Miscellaneous Topics
SSC-CGL Exam
1. Overview
SSC CGL often tests mixed topics that require:
Counting Methods
Permutation & Combination
Likelihood
Probability
Quick Calculation
Algebraic Simplification
Focus: Shortcuts, formulas, logical reasoning
2. Permutation & Combination (P&C)
Permutation
Arrangement of objects where order matters
nPr = n! / (n-r)!
- n = total items
- r = items to arrange
Combination
Selection of objects where order does not matter
nCr = n! / [r!(n-r)!]
- n = total items
- r = items to select
Example 1: Permutation
Arrange 3 letters from A, B, C, D
4P3 = 4×3×2 = 24 ways
Example 2: Combination
Select 2 letters from A, B, C, D
4C2 = 6 ways
SSC Short Tricks / Tips:
Permutation = order matters → use P formula
Combination = order doesn't matter → use C formula
Factorial shortcuts: 5! = 120, 6! = 720
SSC pattern: Problems usually ≤10 objects
3. Probability
Probability = Favorable outcomes / Total outcomes
P(E) = Number of favorable outcomes / Total number of outcomes
Always check sample space
Express answer as fraction, decimal, or percentage
Example 3:
A die is rolled → probability of getting even number?
Favorable = {2,4,6} → 3 outcomes
Total = 6 outcomes
P = 3/6 = 1/2
Example 4:
A bag has 3 red, 2 blue balls → probability of blue?
P = 2/(3+2) = 2/5
2/5
SSC Short Tricks / Tips:
Total outcomes = count of all possible cases
For multiple events → multiply probabilities (independent events)
Complement rule: P(not E) = 1 - P(E)
4. Simplification of Algebraic Expressions
Techniques:
Factorization
Using identities
Cancel common terms
Apply BODMAS / PEMDAS
Common Identities:
(a+b)² = a² + 2ab + b²
(a-b)² = a² - 2ab + b²
a²-b² = (a-b)(a+b)
(x+y)³ = x³ + y³ + 3xy(x+y)
Example 5:
Simplify: (x²-9)/(x+3)
x²-9 = (x-3)(x+3)
→ (x-3)(x+3)/(x+3) = x-3
x−3
Example 6:
Simplify: (a²+b²+2ab)/(a+b)
a²+b²+2ab = (a+b)²
→ (a+b)²/(a+b) = a+b
a+b
5. SSC Short Tricks / Tips
Memorize factorials 1! → 10!
Apply algebraic identities → avoid full expansion
For probability, use complement → often faster
P&C problems → check repetition allowed / not allowed
Simplification → always look for common factors first
6. Practice Section
Q1. How many ways to arrange 3 letters from A,B,C,D?
View Answer
4P3 = 4×3×2 = 24
Q2. Select 2 letters from A,B,C,D → number of ways?
View Answer
4C2 = 6
Q3. Roll a die → probability of odd number?
View Answer
Odd = {1,3,5} → P = 3/6 = 1/2
1/2
Q4. Bag with 4 red, 3 green balls → probability of picking red?
View Answer
P = 4/(4+3) = 4/7
4/7
Q5. Simplify: (x² - 16)/(x-4)
View Answer
x²−16 = (x−4)(x+4) → (x+4)
x+4
Q6. Simplify: (a² - b² + 2ab)/(a+b)
View Answer
a²−b²+2ab = (a+b)² → (a+b)²/(a+b) = a+b
a+b
7. Quick Recap Table
| Topic | Formula / Key Point | SSC Shortcut |
|---|---|---|
| Permutation | nPr = n!/(n−r)! | Order matters → P |
| Combination | nCr = n!/(r!(n−r)!) | Order doesn't matter → C |
| Probability | P = Favorable / Total | Complement → 1−P(E) |
| Simplification | Factorize / Identities | Check common factors first |
You've completed Article 16: Miscellaneous Topics!
Courage Tip: For SSC, practice factorials, quick probability, and algebra simplifications daily. Shortcuts save time in exams.
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