q. How many quadrilaterals can be formed using these points?

Detailed Solution: Question 4

Number of quadrilaterals = 12C4 – [5C4 + 5C3 × 7C1]

= 495 – (5 + 70) = 420

Test: Permutations and Combinations- Case Based Type Questions - Question 5

There are 12 points in a plane of which 5 are collinear.

Q. How many triangles can be formed using these points?

Detailed Solution: Question 5

Number of triangles = 12C35C3 = 220 – 10 = 210

Test: Permutations and Combinations- Case Based Type Questions - Question 6

Thejasree is playing with scramble word cubes. She needs to form a word using all the letters of the word ‘ORGANIC’ without repetition of the letters.

Q. How many words begin and end with consonants?

Detailed Solution: Question 6

Required number of words = 4 × 5! × 3 = 1440

Test: Permutations and Combinations- Case Based Type Questions - Question 7

Thejasree is playing with scramble word cubes. She needs to form a word using all the letters of the word ‘ORGANIC’ without repetition of the letters.

Q. In how many words vowels and consonants alternate between each other?

Detailed Solution: Question 7

C V V C V C Number of words = 4! × 3! = 24 × 6 = 144

Test: Permutations and Combinations- Case Based Type Questions - Question 8

Thejasree is playing with scramble word cubes. She needs to form a word using all the letters of the word ‘ORGANIC’ without repetition of the letters.

Q. In how many words the all vowels are together?

Detailed Solution: Question 8

Vowels - OAI
OAI, R, G, N, C - 5 Places, Ways to arrange = 5!
OAI, Ways to arrange = 3!
Number of words beginning with vowel = 5! × 3!

= 120 × 6 = 720

Test: Permutations and Combinations- Case Based Type Questions - Question 9

Thejasree is playing with scramble word cubes. She needs to form a word using all the letters of the word ‘ORGANIC’ without repetition of the letters.

Q. How many words begin with a vowel?

Detailed Solution: Question 9

Number of words beginning with vowel = 3 × 6!

= 3 × 720 = 2160

Test: Permutations and Combinations- Case Based Type Questions - Question 10

Thejasree is playing with scramble word cubes. She needs to form a word using all the letters of the word ‘ORGANIC’ without repetition of the letters.

Q. How many words begin with O?

Detailed Solution: Question 10

ORGANIC is a seven letter word.

O _ _ _ _ _ _

Number of words beginning with O = 6! = 720

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