The length of the diameter of the circle
Question: The length of the diameter of the circle which touches the x-axis at the point (1, 0) and passes through the point (2, 3) is :5/310/33/56/5Correct Option: , 2 Solution:...
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Question: Let $f(\mathrm{x})$ be a polynomial of degree four having extreme values at $\mathrm{x}=1$ and $\mathrm{x}=2$. If $\lim _{x \rightarrow 0}\left[1+\frac{\mathrm{f}(\mathrm{x})}{\mathrm{x}^{2}}\right]=3$, then $f(2)$ is equal to :04$-8$$-4$Correct Option: 1 Solution:...
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Question: If $x=-1$ and $x=2$ are extreme points of $f(x)=\alpha \log |x|+\beta x^{2}+x$ then : $\alpha=-6, \beta=\frac{1}{2}$$\alpha=-6, \beta=-\frac{1}{2}$$\alpha=2, \beta=-\frac{1}{2}$$\alpha=2, \beta=\frac{1}{2}$Correct Option: , 3 Solution:...
Read More →The equation of the circle passing
Question: The equation of the circle passing through the points (1, 0) and (0, 1) and having the smallest radius is -$x^{2}+y^{2}+x+y-2=0$$x^{2}+y^{2}-2 x-2 y+1=0$$x^{2}+y^{2}-x-y=0$$x^{2}+y^{2}+2 x+2 y-7=0$Correct Option: , 3 Solution:...
Read More →The two circles
Question: The two circles $x^{2}+y^{2}=a x$ and $x^{2}+y^{2}=c^{2}(c0)$ touch each other if :-a = 2c$|\mathrm{a}|=2 \mathrm{c}$$|2| \mathrm{a} \mid=\mathrm{c}$$|\mathrm{a}|=\mathrm{c}$Correct Option: , 4 Solution:...
Read More →Allyl phenyl ether can be prepared
Question: Allyl phenyl ether can be prepared by heating:$\mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{Br}+\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{ONa}$$\mathrm{C}_{6} \mathrm{H}_{5}-\mathrm{CH}=\mathrm{CH}-\mathrm{Br}+\mathrm{CH}_{3}-\mathrm{ONa}$$\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{Br}+\mathrm{CH}_{2}=\mathrm{CH}-\mathrm{CH}_{2}-\mathrm{ONa}$$\mathrm{CH}_{2}=\mathrm{CH}-\mathrm{Br}+\mathrm{C}_{6} \mathrm{H}_{5}-\mathrm{CH}_{2}-\mathrm{ONa}$Correct Option: 1 Solution:...
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Question: The real number $\mathrm{k}$ for which the equation $2 \mathrm{x}^{3}+3 \mathrm{x}+\mathrm{k}=0$ has two distinct real roots in $[0,1]$lies between 1 and 2 .lies between 2 and 3 .lies between $-1$ and 0does not existCorrect Option: , 4 Solution:...
Read More →The most suitable reagent for the conversion
Question: The most suitable reagent for the conversion of $\mathrm{R}-\mathrm{CH}_{2}-\mathrm{OH} \rightarrow \mathrm{R}-\mathrm{CHO}$ is :$\mathrm{CrO}_{3}$PCC (Pyridinium chlorochromate)$\mathrm{KMNO}_{4}$$\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}$Correct Option: , 2 Solution:...
Read More →The circle
Question: The circle $x^{2}+y^{2}=4 x+8 y+5$ intersects the line $3 x-4 y=m$ at two distinct points if :-$-85m-35$$-35m15$$15m65$$35\mathrm{m}85$Correct Option: , 2 Solution:...
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Question: Let $a, b \in R$ be such that the function $f$ given by $f(x)=\ln |x|+b x^{2}+a x, x \neq 0$ has extreme values at $\mathrm{x}=-1$ and $\mathrm{x}=2$. Statement-1 : $\mathrm{f}$ has local maximum at $\mathrm{x}=-1$ and at $\mathrm{x}=2$ Statement-2 : $\mathrm{a}=\frac{1}{2}$ and $\mathrm{b}=\frac{-1}{4}$. Statement-1 is true, Statement $-2$ is false.Statement- 1 is false, Statement- 2 is true.Statement-1 is true, Statement-2 is true ;Statement-2 is a correct explanation for Statement-1...
Read More →An unknown alcohol is treated with the "Lucas reagent' to determine
Question: An unknown alcohol is treated with the "Lucas reagent' to determine whether the alcohol is primary, secondary or tertiary. Which alcohol reacts fastest and by what mechanism :-secondary alcohol by $\mathrm{SN}^{1}$tertiary alcohol by $\mathrm{SN}^{1}$secondary alcohol by $\mathrm{SN}^{2}$tertiary alcohol by $\mathrm{SN}^{2}$Correct Option: , 2 Solution: Solution not required...
Read More →For a regular polygon, let r and R be the radii of
Question: For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is :-There is a regular polygon with $\frac{\mathrm{r}}{\mathrm{R}}=\frac{1}{2}$There is a regular polygon with $\frac{\mathrm{r}}{\mathrm{R}}=\frac{1}{\sqrt{2}}$There is a regular polygon with $\frac{r}{R}=\frac{2}{3}$There is a regular polygon with $\frac{\mathrm{r}}{\mathrm{R}}=\frac{\sqrt{3}}{2}$Correct Option: , 3 Solution:...
Read More →Iodoform can be prepared
Question: Iodoform can be prepared from all except :-Isobutyl alcoholEthyl methyl ketoneIsopropyl alcohol3-Methyl-2-butanoneCorrect Option: 1 Solution: Solution not required...
Read More →If P and Q are the points of intersection of the circles
Question: If $P$ and $Q$ are the points of intersection of the circles $x^{2}+y^{2}+3 x+7 y+2 p-5=0$ and $\mathrm{x}^{2}+\mathrm{y}^{2}+2 \mathrm{x}+2 \mathrm{y}-\mathrm{p}^{2}=0$, then there is a circle passing through $\mathrm{P}, \mathrm{Q}$ and (1, 1)is possible for :-All except two values of pExactly one value of pExactly one value of pAll except one value of pCorrect Option: , 4 Solution:...
Read More →Consider the following reaction :
Question: Consider the following reaction : $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}+\mathrm{H}_{2} \mathrm{SO}_{4} \rightarrow$ Produce Among the following, which one cannot be formed as a product under any conditions ?Ethyl-hydrogen sulphateEthyleneAcetyleneDiethyl etherCorrect Option: , 3 Solution: Solution not required...
Read More →A spherical balloon is filled with
Question: A spherical balloon is filled with $4500 \pi$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $72 \pi$ cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is :$9 / 2$$9 / 7$$7 / 9$$2 / 9$Correct Option: , 4 Solution:...
Read More →On heating an aliphatic
Question: On heating an aliphatic primary amine with chloroform and ethanolic potassium hydroxide, the organic compound formed is :-An alkyl cyanideAn alkyl isocyanideAn alkanolAn alkanediolCorrect Option: , 2 Solution: Solution not required...
Read More →The gas leaked
Question: The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was:-MethylisocyanateMethylamineAmmoniaPhosgeneCorrect Option: 1 Solution: Solution not required...
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Question: Let $\mathrm{f}$ be a function defined by $\mathrm{f}(\mathrm{x})=\left\{\begin{array}{cc}\frac{\tan \mathrm{x}}{\mathrm{x}}, \mathrm{x} \neq 0 \\ 1, \mathrm{x}=0\end{array}\right.$ Statement - 1: $x=0$ is point of minima of $f$. Statement - 2: $\mathrm{f}^{\prime}(0)=0 .$ Statement-1 is false, statement- 2 is true.Statement-1 is true, statement- 2 is true; Statement- 2 is correct explanation for statement-1.Statement- 1 is true, statement- 2 is true; Statement- 2 is not a correct expl...
Read More →Three distinct points A, B and C are given in the 2–dimensional
Question: Three distinct points $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are given in the 2 -dimensional coordinate plane such that the ratio of the distance of any one of them from the point $(1,0)$ to the distance from the point $(-1,0)$ is equal to $\frac{1}{3}$. Then the circumcentre of the triangle $\mathrm{ABC}$ is at the point :-$(0,0)$Correct Option: , 4 Solution:...
Read More →An organic compound
Question: An organic compound $\mathrm{A}$ upon reacting with $\mathrm{NH}_{3}$ gives $\mathrm{B} .$ On heating, B gives $\mathrm{C}$. $\mathrm{C}$ in presence of $\mathrm{KOH}$ reacts with $\mathrm{Br}_{2}$ to give $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{NH}_{2} .$ A is :-$\mathrm{CH}_{3} \mathrm{COOH}$$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{COOH}$$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH}$Correct Option: , 4 Solution: Solution not required...
Read More →The shortest distance between line
Question: The shortest distance between line $\mathrm{y}-\mathrm{x}=1$ and curve $\mathrm{x}=\mathrm{y}^{2}$ is :-$\frac{8}{3 \sqrt{2}}$$\frac{4}{\sqrt{3}}$$\frac{\sqrt{3}}{4}$$\frac{3 \sqrt{2}}{8}$Correct Option: , 4 Solution:...
Read More →From amongst the following alcohols the one that would react fastest with conc.
Question: From amongst the following alcohols the one that would react fastest with conc. $\mathrm{HCl}$ and anhydrous $\mathrm{ZnCl}_{2}$, is :-1-Butanol2-Butanol2-Methylpropan-2-ol2-MethylpropanolCorrect Option: 3, Solution: Solution not required...
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Question: For $x \in\left(0, \frac{5 \pi}{2}\right)$, define $f(x)=\int_{0}^{x} \sqrt{t} \sin t d t$. Then $f$ has :- local minimum at $\pi$ and local maximum at $2 \pi$local maximum at $\pi$ and local minimum at $2 \pi$local maximum at $\pi$ and $2 \pi$local minimum at $\pi$ and $2 \pi$Correct Option: , 2 Solution: $f^{\prime}(x)=\sqrt{x} \sin x$...
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