Q87.Let P(x) be a real polynomial of degree 3 which vanishes at x = −3. Let P(x) have local minima at x = 1 , local maxima at x = −1 and ∫1−1 P(x)dx = 18 , then the sum of all the coefficients of the polynomial P(x) is equal to ___ .
What This Question Tests
This is a multi-concept problem requiring the use of derivative properties for local extrema to find the form of the polynomial, integrating it to determine coefficients, and then finding the sum of coefficients by evaluating the polynomial at x=1.
Concepts Tested
Formulas Used
P'(x) = k(x-x1)(x-x2) for critical points x1, x2
∫ P(x) dx
Sum of coefficients P(1)
📚 NCERT Sections This Tests
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
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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.
1.18 — A Point Charge Of 2.0 Mc Is At The Centre Of A Cubic Gaussian
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1.18 A point charge of 2.0 mC is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?
9.15 — Apply Mirror Equation And The Condition:
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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
- Applications of Derivatives
- Topic
- Local maxima/minima and polynomial properties
- Year
- 2021
- Shift
- 18 Mar Shift 2
- Q Number
- Q87
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
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