Q72. sin(πcos2x) lim is equal to x→0 x2 (1) −π (2) π (3) π (4) 1 2
What This Question Tests
This question tests the evaluation of limits involving trigonometric functions, requiring algebraic manipulation to apply standard limit forms or the use of L'Hopital's rule.
Concepts Tested
Formulas Used
lim(u→0) sin(u)/u = 1
cos 2x = 1 - 2sin²x
lim(u→0) (1-cos u)/u² = 1/2
📚 NCERT Sections This Tests
12.5 — A Hydrogen Atom Initially In The Ground Level Absorbs A Photon,
Physics Class 12 · Chapter 12
12.5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
11.6 — The Threshold Frequency For A Certain Metal Is 3.3 × 1014 Hz. If Light
Physics Class 12 · Chapter 11
11.6 The threshold frequency for a certain metal is 3.3 × 1014 Hz. If light of frequency 8.2 × 1014 Hz is incident on the metal, predict the cut- off voltage for the photoelectric emission.
11.8 — Light Of Frequency 7.21 × 1014 Hz Is Incident On A Metal Surface.
Physics Class 12 · Chapter 11
11.8 Light of frequency 7.21 × 1014 Hz is incident on a metal surface. Electrons with a maximum speed of 6.0 × 105 m/s are ejected from the surface. What is the threshold frequency for photoemission of electrons?
📋 Question Details
- Chapter
- Limits & Continuity
- Topic
- Limits using L'Hopital's rule or standard limits
- Year
- 2014
- Shift
- 06 Apr
- Q Number
- Q72
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 13: Limits and Derivatives
More from this Chapter
Q97.The function f : R ∼{0} →R given by f(x) = x1 − e2x−12 can be made continuous at x = 0 by defining f(0) as (1) 2 (2) −1 (3) 0 (4) 1
Q92.Let f(x) = −1) sin ( {(x0, if x = 1 JEE Main 2008 JEE Main Previous Year Paper (1) f is neither differentiable at x = 0 nor at x = 1 (2) f is differentiable at x = 0 and at x = 1 (3) f is differentiable at x = 0 but not at x = 1 (4) f is differentiable at x = 1 but not at x = 0
Q70.Let f : R →R be a positive increasing function with limx→∞ f(3x)f(x) = 1. Then limx→∞ f(2x)f(x) (1) 2 (2) 3 3 2 (3) 3 (4) 1
Q71.Consider the following statements P : Suman is brilliant Q : Suman is rich R : Suman is honest The negation of the statement "Suman is brilliant and dishonest if and only if Suman is rich" can be expressed as (1) ∼(Q ↔(P∧∼R)) (2) ∼Q ↔∼P ∧R (3) ∼(P∧∼R) ↔Q (4) ∼P ∧(Q ↔∼R)