Arrange the following
Question: Arrange the following compounds in order of decreasing acidity : $\mathrm{II}\mathrm{IV}\mathrm{I}\mathrm{III}$$\mathrm{I}\mathrm{II}\mathrm{III}\mathrm{IV}$$\mathrm{III}\mathrm{I}\mathrm{II}\mathrm{IV}$$\mathrm{IV}\mathrm{III}\mathrm{I}\mathrm{II}$Correct Option: , 3 Solution:...
Read More →The order of basicity of amines in gaseous state is :-
Question: The order of basicity of amines in gaseous state is :-$3^{\circ}2^{\circ}\mathrm{NH}_{3}1^{\circ}$$1^{\circ}2^{\circ}3^{\circ}\mathrm{NH}_{3}$$\mathrm{NH}_{3}1^{\circ}2^{\circ}3^{\circ}$$3^{\circ}2^{\circ}1^{\circ}\mathrm{NH}_{3}$Correct Option: , 4 Solution:...
Read More →The most basic compound among the following is :-
Question: The most basic compound among the following is :-AcetanilideBenzylaminep-Nitro anilineAnilineCorrect Option: , 2 Solution:...
Read More →In the following compounds :
Question: In the following compounds : the order of basicity is as follows :$\mathrm{IV}\mathrm{III}\mathrm{II}\mathrm{I}$$\mathrm{II}\mathrm{III}\mathrm{I}\mathrm{IV}$$\mathrm{I}\mathrm{III}\mathrm{II}\mathrm{IV}$$\mathrm{III}\mathrm{I}\mathrm{II}\mathrm{IV}$Correct Option: , 3 Solution: Solution not required...
Read More →The correct order
Question: The correct order of acid strength of the following compounds :- A. Phenol B. $\mathrm{p}-$ Cresol C. m-Nitrophenol D. $\mathrm{p}$ - Nitrophenol$\mathrm{C}\mathrm{B}\mathrm{A}\mathrm{D}$$\mathrm{D}\mathrm{C}\mathrm{A}\mathrm{B}$$\mathrm{B}\mathrm{D}\mathrm{A}\mathrm{C}$$\mathrm{A}\mathrm{B}\mathrm{D}\mathrm{C}$Correct Option: , 2 Solution: Solution not required...
Read More →Solve this following
Question: $\lim _{x \rightarrow 0} \frac{x \tan 2 x-2 x \tan x}{(1-\cos 2 x)^{2}}$ equals :-$-\frac{1}{2}$$\frac{1}{4}$$\frac{1}{2}$1Correct Option: , 3 Solution: Solution not required...
Read More →Solve this following
Question: $\lim _{x \rightarrow 0} \frac{(27+x)^{1 / 3}-3}{9-(27+x)^{2 / 3}}$ equals :$-\frac{1}{3}$$\frac{1}{6}$$-\frac{1}{6}$$\frac{1}{3}$Correct Option: , 3 Solution: Solution not required...
Read More →Solve this following
Question: For each $\mathrm{t} \in \mathrm{R}$, let $[\mathrm{t}]$ be the greatest integer less than or equal to $\mathrm{t}$. Then $\lim _{x \rightarrow 0+} x\left(\left[\frac{1}{x}\right]+\left[\frac{2}{x}\right]+\ldots \ldots+\left[\frac{15}{x}\right]\right) \backslash$ is equal to $15 .$is equal to 120 .does not exist (in $\mathrm{R}$ ).is equal to 0 .Correct Option: , 2 Solution:...
Read More →Solve this following
Question: $\lim _{x \rightarrow \frac{\pi}{2}} \frac{\cot x-\cos x}{(\pi-2 x)^{3}}$ equals :-$\frac{1}{4}$$\frac{1}{24}$$\frac{1}{16}$$\frac{1}{8}$Correct Option: , 3 Solution:...
Read More →Solve this following
Question: $\lim _{n \rightarrow \infty}\left(\frac{(n+1)(n+2) \ldots . .3 n}{n^{2 n}}\right)^{1 / n}$ is equal to :-$3 \log 3-2$$\frac{18}{\mathrm{e}^{4}}$$\frac{27}{\mathrm{e}^{2}}$$\frac{9}{e^{2}}$Correct Option: , 3 Solution:...
Read More →Solve this following
Question: Let $\mathrm{p}=\lim _{\mathrm{x} \rightarrow 0+}\left(1+\tan ^{2} \sqrt{\mathrm{x}}\right)^{\frac{1}{2 x}}$ then $\log \mathrm{p}$ is equal to :-$\frac{1}{4}$21$\frac{1}{2}$Correct Option: , 4 Solution:...
Read More →Solve this following
Question: If $\lim _{x \rightarrow 2} \frac{\tan (x-2)\left\{x^{2}+(k-2) x-2 k\right\}}{x^{2}-4 x+4}=5$ then $k$ is equal to3102Correct Option: 1 Solution:...
Read More →Solve this following
Question: $\lim _{x \rightarrow 0} \frac{\sin \left(\pi \cos ^{2} x\right)}{x^{2}}$ is equal to:$\frac{\pi}{2}$1$-\pi$$\pi$Correct Option: , 4 Solution:...
Read More →Solve this following
Question: Let $f: \mathrm{R} \rightarrow[0, \infty)$ be such that $\lim _{x \rightarrow 5} f(x)$ exists and $\lim _{x \rightarrow 5} \frac{(f(x))^{2}-9}{\sqrt{|x-5|}}=0$. Then $\operatorname{Lim}_{x \rightarrow 5} f(x)$ equal -3012Correct Option: , 3 Solution:...
Read More →Solve this following
Question: Let $f: R \rightarrow R$ be a positive increasing function with $\lim _{x \rightarrow \infty} \frac{f(3 x)}{f(x)}=1$. Then $\lim _{x \rightarrow \infty} \frac{f(2 x)}{f(x)}=$1$\frac{2}{3}$$\frac{3}{2}$3Correct Option: 1 Solution:...
Read More →Solve this following
Question: Suppose $A$ is any $3 \times 3$ non-singular matrix and $(A-3 I)(A-5 I)=0$, where $I=I_{3}$ and $O$ $=\mathrm{O}_{3}$. If $\alpha \mathrm{A}+\beta \mathrm{A}^{-1}=4 \mathrm{I}$, then $\alpha+\beta$ is equal to :137128Correct Option: , 4 Solution: Solution not required...
Read More →Solve this following
Question: Let $A$ be a matrix such that $A .\left[\begin{array}{ll}1 2 \\ 0 3\end{array}\right]$ is a scalar matrix and $|3 \mathrm{~A}|=108$. Then $\mathrm{A}^{2}$ equals :$\left[\begin{array}{cc}36 -32 \\ 0 4\end{array}\right]$$\left[\begin{array}{cc}4 0 \\ -32 36\end{array}\right]$$\left[\begin{array}{cc}4 -32 \\ 0 36\end{array}\right]$$\left[\begin{array}{cc}36 0 \\ -32 4\end{array}\right]$Correct Option: 1 Solution: Solution not required...
Read More →Solve this following
Question: Let $\mathrm{A}=\left[\begin{array}{lll}1 0 0 \\ 1 1 0 \\ 1 1 1\end{array}\right]$ and $\mathrm{B}=\mathrm{A}^{20}$. Then the sum of the elements of the first column of $\mathrm{B}$ is :211251231210Correct Option: , 3 Solution: Solution not required...
Read More →Solve this following Question
Question: If $\mathrm{L}_{\mathrm{l}}$ is the line of intersection of the planes $2 \mathrm{x}-2 \mathrm{y}+3 \mathrm{z}-2=0, \mathrm{x}-\mathrm{y}+\mathrm{z}+1=0$ and $\mathrm{L}_{2}$ is the line of intersection of the planes $\mathrm{x}+2 \mathrm{y}-\mathrm{z}-3=0,3 \mathrm{x}-\mathrm{y}+2 \mathrm{z}-1=0$, then the distance of the origin from the plane, containing the lines $L_{1}$ and $L_{2}$ is $z$$\frac{1}{3 \sqrt{2}}$$\frac{1}{2 \sqrt{2}}$$\frac{1}{\sqrt{2}}$$\frac{1}{4 \sqrt{2}}$Correct O...
Read More →Prove the following
Question: Let $\mathrm{y}=\mathrm{y}(\mathrm{x})$ be the solution of the differential equation $\sin \mathrm{x} \frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{y} \cos \mathrm{x}=4 \mathrm{x}, \mathrm{x} \in(0$, $\pi)$. If $\mathrm{y}\left(\frac{\pi}{2}\right)=0$, then $\mathrm{y}\left(\frac{\pi}{6}\right)$ is equal to :$\frac{-8}{9 \sqrt{3}} \pi^{2}$$-\frac{8}{9} \pi^{2}$$-\frac{4}{9} \pi^{2}$$\frac{4}{9 \sqrt{3}} \pi^{2}$Correct Option: , 2 Solution:...
Read More →Solve this following
Question: If $\mathrm{A}=\left[\begin{array}{cc}2 -3 \\ -4 1\end{array}\right]$, then adj $\left(3 \mathrm{~A}^{2}+12 \mathrm{~A}\right)$ is equal to :-$\left[\begin{array}{cc}72 -63 \\ -84 51\end{array}\right]$$\left[\begin{array}{cc}72 -84 \\ -63 51\end{array}\right]$$\left[\begin{array}{ll}51 63 \\ 84 72\end{array}\right]$$\left[\begin{array}{ll}51 84 \\ 63 72\end{array}\right]$Correct Option: , 3 Solution:...
Read More →The length of the projection of the line segment joining
Question: The length of the projection of the line segment joining the points $(5,-1,4)$ and $(4,-1,3)$ on the plane, $x+y+z=7$ is:$\frac{2}{3}$$\frac{1}{3}$$\sqrt{\frac{2}{3}}$$\frac{2}{\sqrt{3}}$Correct Option: , 3 Solution:...
Read More →Prove the following
Question: If $(2+\sin x) \frac{d y}{d x}+(y+1) \cos x=0$ and $y(0)=1$, then $y\left(\frac{\pi}{2}\right)$ is equal to :-$\frac{4}{3}$$\frac{1}{3}$$-\frac{2}{3}$$-\frac{1}{3}$Correct Option: , 2 Solution:...
Read More →Solve this following
Question: If $\mathrm{A}=\left[\begin{array}{cc}5 \mathrm{a} -\mathrm{b} \\ 3 2\end{array}\right]$ and $\mathrm{A}$ adj $\mathrm{A}=\mathrm{A} \mathrm{} \mathrm{A}^{\mathrm{T}}$, then $5 \mathrm{a}+\mathrm{b}$ is equal to :13$-1$54Correct Option: , 3 Solution:...
Read More →If a curve y=f(x) passes through the point (1,-1)
Question: If a curve $y=f(x)$ passes through the point $(1,-1)$ and satisfies the differential equation, $y(1+x y) d x=x$ dy, then $f\left(-\frac{1}{2}\right)$ is equal to :$\frac{4}{5}$$-\frac{2}{5}$$-\frac{4}{5}$$\frac{2}{5}$Correct Option: 1 Solution:...
Read More →