Q85.Let a > 0 be a root of the equation 2x2 + x −2 = 0. If limx→1a 16(1−cos(2+x−2x2))(1−ax)2 α, β ∈Z , then α + β is equal to_______
What This Question Tests
This question is complex, involving finding roots of a quadratic, evaluating a limit with an indeterminate form, and then solving for integer values. It tests advanced limit techniques, likely L'Hopital's rule or series expansion, multiple times.
Concepts Tested
Formulas Used
lim(x->0) (1-cos(kx))/x^2 = k^2/2
lim(x->0) (e^(kx)-1)/x = k
L'Hopital's Rule
📚 NCERT Sections This Tests
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Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
1.27 — If The Solubility Product Of Cus Is 6 × 10–16, Calculate The Maximum Molarity Of
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1.27 If the solubility product of CuS is 6 × 10–16, calculate the maximum molarity of CuS in aqueous solution.
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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.
📋 Question Details
- Chapter
- Limits & Continuity
- Topic
- Limits involving indeterminate forms
- Year
- 2024
- Shift
- 05 Apr Shift 2
- Q Number
- Q85
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 5: Continuity and Differentiability
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