Mathematics
गणित · BCA · BCA Entrance
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chapters done
- Arithmetic
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The syllabus asks for
- Integers, primes, divisibility, remainders, even and odd results
- HCF and LCM and their word problems
- Ratio, proportion, variation and ages
- Percentage and successive change
- Averages and weighted averages
Key points
- Check divisibility by digit sums and last digits before dividing; primes up to 120 need testing by 2, 3, 5, 7 only.
- n(n+1) is always even; n^3-n is always a multiple of 6.
- HCF × LCM equals the product of the two numbers, and of no other count of numbers.
- "Greatest divisor" means HCF of the differences from the remainders; "least number" means LCM plus the remainder.
- Chain ratios by matching the common term, then divide in parts.
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The syllabus asks for
- Profit, loss, discount and marked price
- Simple and compound interest
- Time and work, pipes and cisterns
- Speed, distance, time, trains and boats
- Mixtures and alligation
- Area, perimeter and volume of plane and solid figures
Key points
- Profit and loss use the cost price; discount uses the marked price.
- Mark up 25 % and discount 20 % gives no gain, no loss.
- For two years, compound interest exceeds simple interest by P(R/100)^2.
- Two workers together take ab/(a+b) days; a leaking pipe subtracts its rate.
- 36 km/h is 10 m/s; multiply by 5/18 to go from km/h to m/s.
- Algebra
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The syllabus asks for
- Sets, subsets, operations and Venn-diagram word problems
- Relations and their types
- Functions, domain, range, composite and inverse functions
Key points
- Count with n(A∪ B)=n(A)+n(B)-n(A∩ B); "neither" is the total minus the union.
- A set of n elements has 2^n subsets, one of them the empty set.
- A-B means A∩ B'.
- Equivalence = reflexive + symmetric + transitive.
- A function gives each input exactly one output; check one-one and onto separately.
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The syllabus asks for
- Laws of indices and surds
- Logarithms and their laws
- Polynomials, remainder and factor theorem
- Quadratic equations, nature and sum and product of roots
- Linear and simultaneous equations, inequalities, equation word problems
Key points
- Reduce to a common base before equating indices.
- log(m+n) cannot be split; log(mn) can.
- D decides the nature of roots; D=0 gives equal roots.
- Use α+β and αβ instead of solving for the roots.
- f(a) is the remainder on division by (x-a).
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The syllabus asks for
- Arithmetic progression
- Geometric progression
- Special sums and mixed problems
Key points
- Count terms first: n=(l-a)/(d)+1.
- Sn for AP is n times the average of first and last.
- Use (a)/(r),a,ar for three GP numbers and a-d,a,a+d for AP.
- S_∞ exists only when |r|<1.
- an=Sn-Sn-1 recovers terms from sums.
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The syllabus asks for
- Types, order and operations on matrices
- Determinants, minors and cofactors
- Adjoint, inverse and solution of linear systems
Key points
- Order m× n: m rows, n columns; a column holds m elements.
- AB exists only if inner orders match, and AB≠ BA in general.
- A zero determinant means singular: no inverse, and a row dependency.
- |kA|=k^n|A|: the factor is raised to the order.
- Reverse the order for (AB)^T and (AB)^-1.
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The syllabus asks for
- Fundamental principle of counting, permutations and combinations
- Probability of events
- Mean, median, mode and measures of dispersion
Key points
- Order matters: permutation. Order does not matter: combination.
- Divide by factorials of repeated letters.
- Subtract from the total for "at least one".
- Independent events multiply; overlapping events subtract the intersection.
- SD ignores a constant shift.
- Trigonometry
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The syllabus asks for
- Trigonometric ratios, standard angles and identities
- Compound, multiple and half angles
- Trigonometric equations and inverse functions
- Heights and distances, triangle properties
Key points
- Memorise the 0°–90° table; every other value reduces to it.
- Complementary angles swap sin with cos, tan with cot.
- Three forms of cos2A; pick the one that fits the data.
- General solution needs nπ for tan and sine, 2nπ for cosine.
- In height problems, draw a right triangle and use tan.
- Coordinate Geometry
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The syllabus asks for
- Distance, section and area formulas
- Slope and forms of the equation of a line
- Angle between lines, parallel and perpendicular lines, distance of a point from a line
Key points
- Use d=√Δ x^2+Δ y^2; memorise 3-4-5 and 5-12-13.
- Convert Ax+By+C=0 to slope -A/B.
- Intercept form needs both intercepts non-zero.
- Parallel lines have equal slopes; perpendicular slopes multiply to -1.
- In the point-line formula the denominator is √A^2+B^2.
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The syllabus asks for
- Equation of a circle, centre and radius, tangent
- Parabola, ellipse and hyperbola in standard form
Key points
- Complete the square or use g,f,c to read a circle off its equation.
- For y^2=4ax read a from the coefficient: y^2=12x gives a=3.
- Ellipse: e<1; hyperbola: e>1.
- Major axis follows the larger denominator.
- Tangent length is √S1, the power of the point.
- Vectors
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The syllabus asks for
- Vector algebra, position vectors and unit vectors
- Dot product, cross product and their applications
Key points
- A vector from A to B is B-A.
- Dot product gives a number, cross product gives a vector.
- Perpendicular means dot product zero.
- |atimesb| is a parallelogram area.
- Unit vectors are found by dividing by the magnitude.
- Calculus
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The syllabus asks for
- Limits of algebraic and trigonometric functions
- Continuity
- Derivatives, rules and standard results
- Tangents, maxima, minima and rates
Key points
- Substitute, then factor or use a standard limit for (0)/(0).
- lim(|sin x|)/(x) does not exist at 0.
- Differentiate by the product rule when two functions of x multiply.
- Stationary points need f'=0; the sign of f'' decides the type.
- Rates multiply by the chain rule.
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The syllabus asks for
- Standard integrals and rules
- Methods: substitution and parts
- Definite integrals and area
Key points
- Add +C to every indefinite integral and omit it in definite ones.
- ∫(1)/(x)dx=ln|x|, not x^0.
- An odd function over a symmetric interval integrates to zero.
- Use parts when a product has a log, inverse-trig or x× e^x.
- Area under y=x^2 from 0 to 3 is 9.
- Reasoning
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The syllabus asks for
- Coding and decoding
- Blood relations and direction sense
- Ranking, ordering and seating
- Syllogisms and statement-conclusion
Key points
- Decode with the first letter, test on the second.
- Draw the family tree; take one link at a time.
- Right turn clockwise, left turn anticlockwise.
- Rankings overlap by exactly one person.
- A conclusion must follow from the statements alone.
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The syllabus asks for
- Number and letter series, odd one out
- Calendar and clock problems
- Counting figures, dice and cubes
- Mixed reasoning
Key points
- Check first and second differences, then squares, cubes, primes.
- Count odd days, then take the remainder by 7.
- Century years are leap only if divisible by 400.
- Use 5.5M for the clock; reduce reflex angles.
- Count squares of every size, not just the smallest.
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The paper
2 hours, 100 single-best-answer MCQs with four options, 100 marks, 1 mark each, no negative marking (third-party sources agree; confirm in the year's notice)
| Section | Questions | Marks each | Total |
|---|---|---|---|
| English grammar 40 | — | — | — |
| Mathematics 50 | — | — | — |
| General Knowledge and IT 10 | — | — | — |
Where the questions are
Questions each part carries in the paper, out of 50. Area totals follow the official syllabus; where single chapters are shown, the split between them is the NEBians estimate.
- Arithmetic10 Qs
- Algebra10 Qs
- Reasoning10 Qs
- Coordinate Geometry7 Qs
- Calculus7 Qs
- Trigonometry4 Qs
- Vectors2 Qs