NDA MATHEMATICS QUIZ - 7

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Question 1:

Consider the function $f(x)=\left\{\begin{array}{l}\frac{a^{[x]}+x}{[x]+x} \quad x \neq 0 \\ \text { log a at } x=0\end{array}\right.$  is?

Question 2:

If $f(x)=\cos (\log x)$ then

$f(x y)+f\left(\frac{x}{y}\right)$ equals.

Question 3:

The function defined by $f(x)=\frac{3 x}{\frac{2}{x}}+1+2 \mathrm{c}$, when $x \neq 0=0, x=0$ then $\mathrm{f}^{\prime}(0)$

Question 4:

The function $y=\cos ^{-1}(\sin x)$ is not differentiable at:

Question 5:

Domain of definitin of The function $f(x)= \log _{x\left(x^{2}+1\right)}(x ^2-5 x+6)$ will be

Question 6:

The function $y=x-\tan ^{-1} x$ decreases in the interval.

Question 7:

$\operatorname{Lt}_{x \rightarrow 0}(\cos x)^{1 /x3}$ equals:

Question 8:

$\lim\limits_{x \to \infty}\left(\frac{1}{e^{x}-1}-\frac{1}{x}\right)$. . . . . . . 

Question 9:

$\lim\limits_{n \to \infty}\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\ldots \ldots\right.$ up to $\left.\infty\right)$ is:

Question 10:

A funciton $f(x)$ be defined in such a way that

$f^{\prime}(x)=\frac{x ^3}{3}+c x+2$ where

$f(0)=0$ and $f(6)=210$ then the value of $\mathrm{c}$ is.

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