Analytical and Mathematical Capability
60%of exam
Logical Capability
20%of exam
Mental Reasoning
20%of exam
Quick Facts
- Recruitment cycle
- CEN 03/2026 written CBT
- Questions
- 100 one-mark MCQs
- Time
- 120 minutes; approved compensatory time applies
- Wrong answer
- −⅓ mark per wrong answer
- Section allocation
- Indicative counts; actual papers may vary
- UR/EWS minimum
- 40% eligibility minimum
- OBC-NCL/SC minimum
- 30% eligibility minimum
- ST minimum
- 25% eligibility minimum
- CBAT qualification
- T-score ≥42 in every battery
- Final merit
- CBAT qualifiers: CBT 70%; CBAT 30%
- Calculator
- Prohibited at the test centre
Percentage Base Memory
Profit uses cost; discount uses marked.
CP: cost priceMP: marked priceChange: original value
HCF vs LCM
HCF
- Divides both positive integers
- Cannot exceed either integer
LCM
- Multiple of both positive integers
- Cannot be below either integer
Positive integers; factor versus multiple
Mathematical Method Picker
- Percent rise then fall→Multiply successive factors(Use each new base)
- Profit or loss percent→Divide change by CP(CP includes stated overheads)
- Discount percentage requested→Divide discount by MP(Multiply fraction by 100)
- Two constant workers cooperate→Add job-completion rates(Same job and time-unit)
- Opposite movers approach→Add speeds(Same line; consistent units)
- Equal-distance average speed→Use 2uv÷(u+v)(Positive speeds; two equal distances)
- Probability by outcome counting→Verify equally likely outcomes(Then favourable÷total)
- Data-sufficiency question→Test separately, then jointly(Require a unique requested answer)
Number Foundations
- Prime
- Positive integer; exactly two positive divisors
- Composite
- Positive integer; ≥3 positive divisors
- One
- Neither prime nor composite
- HCF
- Largest common positive integer factor
- LCM
- Smallest common positive integer multiple
- HCF×LCM
- a×bTwo positive integers a,b
- Divisibility by 3
- Digit sum divisible by 3Nonnegative decimal integers
- Integer count [a,b]
- b−a+1Integers; a≤b; endpoints included
Percent vs Percentage Points
Relative percent change
- Divide change by original value
- Then multiply by 100
Percentage-point change
- Subtract the two percentages
- No division by original percentage
20%→30%: 10pp; 50% relative rise
Percentage Bases
- CP
- Cost price, including stated overheads
- SP
- Selling price
- MP
- Marked price
- Profit %
- (SP−CP)÷CP × 100Positive CP; SP>CP
- Loss %
- (CP−SP)÷CP × 100Positive CP; SP<CP
- Discount %
- (MP−SP)÷MP × 100Positive MP; SP≤MP
- Percentage change
- (new−old)÷old × 100Positive old value
- Successive discounts d%,e%
- Final SP=MP×(1−d÷100)×(1−e÷100)Apply discounts to successive prices
Equal Times vs Equal Distances
Two equal-duration segments
- Average speed=(u+v)÷2
- Use constant speeds u,v
Two equal-distance segments
- Average speed=2uv÷(u+v)
- Use positive constant speeds u,v
Match distances or durations first
Ratios and Work
- Ratio a:b
- a÷b; same unitsb≠0
- Share a from a:b
- Total×a÷(a+b)a,b>0; split total into two parts
- Direct proportion
- y÷x remains constantx≠0
- Inverse proportion
- x×y remains constantNonzero quantities
- Finishing time t
- Rate=1÷t jobs per time-unitOne job; t>0; constant rate
- Two workers finishing in a,b
- Combined rate=1÷a+1÷bSame job, time-unit; independent constant rates
- Draining outlet
- Subtract its rate from filling ratesSimultaneous constant rates; consistent units
Motion and Units
- Speed
- Distance÷timeConsistent units; time>0
- km/h → m/s
- Multiply by 5÷18
- m/s → km/h
- Multiply by 18÷5
- Opposite-direction relative speed
- v₁+v₂Same line; approaching each other
- Same-direction relative speed
- |v₁−v₂|Same line; overtaking
- Train clearing platform
- Time=(train length+platform length)÷speedConstant speed; consistent length/time units
- Average speed
- Total distance÷total elapsed time
- Equal-distance average speed
- 2uv÷(u+v)u,v>0; two equal distances
Algebra and Progressions
- Linear equation ax+b=c
- x=(c−b)÷aa≠0
- Unique solution; two linear equations
- a₁b₂−a₂b₁≠0aᵢx+bᵢy=cᵢ; i=1,2
- AP common difference d
- Successive terms differ by d
- AP nth term
- a+(n−1)da=first term; positive integer n
- AP sum of n terms
- n[2a+(n−1)d]÷2a=first term; positive integer n
- Sum 1 through n
- n(n+1)÷2Positive integer n
- Difference of squares
- x²−y²=(x−y)(x+y)All real x,y
Geometry Measures
- Area units
- Squared length units
- Volume units
- Cubed length units
- Triangle area
- base×perpendicular height÷2
- Rectangle area
- length×width
- Circle circumference
- 2πrr=radius
- Circle area
- πr²r=radius
- Cuboid volume
- length×width×height
- Cylinder volume
- πr²hr=radius; h=perpendicular height
Data and Statistics
- Arithmetic mean; n observations
- Sum÷nn>0
- Frequency-weighted mean
- Σfx÷Σfx=value; f=frequency; Σf>0
- Median; odd n
- Sorted value at (n+1)÷2n=positive observation count
- Median; even n
- Mean of two middle sorted valuesn=positive observation count
- Mode
- Value(s) with maximum frequency
- Outcome-counting probability
- Favourable÷total equally likely outcomesFinite nonempty sample space
- Complement
- P(not A)=1−P(A)Same sample space
- Pie-chart sector angle
- Category share×360°Share as fraction of total
Clock Angle Memory
30h against 5.5m; fold angles above 180°.
h: hour modulo 12m: minutes past hourθ: absolute hand-angle differenceSmaller angle: min(θ,360−θ)
Necessary vs Possible
Necessary
- Every permitted case
- Counterexample defeats claim
Possible
- At least one permitted case
- One witness establishes possibility
Must versus can
Logical Method Picker
- Claim: all A are B→Draw A inside B(Converse needs extra evidence)
- Claim: some A are B→Mark a shared member(Existence established)
- Must-be-true conclusion asked→Search for a counterexample(One valid counterexample refutes necessity)
- Necessary assumption asked→Negate the proposed assumption(Argument must fail)
- Calendar date crosses February→Check Gregorian leap status(Count actual elapsed days)
- Passage main idea asked→Choose whole-passage scope(Avoid one supporting detail)
Binary Logic, Clocks, Calendars
- AND
- True only when both true
- Inclusive OR
- True if either/both true
- NOT
- Reverses true and false
- Clock hand-angle difference θ
- |30h−5.5m| degreesh=hour mod12; m=minute reading
- Smaller clock-hand angle
- min(θ,360−θ)θ=absolute hand-angle difference
- Gregorian century leap year
- Divisible by 400
- Gregorian noncentury leap year
- Divisible by 4
- Weekday shift
- Elapsed days modulo 7Use actual Gregorian month lengths
CBT vs CBAT
Written CBT
- 100 MCQs; 120 minutes
- Wrong answer deducts ⅓ mark
- Category eligibility minima apply
Later CBAT
- T-score ≥42 in each battery
- No category relaxation
- No negative marking
CBAT qualifiers: CBT 70%; CBAT 30%
Inference and Reading
- All A are B
- A lies entirely inside B
- Some A are B
- At least one shared member
- No A is B
- A,B share no members
- Main idea
- Central claim spanning the passage
- Supporting detail
- Evidence for a narrower claim
- Necessary assumption
- Its denial defeats the argument
- Required conclusion
- Must follow from stated premises
Eligibility Minimum vs Merit Shortlisting
CBT eligibility
- UR/EWS 40%; OBC-NCL/SC 30%
- ST 25%; ExSM follow community
- Conditional PwBD relaxation: 2 marks
CBAT shortlisting
- CBT merit determines shortlisting
- Multiple-shift CBT scores normalized
- Minimum alone never guarantees selection
PwBD candidate shortage against reserved vacancies
Rank Total
Top plus bottom minus one gives total.
Same personNo tied ranksCount that person only once
Mental Method Picker
- Series pattern seems unclear→Split alternate-position subsequences(Check all supplied terms)
- Alphabet shift crosses Z→Wrap modulo 26(Follow the stated mapping)
- Ranks describe same person→Use top+bottom−1(Distinct ranks; no ties)
- Persons face circle centre→Left moves clockwise(Use each person's viewpoint)
- Persons face circle exterior→Left moves anticlockwise(Use each person's viewpoint)
- Clues allow several arrangements→Test answers across all arrangements(Necessary answers survive every valid case)
Series and Codes
- Analogy
- Preserve the same ordered relationship
- Numeric series
- Check differences, ratios, alternating subsequences
- Wrapping alphabet shift
- Reduce shifted positions modulo 26A=0,…,Z=25
- Mirror alphabet
- New position=27−old positionA=1,…,Z=26
- Codes from examples
- Verify rule against every example
- Finite sequence
- Multiple rules may fit
Ranks and Arrangements
- Top rank r
- Bottom rank=N−r+1N=total; distinct ranks
- Same person's two ranks
- N=top+bottom−1N=total; no tied ranks
- People between ranks r,s
- |r−s|−1Distinct positions; same ranking direction
- Linear-row endpoints
- One adjacent neighbour eachAt least two people
- Circular-row neighbours
- Two adjacent neighbours eachAt least three people
- Inward-facing person's left
- Clockwise from that person's position
- Outward-facing person's left
- Anticlockwise from that person's position
Common Traps
HCF–LCM product boundary
Two positive integers: equals product ≠ Three integers: identity may fail
Prime boundary
One: not prime ≠ Two: only even prime
Percentage reversal
10% rise; 10% fall yields 99% ≠ Equal opposite percentages cancel
Average-speed conditions
Equal times: arithmetic mean ≠ Equal distances: harmonic mean
Converse inference
All A are B ≠ All B are A unproven
CBAT battery threshold
T-score ≥42 in every battery ≠ High total cannot compensate
CBT qualification vs selection
Eligibility minimum reached ≠ Merit shortlisting still required
Last Minute
- 1.CBT: 100MCQs; 120min; wrong answers −⅓
- 2.60/20/20 allocation is indicative
- 3.CBT minima differ from selection cutoffs
- 4.CBAT: T42 in every battery
- 5.CBAT qualifiers: CBT 70%; CBAT 30%
- 6.Profit denominator CP; discount denominator MP
- 7.Speed units must match distance/time
- 8.Outcome-counting probability requires equally likely outcomes
- 9.Leap centuries must divide by 400
- 10.Rank total requires same untied person
- 11.Logical necessity survives every valid case
- 12.Circle left uses the person's facing
- 13.Calculator prohibited; follow current e-call instructions
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