Skip to main content
JEE Main · JEE Advanced · CUET

Common traps in JEE and CUET maths

The mistakes that cost the most marks, from the 13 chapter sets and the timed sets, with the fix for each. Read the general list first, then the chapters you are working on.

Traps in every chapter

  • Answering every question. With negative marking, a wrong answer costs more than a blank. Guess only when you can rule out at least one option.
  • Stopping at the first option that looks right. Substitute it back, or check it against a quick special case (put x = 0 or x = 1) before you move on.
  • Principal values. sin⁻¹ and tan⁻¹ give angles in [−π/2, π/2]; cos⁻¹ gives [0, π]. Check the range before you write the answer.
  • Dividing by something that can be zero. Dividing both sides by cos x, or by (x − 1), throws away solutions. Factorise instead.
  • Strict and non-strict inequalities. A square root in a denominator needs > 0, not ≥ 0; check the end points of every interval.
  • Determinants of multiples. For an n × n matrix, |kA| = kⁿ|A| and |adj A| = |A|ⁿ⁻¹.
  • Numerical-value answers. There are no options to check against: re-read what the question asks for (2L, 3A, the larger root) before you type.

Sets, relations and functions

  • Relations. Counting the 12 off-diagonal pairs one by one (giving \(2^{12}\)) forgets that symmetry ties each pair to its mirror image.
  • Inverse of a function. The reciprocal \(\dfrac{x-1}{2x+3}\) is \(1/f(x)\), not the inverse function.
  • Onto functions. Subtracting \(3 \times 2^5\) and stopping gives 147: the three constant functions were removed twice.
  • Domain. Using \(\ge 0\) under a square root in a denominator lets in \(x = 2\) and \(x = 3\), where the function is undefined.

Practise sets, relations and functions

Trigonometry and inverse trigonometric functions

  • Trigonometric equations. Dividing both sides by \(\cos x\) throws away the two solutions where \(\cos x = 0\).
  • Principal values. \(\sin^{-1}(\sin\theta) = \theta\) only when \(\theta\) is already in \([-\pi/2, \pi/2]\); \(5\pi/6\) is not.
  • Maximum value. Adding the largest values of the two terms separately (7 + 24 + 5 = 36) is wrong: \(\sin x = 1\) and \(\cos x = -1\) never happen together.
  • Inverse trigonometric functions. Using \(\tan^{-1}a + \tan^{-1}b = \tan^{-1}\frac{a+b}{1-ab}\) when \(ab > 1\) gives \(-\pi/4\), a negative sum of positive angles: add \(\pi\).
  • Principal values. \(-\pi/6\) has the right cotangent but is outside \(\cot^{-1}\)'s principal range \((0, \pi)\).

Practise trigonometry and inverse trigonometric functions

Complex numbers and quadratic equations

  • Nature of roots. \(k = \pm 6\) give equal (real) roots, so they are excluded.
  • Locus. \(|z + 2i|\) is the distance from \(-2i\), not from \(2i\).

Practise complex numbers and quadratic equations

Permutations, combinations and the binomial theorem

  • Binomial coefficients. Forgetting to raise the 2 to the fourth power gives \(\binom64 = 15\) or \(2 \times 15\).
  • Term independent of x. Forgetting the \(2^r\) from \(\left(\tfrac{2}{x}\right)^r\) gives 28.
  • Counting numbers. Treating all four even endings alike (\(4 \times 6 \times 5 \times 4 = 480\)) lets 0 lead the number when the last digit is not 0.
  • Selections with a condition. Choosing 2 women first and then any 3 of the remaining 8 counts some committees more than once.

Practise permutations, combinations and the binomial theorem

Sequences and series

  • nth term from the sum. \(S_{10}/10 = 35\) is the average of the first ten terms, not the tenth term.

Practise sequences and series

Straight lines and conic sections

  • Distance between parallel lines. Using \(|c_1 - c_2|\) before making the \(x\) and \(y\) coefficients equal gives \(22/13\).
  • Ellipse. \(25/169\) is \(e^2\): take the square root.
  • Hyperbola. \(c^2 = a^2 - b^2\) is the ellipse rule; for a hyperbola it is \(a^2 + b^2\).

Practise straight lines and conic sections

Matrices and determinants

  • Adjoint. \(|3A| = 3|A|\) is wrong for a \(3 \times 3\) matrix: each of the three rows is multiplied by 3.
  • Systems of equations. A zero determinant alone could also mean no solution: always check the equations are consistent.
  • Area by determinants. The determinant gives twice the area: forgetting the \(\tfrac12\) gives 15.

Practise matrices and determinants

Limits, continuity and differentiability

  • Standard limits. Using \(1 - \cos 6x \approx \tfrac{6x^2}{2}\) instead of \(\tfrac{(6x)^2}{2}\) gives 3: square the whole angle.
  • Limits of the form 1 to the infinity. A base tending to 1 does not make the limit 1 when the power tends to infinity.

Practise limits, continuity and differentiability

Application of derivatives

  • Absolute maximum. Looking only at critical points misses that an end point can tie with, or beat, a local maximum.

Practise application of derivatives

Integrals, areas and differential equations

  • Integrals with modulus. Integrating \(x^2 - 1\) straight through gives \(4/3\): the part below the axis counts negatively.
  • Order and degree. The degree is the power of the highest-order derivative, not the largest power anywhere in the equation.

Practise integrals, areas and differential equations

Vectors and three-dimensional geometry

  • Area of a parallelogram. \(\tfrac12|\vec a \times \vec b|\) is the area of the triangle, not the parallelogram.
  • Direction cosines. Direction ratios \((2, 3, 6)\) are not direction cosines until they are divided by the length.

Practise vectors and three-dimensional geometry

Statistics and probability

  • Independent events. Adding \(P(A) + P(B) = 13/20\) counts the overlap twice.
  • Bayes' theorem. \(2/5\) is \(P(X \text{ and green})\), not \(P(X \mid \text{green})\).

Practise statistics and probability

Linear inequalities and linear programming

  • Linear programming. Missing the corner \((3, 1)\), where \(x = 3\) meets \(x + y = 4\), gives 12.
  • Multiple optimal points. When two adjacent corners tie, the optimum is the whole edge, not one corner.
  • Systems of inequalities. The strict inequality \(x < 6\) leaves out 6.

Practise linear inequalities and linear programming

From the timed sets

For the board paper's own mark losses, see each chapter's "Where marks are lost" on the Class 11 and Class 12 pages and Common mistakes. To win back time as well as marks, see Formulas and exam strategy.