1st Semester Practice Test (sample)
-
Q1. lim (x → 0) of (sin x) / x is
Solution
This is the standard limit: (sin x)/x → 1 as x → 0 (by the squeeze theorem, cos x ≤ (sin x)/x ≤ 1 near 0).
-
Q2. gcd(56, 98) is
Solution
56 = 2³ × 7 and 98 = 2 × 7². Common part: 2 × 7 = 14.
-
Q3. The derivative of xˣ (x > 0) is
Solution
Let y = xˣ, so ln y = x ln x. Differentiate: y′/y = ln x + 1, so y′ = xˣ (1 + ln x).
-
Q4. The eccentricity of a parabola is
Solution
Circle e = 0, ellipse 0 < e < 1, parabola e = 1, hyperbola e > 1.
-
Q5. How many positive divisors does 36 have?
Solution
36 = 2² × 3². Number of divisors = (2 + 1)(2 + 1) = 9.
-
Q6. ∫₀¹ x² dx equals
Solution
∫ x² dx = x³/3. From 0 to 1: 1/3 − 0 = 1/3.
Prepare 1st Semester with AIFM
Syllabus, PYQs, important questions and full courses.
Open 1st Semester