Q72.The number of real solutions of x7 + 5x3 + 3x + 1 = 0 is equal to _____. (1) 0 (2) 1 (3) 3 (4) 5
What This Question Tests
The problem requires determining the number of real solutions of a polynomial equation by analyzing the monotonicity of the function using its first derivative.
Concepts Tested
Formulas Used
If f'(x) > 0, function is increasing
📚 NCERT Sections This Tests
1.1 — Define The Term Solution. How Many Types Of Solutions Are Formed? Write Briefly
Chemistry Class 11 · Chapter 1
1.1 Define the term solution. How many types of solutions are formed? Write briefly about each type with an example.
1.3 — Define The Following Terms:
Chemistry Class 11 · Chapter 1
1.3 Define the following terms: (i) Mole fraction (ii) Molality (iii) Molarity (iv) Mass percentage.
3.23 — The Rate Constant For The Decomposition Of Hydrocarbons Is 2.418 × 10–5S–1
Chemistry Class 11 · Chapter 3
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.
📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Monotonicity of Functions
- Year
- 2022
- Shift
- 28 Jun Shift 1
- Q Number
- Q72
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
More from this Chapter
Q87.If p and q are positive real numbers such that p2 + q2 = 1 , then the maximum value of (p + q) is (1) 2 (2) 1/2 (3) 1 (4) √2 √2
Q93.Suppose the cube x3 −px + q has three distinct real roots where p > 0 and q > 0. Then which one of the following holds? (1) The cubic has minima at √p3 and maxima at (2) The cubic has minima at −√p3 and maxima at −√p3 √p3 and The cubic has maxima at both and (3) The cubic has minima at both √p3 −√p3 (4) √p3 −√p3
Q94.How many real solutions does the equation x7 + 14x5 + 16x3 + 30x −560 = 0 have? (1) 7 (2) 1 (3) 3 (4) 5
Q81.Given P(x) = x4 + ax3 + bx2 + cx + d such that x = 0 is the only real root of P ′(x) = 0 . If P(−1) < P(1), then in the interval [−1, 1] (1) P(−1) is the minimum and P(1) is the (2) P(−1) is not minimum but P(1) is the maximum maximum of P of P (3) P(−1) is the minimum and P(1) is not the (4) neither P(−1) is the minimum nor P(1) is the maximum of P maximum of P