InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
If y = log x then y2 = (a) \(\frac{1}{x}\)(b) \(-\frac{1}{x^2}\)(c) \(-\frac{2}{x^2}\)(d) e2 |
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Answer» (b) \(-\frac{1}{x^2}\) y = log x ∴ y1 = \(\frac{1}{x}\) ∴ y2 = \(\frac{-1}{x^2}\) |
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| 52. |
Which of the following function is neither even nor odd? (a) f(x) = x3 + 5 (b) f(x) = x5 (c) f(x) = x10 (d) f(x) = x2 |
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Answer» (a) f(x) = x3 + 5 Since it has a constant term 5. f(x) = x3 + 5 f(-x) = (-x)3 + 5 = -x3 + 5. It is not either f(x) or -f(x). |
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| 53. |
If f(x) = x2 and g(x) = 2x + 1 then (fg)(0) is: (a) 0 (b) 2 (c) 1(d) 4 |
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Answer» (a) 0 (fg)(0) = f(0) g(0) = 02 (2(0) + 1) = 0(1) = 0 |
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| 54. |
If f(x) = 2x and g(x) = \(\frac{1}{2^x}\) then (fg)(x) is: (a) 1 (b) 0 (c) 4x (d) \(\frac{1}{4^x}\) |
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Answer» (a) 1 (fg) x = f(x) g(x) = 2x x \(\frac{1}{2^x}\) = 1 |
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| 55. |
If f(x) = ex and g(x) = loge x then find (i) (f + g) (1) (ii) (fg) (1) (iii) (3f) (1) (iv) (5g) (1) |
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Answer» (i) (f + g) (1) = e1 + loge 1 = e + 0 = e (ii) (fg) (1) = f(1) g(1) = e1 loge1 = e x 0 = 0 (iii) (3f) (1) = 3 f(1) = 3 e1 = 3e (iv) (5g) (1) = 5 (g) (1) = 5 loge1 = 5 x 0 = 0 |
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| 56. |
Solve: x3 + y3 = 3axy |
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Answer» Given x3 + y3 = 3axy 3x2 + 3y2\(\frac{dy}{dx}\) = 3a(x .\(\frac{dy}{dx}\) + y.1) \(\frac{dy}{dx}\)(3y2 – 3ax) = 3ay – 3x2 = \(\frac{dy}{dx}\) = \(\frac{ay - x^2}{y^2 - ax}\) |
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