FAST-NU & UET Entrance Exam Prep Portal
Train for FAST-NU, UET ECAT, and NUST NET with rigorous Advanced Mathematics, Analytical Reasoning, and Physics speed drills calibrated for strict negative marking penalties.
Start Engineering Mock DrillFAST-NU Exam Pattern & Critical Strategy
Advanced Mathematics (50%)
Calculus derivatives, definite integrals, conic sections, matrices, permutations & trigonometric series.
Basic & Analytical Math (20%)
Percentages, ratios, word problems, algebraic systems, and rate-of-work questions that demand rapid mental computation.
Physics & English (30%)
Conceptual mechanics, rotational dynamics, electromagnetism, and reading comprehension under time limits.
Sample Advanced Math Entry Test Question
Calculus & Limits
Evaluate the trigonometric limit: lim (x → 0) [sin(5x) / tan(2x)].
A) 5/2 (Correct)
B) 2/5
C) 1
D) 0
Rapid Derivation: Using the standard trigonometric limit theorem lim(u → 0) sin(u)/u = 1 and lim(u → 0) tan(u)/u = 1: [sin(5x) / tan(2x)] = [ (sin(5x)/(5x))*5x ] / [ (tan(2x)/(2x))*2x ]. As x approaches 0, the ratio simplifies directly to 5x / 2x = 5/2. Shortcut: directly divide the coefficients of the trigonometric arguments: 5 / 2.