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Class 11 Mathematics: Limits and Derivatives
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MCQs on limits, trigonometric functions limits, derivatives and its intuitive idea, first and second order derivatives.
 

Class 11 Mathematics: Limits and Derivatives
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25 Questions

1. What will be the domain of the function, if 3x + 3f(x) = minimum of Φ(t), where Φ(t) = minimum of (2t3 – 15t2 + 36t – 25, 2 + |sint|; 2 ≤ t ≤ 4} ?
2. f(x) is a polynomial of degree 4, vanishes at x = -1 and has local minimum/maximum at x = 1, x = 2, and x = 3. If, -2∫2 f(x) dx = -1348/15. Then what is the value of f(x)?
3. What will be the form of the equation after eliminating a and b from the equation y = a sin-1x + b cos-1x?
4. What is the value of \(\frac{d}{dx}\) (sin⁡ x tan⁡ x)?
5. If functions f(x) and g(x) are continuous in [a, b] and differentiable in (a, b) then which of the following is correct if there exists at least one point c, a < c < b, such that \(\begin{vmatrix}f(a) & f(b) \\g(a) & g(b) \end {vmatrix}\)?
6. If, y = tan-1(x/a), then what is the value of y'?
7. What is the value of the limit f(x) = \(\frac{sin^2⁡x+\sqrt 2 sin ⁡x}{x^2-4x}\) if x approaches 0?
8. What is the value of \(\frac{d}{dx}(\frac{a^x}{e^x})\)?
9. What will be the maximum area of an isosceles triangle inscribed in the ellipse x2/a2 + y2/b2 = 1 if its vertex at one end of the major axis?
10. What is the value of (x + y)2y' if x = et sint and y = et cost?
11. At which point will f(x) attain a maxima where, \(\mbox{f}(x)=\left\{
(sin(\frac{\pi x}{2}), & \mbox{$x \gt 1$} \\
3 – 2x, & \mbox{$x \geq 1$}
12. Which of the following limits does not yield 1?
13. Which is greater (1/2)e or 1/e2 if there is a given function sinx(sinx), 0 < x < π?
14. The function y = f(x) is represented parametrically by x = t5 – 5t3 – 20t + 7 and y = 4t3 – 3t2 – 18t + 3 (-2 < t < 2). At which point does y = f(x) has a minimum value?
15. If A (x1, y1) and B (x2, y2) be two points on the curve y = ax2 + bx + c, then as perLagrange’s mean value theorem whichof the following is correct?
16. What is the value of (∞)0 and 1∞?
17. At which point will f(x) attain a minima where, \(\mbox{f}(x)=\left\{
\begin{array}
(x^3+x^2+10x & \mbox{$x \gt 0$} \\
3 sinx, & \mbox{$x \leq 0$}
\end{array} \right.
\)?
18. What is the value of \(\frac{d}{dx}\) (sin⁡ x3 cos⁡ x2)?
19. What is the value of (dy/dx)2 + 1 if x = a sin2θ(1 + cos2θ) and y = a cos2θ(1 – cos2θ)?
20. If f(x) = |4x – x2 – 3| when x € [0, 4], then, which of the following is correct?
21. What is the value of ln ⁡\(\frac{3}{x}\)?
22. What is the value of 4a cos3θ(d2y/dx2) if x = a sin2θ(1 + cos2θ) and y = a cos2θ(1 – cos2θ)?
23. What is the value of the \(\lim\limits_{x \rightarrow \frac{3\pi}{2}}\frac{cos⁡ x sin⁡ x}{sin⁡2x}\)?
24. Let f (x) = (x – a) (x – b) (x – c), a < b < c. Then f'(x) = 0 has two roots. At which interval does these roots belongs?
25. If y = (3x – 4)/(x+2) then what s the value of dy/dx?

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