CUSAT CAT B.Tech common mistakes
CUSAT CAT B.Tech · Understand the traps and how to avoid them.
Solving a radical equation such as √(x+5) = x − 1 by squaring once, getting x = 4 and x = −1, and marking the answer as 'two roots' without substituting either back.
Squaring erases the sign information that the square root carries, so the algebra produces a second root that satisfies the squared equation but not the original one. Nothing in the manipulation signals that a solution was fabricated.
What to do instead
Make back-substitution into the ORIGINAL equation a mandatory written step for every radical, logarithmic and rational equation, and for any answer produced by inverse trigonometry. Reject out-of-domain roots on paper before you touch the option list.
Substituting t = g(x) inside a definite integral, finishing the antiderivative in t, then converting back to x and reusing the original limits a and b instead of the limits g(a) and g(b).
Indefinite-integration practice drills the habit of returning to the original variable, so the substitution step gets automated while limits get skipped. A related form is silently dropping the minus sign when dx = −dt.
What to do instead
Write the new limits on the integral sign in the same line where you write the substitution, and treat returning to x after a definite integral as an error. For sign flips, write dx = −dt explicitly rather than doing it mentally.
Using P(A ∩ B) = P(A)·P(B) for events that are mutually exclusive (for a single die: A = even = {2,4,6}, B = odd = {1,3,5}), and reporting a non-zero joint probability for an impossible intersection.
Independence and mutual exclusivity are both taught as 'the events do not affect each other', and the multiplication rule is the most memorised formula in the chapter, so it gets applied by default whenever two events appear.
What to do instead
Before any probability calculation, write P(A ∩ B) = 0 if the event sets share no outcome, and reserve the product rule for independent events only, justifying independence in one phrase (with replacement, separate trials, etc.).
Applying AM ≥ GM to bound an expression such as x + 1/x, x(1 − x) or a + b when the variables are not restricted to positive values, and reporting a minimum that does not exist on the actual domain.
The inequality is remembered as a tool for 'find the minimum' without its positivity precondition, and the domain given in the question (all reals, or an integer range) is read as decoration rather than as a constraint on the method.
What to do instead
Write the condition 'each term > 0' next to AM ≥ GM before using it; if the variables can be negative, handle the sign cases separately or switch to a derivative-based maximum/minimum. Check the domain line of the question first.
Substituting u = +10 cm for a real object placed 10 cm in front of a lens or mirror in 1/v − 1/u = 1/f, producing an image position on the wrong side or an inverted magnification sign that contradicts the physical setup.
Textbook diagrams show distances as positive magnitudes with arrows, so the number read off the figure is entered directly, and the formula is then used in three different sign conventions across school textbooks.
What to do instead
Fix one axis before any optics or kinematics substitution - distances measured from the pole, positive in the direction of the incident light - write u = −10 cm explicitly, and after solving check that the sign of v and of m agree with a rough ray diagram.
Computing a photoelectric-effect, de Broglie or gas-law answer in the units given (eV, Å, cm, g/cm³, mm of Hg) while the options are printed in joules, nanometres, metres or kg/m³, then choosing the option whose digits match.
The numerical value is produced correctly and the digits in the options often match exactly, so the unit mismatch is invisible unless it is deliberately checked; 1 eV = 1.6 × 10⁻¹⁹ J and 1 Å = 10⁻¹⁰ m conversions are rarely practised under time pressure.
What to do instead
Convert every given quantity to SI on the first line of working, keep the units attached through each step, and finally verify the option by unit as well as by digits. Keep a small conversion table (eV, Å, atm, cal) on your rough sheet.
Treating tension as equal on both sides of a pulley whose mass is stated, or applying F = ma inside a lift, rotating frame or accelerating wedge without adding the pseudo-force or the pulley's rotational term.
Most school problems use a massless, frictionless pulley, so 'T is the same everywhere' becomes an unstated assumption; and pseudo-forces are often memorised as a formula rather than as part of the free-body diagram.
What to do instead
Draw the free-body diagram for each body separately, including the pulley when its mass or moment of inertia is given, and mark the frame of reference at the top of the solution. If the frame accelerates, add −ma before writing Newton's second law.
Calculating the product of a reaction using the reagent present in the larger mass rather than the limiting one, or using the anhydrous formula mass when the question specifies a hydrate such as CuSO₄·5H₂O.
Questions are engineered so the obvious-looking reagent is in excess, and 'limiting reagent' is often identified by comparing masses instead of moles. The water of crystallisation is easy to forget when the formula is written in a familiar short form.
What to do instead
Convert every reactant to moles using the full formula mass including water of crystallisation, divide each by its stoichiometric coefficient, and take the smallest value as the basis. Finish the calculation in moles and convert to mass only at the last step.
Predicting the nitration product of chlorobenzene as meta because 'the substituent is deactivating', or of nitrobenzene as ortho/para for the same slippery reason.
The slogan 'activating = ortho/para, deactivating = meta' is easier to remember than the underlying resonance argument, and the halogens are the one family that breaks the slogan because their lone pairs donate by resonance while withdrawing inductively.
What to do instead
Classify each substituent twice before predicting: resonance effect (+M/−M) decides the position, and inductive/overall effect decides the rate. Mark –Cl, –Br, –I as deactivating but ortho/para directing and test this dichotomy on every aromatic question.
Ordering first ionisation enthalpy strictly by left-to-right position, so N < O and Be < B, and ordering ionic radii by simple cation-smaller, anion-larger rules, missing the Ga < Al-type anomalies.
The periodic trends are learnt as monotonic arrows, and the exceptions come from electron configuration (N 2p³ half-filled, Be 2s² fully filled) and from poor 3d/4f shielding, which are separate facts that are not recalled at the moment of answering.
What to do instead
Write the valence configuration of every species in the comparison before ordering, then override the trend for half-filled and fully filled subshells and for post-d-block elements (Ga vs Al, Zr vs Hf). Two configurations written down take less time than re-guessing the option.