Q85.If f(x) = sin(cos−1( 1+22x1−22x )) and its first derivative with respect to b are integers, then the minimum value of a2 −b2 is _______.
What This Question Tests
This problem requires simplifying a complex inverse trigonometric function using substitution before differentiating, testing knowledge of inverse trigonometric identities and chain rule.
Concepts Tested
Formulas Used
cos⁻¹((-y)) = π - cos⁻¹(y)
d/dx (sin(u)) = cos(u) * du/dx
d/dx (tan⁻¹(x)) = 1/(1+x²)
📚 NCERT Sections This Tests
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2.5 A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = 10–12 F). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?
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2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
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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.
📋 Question Details
- Chapter
- Calculus
- Topic
- Differentiation
- Year
- 2021
- Shift
- 17 Mar Shift 1
- Q Number
- Q85
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 5: Continuity and Differentiability
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