MCQ 11 Mark$\lim _{x \rightarrow 0} \frac{\sqrt{1-\cos 2 x}}{\sqrt{2} x}$ is equal to :✓$1$B$-1$C$0$Ddoes not existAnswerCorrect option: A. $1$AView full question & answer→
MCQ 21 MarkIf $f(x)=\left\{\begin{array}{cc}2 x+b, & x<\alpha \\ x+d, & x \geq \alpha\end{array}\right.$ is such that $\lim _{x \rightarrow \alpha} f(x)=l$, then $l$ is equal to :✓$2 d-b$B$2 b-d$C$2 d+b$D$b-2 d$AnswerCorrect option: A. $2 d-b$AView full question & answer→
MCQ 31 MarkIf $\lim _{x \rightarrow 0}\left(1+\frac{a}{x}+\frac{b}{x^2}\right)^{2 x}=e^2$, then values of $a$ and $b$ are equal to :A$a \in R , b=2$✓$a=1, b \in R$C$a \in R , b \in R$D$a=1, b=2$AnswerCorrect option: B. $a=1, b \in R$BView full question & answer→
MCQ 41 MarkIf $\lim _{x \rightarrow 0} \frac{[(a-n) n x-\tan x] \sin x}{x^2}=0$, where $n$ is non -zero real number, then $a$ is equal to :A$0$B$\frac{n+1}{n}$C$n$✓$n+\frac{1}{n}$AnswerCorrect option: D. $n+\frac{1}{n}$DView full question & answer→
MCQ 51 MarkIf $\lim _{x \rightarrow 0} \frac{\log (3+x)-\log (3-x)}{x}= K$, then value of K is equal to :A$0$B$-\frac{1}{3}$✓$\frac{2}{3}$D$-\frac{2}{3}$AnswerCorrect option: C. $\frac{2}{3}$CView full question & answer→
MCQ 61 MarkDerivative of $\log _e \sqrt{x}$ is equal to :✓$\frac{1}{2 x}$B$\frac{1}{2 \sqrt{x}}$C$2 \sqrt{x}$D$\frac{1}{2} \sqrt{x}$AnswerCorrect option: A. $\frac{1}{2 x}$AView full question & answer→
MCQ 71 MarkIf $f(x)=\frac{2 x+c}{x-1}$ and $f^{\prime}(0)=0$, then value of $c$ is equal to :A$0$B1C2✓-2AnswerCorrect option: D. -2DView full question & answer→
MCQ 81 MarkDerivative of $\sec x^{o}$ is equal to :A$\sec x^{\circ} \tan x^{\circ}$B$\frac{\pi}{180} \sec x \tan x$✓$\frac{\pi}{180} \sec x^{\circ} \tan x^{\circ}$D$\sec x \tan x$AnswerCorrect option: C. $\frac{\pi}{180} \sec x^{\circ} \tan x^{\circ}$CView full question & answer→
MCQ 91 MarkIf $f(x)=x^3+6 x^2-5$, then $f^{\prime}(1)$ is equal to :A$0$B9C4✓15AnswerCorrect option: D. 15DView full question & answer→
MCQ 101 Mark$\frac{d}{d x}\left(\log _a x\right)$ is equal to :✓$\frac{1}{x \cdot \log _e a}$B$\frac{\log _e a}{x}$C$\frac{1}{x}$D$\frac{x}{\log _e a}$AnswerCorrect option: A. $\frac{1}{x \cdot \log _e a}$AView full question & answer→
MCQ 111 Mark$\frac{d}{d x}\left(5^x\right)$ is equal to :A$5^x$B$10^x$C$10^x \log _e 5$✓$5^x \log _e 5$AnswerCorrect option: D. $5^x \log _e 5$DView full question & answer→
MCQ 121 MarkDerivative of $\frac{1}{\sqrt{x}}$ is equal to :A$\frac{1}{2 x \sqrt{x}}$✓$-\frac{1}{2 x \sqrt{x}}$C$2 x \sqrt{x}$D$-2 x \sqrt{x}$AnswerCorrect option: B. $-\frac{1}{2 x \sqrt{x}}$BView full question & answer→
MCQ 131 MarkDerivative of $x^n$ is equal to :A$x^{n-1}$B$(n-1) ~x^{n-2}$✓$n~ x^{n-1}$D$\frac{x^{n+1}}{n+1}$AnswerCorrect option: C. $n~ x^{n-1}$CView full question & answer→
MCQ 141 MarkValue of $\lim _{x \rightarrow 0} \frac{e^{\frac{1}{x}}}{x}$ is :A$0$B$\infty$C$1$✓does not exist.AnswerCorrect option: D. does not exist.DView full question & answer→
MCQ 151 MarkEvaluate $\lim _{x \rightarrow \pi} \frac{1+\cos x}{\tan ^2 x}:$A$-\frac{1}{2}$B$0$✓$\frac{1}{2}$D$1$AnswerCorrect option: C. $\frac{1}{2}$CView full question & answer→
MCQ 161 MarkEvaluate $\lim _{x \rightarrow 0} \frac{x^2-2 x}{2 \sin x}$ :A$2$B$1$C$0$✓$-1$AnswerCorrect option: D. $-1$DView full question & answer→
MCQ 171 MarkThe value of $\lim _{x \rightarrow 0} \frac{e^x-e^{-x}}{x}$ is equal to :A$0$✓$2$C$1$D$-1$AnswerCorrect option: B. $2$BView full question & answer→
MCQ 181 MarkThe value of $\lim _{m \rightarrow \infty}\left(1-\frac{1}{m}\right)^{-m}$ is equal to :A$0$B$\infty$✓$e$D$e^{-1}$AnswerCorrect option: C. $e$CView full question & answer→
MCQ 191 MarkEvaluate $\lim _{x \rightarrow 1}\left(\frac{x^n-1}{x-1}\right)$ :A$n^2$✓$n$C$n-1$D$n+1$AnswerCorrect option: B. $n$BView full question & answer→
MCQ 201 MarkEvaluate $\lim _{x \rightarrow 0} \frac{\sin x^{\circ}}{x}$ :A$0$B$1$✓$\frac{\pi}{180}$D$\pi$AnswerCorrect option: C. $\frac{\pi}{180}$C View full question & answer→
MCQ 211 Mark$\lim _{x \rightarrow \infty} \frac{\sin 2 x}{2 x}$ is equal to :✓$0$B$\frac{1}{2}$C1D2AnswerCorrect option: A. $0$AView full question & answer→
MCQ 221 MarkEvaluate $\lim _{x \rightarrow 0}\left[\frac{\sin \alpha x}{\sin \beta x}\right]^{\frac{1}{n}}$ :✓$\left(\frac{\alpha}{\beta}\right)^{\frac{1}{n}}$B$\left(\frac{\beta}{\alpha}\right)^{\frac{1}{n}}$C$\left(\frac{\alpha}{\beta}\right)^n$D$\left(\frac{\beta}{\alpha}\right)^n$AnswerCorrect option: A. $\left(\frac{\alpha}{\beta}\right)^{\frac{1}{n}}$AView full question & answer→
MCQ 231 MarkWhich of the following limit does not exist?A$\lim _{x \rightarrow 0} \cos \frac{1}{x}$B$\lim _{x \rightarrow \frac{\pi}{2}} \tan x$C$\lim _{x \rightarrow \infty}[x]$✓None of theseAnswerCorrect option: D. None of theseDView full question & answer→
MCQ 241 MarkEvaluate $\lim _{x \rightarrow 0} \frac{\sin 4 x}{\tan 3 x}$ :A$\frac{3}{4}$✓$\frac{4}{3}$C$0$D1AnswerCorrect option: B. $\frac{4}{3}$BView full question & answer→
MCQ 251 MarkEvaluate $\lim _{x \rightarrow \infty} \frac{5 x^2+3 x+2}{x^2+x+1} :$A1B2C3✓5AnswerCorrect option: D. 5DView full question & answer→