Class 11 Math - Permutations and Combinations - MERIT YARD
Class 11 Math - Permutations & Combinations - MERIT YARD
1 / 40What is the exact value of
\( 0! \)?
A) \( 1 \)
B) \( 0 \)
C) \( \infty \)
D) Not defined
2 / 40What is the exact value of
\( 1! \)?
A) \( 0 \)
B) \( 1 \)
C) \( 2 \)
D) \( -1 \)
3 / 40Find the exact value of:
\( 3! \)
A) \( 3 \)
B) \( 9 \)
C) \( 6 \)
D) \( 1 \)
4 / 40Find the exact value of:
\( 4! \)
A) \( 12 \)
B) \( 16 \)
C) \( 20 \)
D) \( 24 \)
5 / 40Find the exact value of:
\( 5! \)
A) \( 120 \)
B) \( 100 \)
C) \( 25 \)
D) \( 60 \)
6 / 40Simplify the following expression:
\( \frac{n!}{(n-1)!} \)
A) \( (n-1) \)
B) \( n \)
C) \( n^2 \)
D) \( 1 \)
7 / 40Evaluate the fraction:
\( \frac{5!}{3!} \)
A) \( 15 \)
B) \( 120 \)
C) \( 20 \)
D) \( 60 \)
8 / 40Evaluate the expression:
\( 4! - 3! \)
A) \( 1 \)
B) \( 12 \)
C) \( 24 \)
D) \( 18 \)
9 / 40Is the mathematical statement \( 3! + 4! = 7! \) true or false?
A) False
B) True
C) True only for odd numbers
D) True only for even numbers
10 / 40Evaluate the fraction:
\( \frac{6!}{4!} \)
A) \( 24 \)
B) \( 30 \)
C) \( 12 \)
D) \( 6 \)
11 / 40What is the standard formula for Permutation
\( ^nP_r \)?
A) \( \frac{n!}{r!} \)
B) \( \frac{r!}{(n-r)!} \)
C) \( \frac{n!}{(n-r)!} \)
D) \( \frac{n!}{r!(n-r)!} \)
12 / 40Find the exact value of
\( ^nP_0 \).
A) \( 0 \)
B) \( n \)
C) \( n! \)
D) \( 1 \)
13 / 40Find the exact value of
\( ^nP_n \).
A) \( n! \)
B) \( 1 \)
C) \( 0 \)
D) \( n \)
14 / 40Find the exact value of
\( ^nP_1 \).
A) \( 1 \)
B) \( n \)
C) \( n! \)
D) \( 0 \)
15 / 40Evaluate the permutation:
\( ^5P_2 \)
A) \( 10 \)
B) \( 15 \)
C) \( 20 \)
D) \( 25 \)
16 / 40Evaluate the permutation:
\( ^4P_4 \)
A) \( 4 \)
B) \( 16 \)
C) \( 1 \)
D) \( 24 \)
17 / 40The number of possible arrangements of \( n \) distinct objects taken all at a time is:
A) \( n! \)
B) \( n \)
C) \( 1 \)
D) \( n^2 \)
18 / 40In mathematics, the term "Permutation" essentially refers to:
A) Selection
B) Arrangement
C) Addition
D) Elimination
19 / 40If repetition is fully allowed, the number of ways to arrange \( r \) objects from \( n \) distinct objects is:
A) \( n \times r \)
B) \( r^n \)
C) \( n^r \)
D) \( n! \)
20 / 40The number of permutations of \( n \) objects where \( p \) objects are exactly of the same kind is given by:
A) \( n! - p! \)
B) \( \frac{p!}{n!} \)
C) \( n! \times p! \)
D) \( \frac{n!}{p!} \)
21 / 40Find the total number of ways to arrange the letters of the word "CAT".
A) \( 6 \)
B) \( 3 \)
C) \( 9 \)
D) \( 1 \)
22 / 40Find the total number of ways to arrange the letters of the word "BOY".
A) \( 3 \)
B) \( 6 \)
C) \( 8 \)
D) \( 9 \)
23 / 40Find the total number of distinct ways to arrange the letters of the word "AAB".
A) \( 6 \)
B) \( 2 \)
C) \( 3 \)
D) \( 4 \)
24 / 40The Fundamental Principle of Addition is applied strictly when two given events:
A) Occur simultaneously
B) Occur one after another
C) Are completely dependent
D) Cannot occur simultaneously
25 / 40The Fundamental Principle of Multiplication is applied strictly when two given events:
A) Occur one after another
B) Cannot occur together
C) Are mutually exclusive
D) Have zero probability
26 / 40What is the standard formula for Combination
\( ^nC_r \)?
A) \( \frac{n!}{(n-r)!} \)
B) \( \frac{n!}{r!(n-r)!} \)
C) \( \frac{r!}{(n-r)!} \)
D) \( \frac{n!}{r!} \)
27 / 40In mathematics, the term "Combination" essentially refers to:
A) Sequence
B) Arrangement
C) Selection
D) Distribution
28 / 40Find the exact value of
\( ^nC_0 \).
A) \( 0 \)
B) \( n \)
C) \( n! \)
D) \( 1 \)
29 / 40Find the exact value of
\( ^nC_n \).
A) \( 1 \)
B) \( 0 \)
C) \( n \)
D) \( n! \)
30 / 40Find the exact value of
\( ^nC_1 \).
A) \( 1 \)
B) \( n \)
C) \( 0 \)
D) \( n! \)
31 / 40Complete the standard combination property:
\( ^nC_r = \)
A) \( ^rC_n \)
B) \( ^{n-1}C_r \)
C) \( ^nC_{n-r} \)
D) \( ^nC_{r-1} \)
32 / 40If \( ^nC_a = ^nC_b \) and \( a \neq b \), then what is the true relation between \( a, b \) and \( n \)?
A) \( a - b = n \)
B) \( ab = n \)
C) \( a = n + b \)
D) \( a + b = n \)
33 / 40Evaluate the combination:
\( ^5C_2 \)
A) \( 10 \)
B) \( 20 \)
C) \( 15 \)
D) \( 5 \)
34 / 40Evaluate the combination:
\( ^4C_4 \)
A) \( 4 \)
B) \( 1 \)
C) \( 24 \)
D) \( 0 \)
35 / 40What is the exact mathematical relation between
\( ^nP_r \) and \( ^nC_r \)?
A) \( ^nP_r = ^nC_r \)
B) \( ^nC_r = r! \times ^nP_r \)
C) \( ^nP_r = r! \times ^nC_r \)
D) \( ^nP_r = \frac{^nC_r}{r!} \)
36 / 40Complete Pascal's famous identity:
\( ^nC_r + ^nC_{r-1} = \)
A) \( ^nC_{r+1} \)
B) \( ^{n-1}C_r \)
C) \( ^{n+1}C_{r-1} \)
D) \( ^{n+1}C_r \)
37 / 40The total number of ways to strictly select \( 2 \) students out of a group of \( 5 \) is:
A) \( 10 \)
B) \( 20 \)
C) \( 5 \)
D) \( 15 \)
38 / 40The total number of ways to select exactly \( 1 \) boy from a group of \( 10 \) boys is:
A) \( 1 \)
B) \( 10 \)
C) \( 5 \)
D) \( 0 \)
39 / 40Out of \( 3 \) distinct books, the number of ways to select all \( 3 \) books is:
A) \( 6 \)
B) \( 3 \)
C) \( 1 \)
D) \( 9 \)
40 / 40In Permutations, the order of objects is ___, while in Combinations, the order is ___.
A) Not Important, Important
B) Random, Fixed
C) Equal, Unequal
D) Important, Not Important
Test Analysis

Correct ✅ 0

Wrong ❌ 0

Unattempted ⚠️ 40

Accuracy 🎯 0%

Time Taken ⏱️ 00m 00s

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