class="wp-custom-logo wp-embed-responsive wp-theme-astra monomath-custom-page ally-default esm-default ast-desktop ast-separate-container ast-two-container ast-no-sidebar astra-4.12.7 ast-inherit-site-logo-transparent ast-hfb-header"
← Back to CBSE-11

Limits and Derivatives - Previous Year Questions

⏱️ Est. Revision Time: 15 Mins
🔍
📅 Year 2024
Q1
CBSE Board Exam 20243 Marks
Evaluate: lim(x→0) (sin 4x)/(sin 6x).
▶ Show Detailed Solution
lim(x→0) sin 4x/sin 6x = lim [ (sin 4x)/(4x) ] / [ (sin 6x)/(6x) ] × (4x/6x)
= (1/1) × 4/6 = 2/3.
Q2
CBSE Board Exam 20242 Marks
Find the derivative of x sin x w.r.t. x, using the product rule.
▶ Show Detailed Solution
d/dx (x sin x) = x·cos x + sin x·1 = x cos x + sin x.
📅 Year 2023
Q1
CBSE Board Exam 20234 Marks
Evaluate: lim(x→0) (1 − cos 2x)/(x²).
▶ Show Detailed Solution
1 − cos 2x = 2 sin² x.
Limit = lim(x→0) 2 sin² x / x² = 2 [lim(sin x/x)]² = 2 × 1 = 2.