Mathematics
गणित · IOE · BE/BArch Engineering Entrance
0 / 7
chapters done
-
The syllabus asks for
- Set, real number system, intervals, absolute value, logic, connectives, laws of logic
- Function, types of functions: injective, surjective, bijective, algebraic, trigonometric, exponential and logarithmic; inverse of a function, composite functions
Key points
- A set of n elements has 2^n subsets, 2^n-1 proper ones.
- Use inclusion-exclusion; keep the three-set formula's alternating signs.
- |x-a|<r is an interval around a; >r is its outside.
- p→ q is false only for T → F; the contrapositive is equivalent, the converse is not.
- Injective means distinct inputs give distinct outputs; onto means range = codomain.
-
The syllabus asks for
- Matrices and determinants, types and properties, inverse of a matrix
- Complex numbers and polynomial equations
- Sequence and series, permutation and combination
- Binomial theorem, exponential and logarithmic series
Key points
- Determinants scale as k^n; rows in AP, or two proportional rows, give zero.
- A^-1 needs |A|≠0; for 2×2 swap the diagonal and negate the rest.
- Reduce powers of i and ω by their cycles (4 and 3).
- For any quadratic question first write the sum and product of the roots.
- tn=Sn-Sn-1 and the infinite GP needs |r|<1.
-
The syllabus asks for
- Trigonometric equations and general values
- Inverse trigonometric functions, principal value
- Properties of triangles, in-centre, ortho-centre and circum-centre, solution of triangles
Key points
- Reduce to one trig function, factorise, then write the general solution of each factor.
- |c|>√a^2+b^2 means no solution to asinθ+bcosθ=c.
- Know the three principal ranges; sin^-1(sin x) folds x into [-π/2,π/2].
- For two triangle quantities, find Δ first (Heron), then r=Δ/s or R=abc/4Δ.
- A right triangle has R= half the hypotenuse.
-
The syllabus asks for
- Straight lines, pair of lines
- Circles, equations of circle in different forms, tangent and normal
- Conic sections: parabola, ellipse and hyperbola, standard equations and simple properties
- Coordinates in space, plane and its equation
Key points
- Distance, angle and area formulas for lines are one-liners; learn them exactly.
- x^2+y^2+2gx+2fy+c=0: centre (-g,-f), radius √g^2+f^2-c.
- Tangency to a circle is c^2=r^2(1+m^2); to a parabola c=a/m.
- Latus rectum: 4a for the parabola, 2b^2/a for ellipse and hyperbola.
- A plane's normal is (a,b,c); parallel planes differ only in d.
-
The syllabus asks for
- Limit and continuity of functions, indeterminate forms, L'Hospital's rule
- Derivatives, rules of derivatives, geometrical and physical meanings, higher order derivatives, applications of derivative: tangent and normal, rate of change, maxima and minima
- Integration, linear properties, rules of integration, standard integrals, definite integral, applications of definite integral: area under a curve and area between two curves
- Differential equations: definition, order and degree, first order and first degree: variable separable, homogeneous, linear and exact equations, integrating factor
Key points
- Standard limits plus L'Hôpital settle every limit; check the form before using L'Hôpital.
- Chain rule, parametric and logarithmic differentiation cover all derivative types.
- Critical points from f'=0; the sign of f'' decides max or min; compare endpoints on closed intervals.
- Integrate by substitution, by parts (ILATE) or by the e^x(f+f') pattern; use symmetry for definite integrals.
- Areas: find the intersections, then integrate top minus bottom.
-
The syllabus asks for
- Vectors in plane and space, algebra of vectors, linear combination of vectors, linearly dependent and independent sets of vectors
- Product of two vectors, scalar and vector product of two vectors, scalar triple product
Key points
- Head minus tail gives overrightarrowAB; the section formula weights the opposite end.
- Dot product zero means perpendicular; cross product zero means parallel; triple product zero means coplanar.
- Projection is (vec a·vec b)/(|vec a|), a signed scalar.
- Areas come from |vec a×vec b|, volumes from the scalar triple product.
-
The syllabus asks for
- Measures of location and measures of dispersion
- Correlation and regression
- Basic terms of probability, conditional and compound probability, additive and multiplicative rules, Bayes' theorem, binomial distribution
Key points
- Mean, median, mode answer "where"; σ and CV answer "how spread out"; spread ignores a shift.
- Both regression lines meet at the means; r^2=byxbxy.
- For "at least one", use the complement.
- Bayes' theorem reverses a conditional: weigh each cause by prior × likelihood, then normalise.
- Binomial needs a fixed n, independent trials and a constant p.
No chapter matches. Try another word.
The paper
computer-based, 2 hours, 100 MCQs with four options, 140 marks: Section A 60 x 1, Section B 40 x 2; 10% of a question's marks deducted for a wrong answer
| Section | Questions | Marks each | Total |
|---|---|---|---|
| Mathematics 50 | — | — | — |
| Physics 40 | — | — | — |
| Chemistry 30 | — | — | — |
| English 20 | — | — | — |
Where the questions are
Questions each part carries in the paper, out of 35. Area totals follow the official syllabus; where single chapters are shown, the split between them is the NEBians estimate.
- Chapter 2 · Algebra8 Qs
- Chapter 5 · Calculus8 Qs
- Chapter 4 · Coordinate Geometry6 Qs
- Chapter 3 · Trigonometry4 Qs
- Chapter 1 · Set, Logic and Functions3 Qs
- Chapter 6 · Vectors and their Products3 Qs
- Chapter 7 · Statistics and Probability3 Qs