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Test: Permutations and Combinations- Case Based Type Questions - Commerce MCQ


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

Test: Permutations and Combinations- Case Based Type Questions for Commerce 2024 is part of Commerce preparation. The Test: Permutations and Combinations- Case Based Type Questions questions and answers have been prepared according to the Commerce exam syllabus.The Test: Permutations and Combinations- Case Based Type Questions MCQs are made for Commerce 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Permutations and Combinations- Case Based Type Questions below.
Solutions of Test: Permutations and Combinations- Case Based Type Questions questions in English are available as part of our course for Commerce & Test: Permutations and Combinations- Case Based Type Questions solutions in Hindi for Commerce course. Download more important topics, notes, lectures and mock test series for Commerce Exam by signing up for free. Attempt Test: Permutations and Combinations- Case Based Type Questions | 10 questions in 20 minutes | Mock test for Commerce preparation | Free important questions MCQ to study for Commerce Exam | Download free PDF with solutions
Test: Permutations and Combinations- Case Based Type Questions - Question 1
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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 for Test: Permutations and Combinations- Case Based Type Questions - Question 1
Number of straight lines

= 12C2 – 5C2 + 1

= 66 – 10 + 1 = 57

Test: Permutations and Combinations- Case Based Type Questions - Question 2
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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 for Test: Permutations and Combinations- Case Based Type Questions - Question 2
Number of chords = 7C2 = 21
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Test: Permutations and Combinations- Case Based Type Questions - Question 3
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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 for Test: Permutations and Combinations- Case Based Type Questions - Question 3
We can draw only one straight line through the 5 collinear points.
Test: Permutations and Combinations- Case Based Type Questions - Question 4
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There are 12 points in a plane of which 5 are collinear.

Q. How many quadrilaterals can be formed using these points?
Detailed Solution for Test: Permutations and Combinations- Case Based Type Questions - Question 4
Number of quadrilaterals = 12C4 – [5C4 + 5C3 × 7C1]

= 495 – (5 + 70) = 420

Test: Permutations and Combinations- Case Based Type Questions - Question 5
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There are 12 points in a plane of which 5 are collinear.

Q. How many triangles can be formed using these points?
Detailed Solution for Test: Permutations and Combinations- Case Based Type Questions - Question 5
Number of triangles = 12C3 – 5C3 = 220 – 10 = 210
Test: Permutations and Combinations- Case Based Type Questions - Question 6
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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 for Test: Permutations and Combinations- Case Based Type Questions - Question 6

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

Test: Permutations and Combinations- Case Based Type Questions - Question 7
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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 for Test: Permutations and Combinations- Case Based Type Questions - 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
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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 for Test: Permutations and Combinations- Case Based Type Questions - 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
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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 for Test: Permutations and Combinations- Case Based Type Questions - Question 9
Number of words beginning with vowel = 3 × 6!

= 3 × 720 = 2160

Test: Permutations and Combinations- Case Based Type Questions - Question 10
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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 for Test: Permutations and Combinations- Case Based Type Questions - Question 10
ORGANIC is a seven letter word.

O _ _ _ _ _ _

Number of words beginning with O = 6! = 720

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