NDA MATHEMATICS QUIZ - 32

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Question 1:

$\lim _{x \rightarrow 0} \frac{x+\log (1-x)}{x^{2}}$ equals

Question 2:

If $\lim _{x \rightarrow 0} \frac{5\left(\sin x-x+\frac{1}{6} x^{3}\right)}{x^{5}}=\frac{1}{k}$ then $\mathrm{k}$ equals:

Question 3:

$\operatorname{Lim}_{t\rightarrow 0} \frac{\log (1+2 t)-2 \log (1+t)}{t^{2}}=\ldots .$

Question 4:

$\operatorname{Lt}_{x \rightarrow 1}$   $(1-x) \tan \frac{\pi x}{2}=\ldots .$

Question 5:

$\operatorname{Lim}_{x \rightarrow 0} \frac{5^{x}-3^{x}}{3^{x}-2^{x}}=\ldots \ldots$

Question 6:

$\operatorname{Lim}_{x \rightarrow 0} \frac{e^{x^{2}}-\cos x}{x^{2}}$ equals:

Question 7:

$\operatorname{Lim}_{\theta \rightarrow \tan ^{-1} 2}  \quad \frac{\left(\tan ^{2} \theta-2 \tan \theta-3\right)}{\left(\tan ^{2} \theta -4 \tan \theta+3\right)}$ equals:

Question 8:

$\operatorname{Lim}_{t\rightarrow 0} \frac{|t|}{\sqrt{t^{4}+4 t^{2}+9}}$ equals:

Question 9:

$\operatorname{Lim}_{y\rightarrow 0} \frac{\left(1+y^{2}\right)^{\frac{1}{6}}-\left(1-y^{2}\right)^{\frac{1}{6}}}{y^{2}}=\ldots \ldots$

Question 10:

$\operatorname{Lim}_{x \rightarrow 0} \frac{2\left(1-\cos ^{3} x\right)}{x \cdot \sin 2 x}$ is equals to:

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