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Class 11 Maths Practice Test - First Order Derivative
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Class 11 Maths Practice Test - First Order Derivative
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19 Questions

1. 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 \(\begin{vmatrix}f(a) & f(b) \\g(a) & g(b) \end {vmatrix}\)?
2. What will be the value of dy/dx if x = asec2θ and y = atan3θ at θ = π/4?
3. If y = (3x – 4)/(x+2) then what s the value of dy/dx?
4. What will be the value of \(\lim\limits_{x \rightarrow 1} x^{\frac{1}{1-x}}\)?
5. At which point will f(x) attain a minima where, \(\mbox{f}(x)=\left\{
\begin{array}
(x^3+x^2+10x & \mbox{$x \gt 0$} \\
3 sinx, & \mbox{$x \leq 0$}
\end{array} \right.
\)?
6. At which point will f(x) attain a maxima where, \(\mbox{f}(x)=\left\{
\begin{array}
(sin(\frac{\pi x}{2}), & \mbox{$x \gt 1$} \\
3 – 2x, & \mbox{$x \geq 1$}
\end{array} \right.
\)?
7. 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?
8. At which point will f(x) attain a maxima where, \(\mbox{f}(x)=\left\{
\begin{array}
(sin(\frac{\pi x}{2}), & \mbox{$x \gt 1$} \\
3 – 2x, & \mbox{$x \geq 1$}
\end{array} \right.
\)?
9. If \(\lim\limits_{x \rightarrow a}\frac{(a^x-x^a)}{x^x-a^a}\) = -1 then, what is the value of a?
10. 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)?
11. What is the value of (dy/dx)2 + 1 if x = a sin2θ(1 + cos2θ) and y = a cos2θ(1 – cos2θ)?
12. What is the value of (∞)0 and 1∞?
13. If \(\lim\limits_{x \rightarrow a}\frac{(a^x-x^a)}{x^x-a^a}\) = -1 then, what is the value of a?
14. 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 \(\begin{vmatrix}f(a) & f(b) \\g(a) & g(b) \end {vmatrix}\)?
15. What will be the value of \(\lim\limits_{x \rightarrow 1} x^{\frac{1}{1-x}}\)?
16. If, y = 1/(1 + x + x2 + x3), then what is the value of y’ at x = 0?
17. Is Rolle’s theorem valid for f(x) = x2 – 3x + 4 in the interval [1, 2]?
18. What is the value of (dy/dx)2 + 1 if x = a sin2θ(1 + cos2θ) and y = a cos2θ(1 – cos2θ)?
19. What is the number of critical points of f(x) = |x2 – 1| / x2?

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