Q67.The equation esin x −e−sin x −4 = 0 has (1) infinite number of real roots (2) no real roots (3) exactly one real root (4) exactly four real roots
What This Question Tests
This question tests the ability to transform an equation involving exponential and trigonometric functions into a simpler form and then analyze the existence of real roots based on the range of the trigonometric function.
Concepts Tested
Formulas Used
Let t = e^(sin x), then t - 1/t - 4 = 0
Range of sin x is [-1, 1]
📚 NCERT Sections This Tests
9.15 — Apply Mirror Equation And The Condition:
Physics Class 12 · Chapter 9
9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
9.18 — For Fixed Distance S Between Object And Screen, The Lens Equation
Physics Class 12 · Chapter 9
9.18 For fixed distance s between object and screen, the lens equation does not give a real solution for u or v if f is greater than s/4. Therefore, fmax = 0.75 m.
1.27 — If The Solubility Product Of Cus Is 6 × 10–16, Calculate The Maximum Molarity Of
Chemistry Class 11 · Chapter 1
1.27 If the solubility product of CuS is 6 × 10–16, calculate the maximum molarity of CuS in aqueous solution.
📋 Question Details
- Chapter
- Functions
- Topic
- Range of functions, existence of roots
- Year
- 2012
- Shift
- Offline
- Q Number
- Q67
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 2: Relations and Functions
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