Q81.The number of real roots of the equation e4x −e3x −4e2x −ex + 1 = 0 is equal to
What This Question Tests
This question tests the ability to transform an exponential equation into a polynomial equation using substitution and then find the number of real roots based on the range of the substituted variable.
Concepts Tested
Formulas Used
Quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a
📚 NCERT Sections This Tests
3.23 — The Rate Constant For The Decomposition Of Hydrocarbons Is 2.418 × 10–5S–1
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3.23 The rate constant for the decomposition of hydrocarbons is 2.418 × 10–5s–1 at 546 K. If the energy of activation is 179.9 kJ/mol, what will be the value of pre-exponential factor.
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3.26 The decomposition of hydrocarbon follows the equation k = (4.5 × 1011s–1) e-28000K/T Calculate Ea. 87 Chemical Kinetics Reprint 2025-26
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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.
📋 Question Details
- Chapter
- Quadratic Equations
- Topic
- Roots of equations by substitution
- Year
- 2021
- Shift
- 27 Jul Shift 2
- Q Number
- Q81
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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