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


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10 Questions MCQ Test Mathematics (Maths) Class 11 - Test: Permutations and Combinations- Case Based Type Questions

Test: Permutations and Combinations- Case Based Type Questions for Commerce 2024 is part of Mathematics (Maths) Class 11 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 Mathematics (Maths) Class 11 for Commerce & Test: Permutations and Combinations- Case Based Type Questions solutions in Hindi for Mathematics (Maths) Class 11 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 Mathematics (Maths) Class 11 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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