The number of complex numbers z
Question: The number of complex numbers $\mathrm{z}$ such that $|\mathrm{z}-1|=|\mathrm{z}+1|=|\mathrm{z}-\mathrm{i}|$ equals :-012$\infty$Correct Option: , 2 Solution:...
Read More →The bond dissociation energy
Question: The bond dissociation energy of $\mathrm{B}-\mathrm{F}$ in $\mathrm{BF}_{3}$ is $646 \mathrm{~kJ} \mathrm{~mol}^{-1}$ whereas that of $\mathrm{C}-\mathrm{F}$ in $\mathrm{CF}_{4}$ is $515 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The correct reason for higher $\mathrm{B}-\mathrm{F}$ bond dissociation energy as compared to that of $\mathrm{C}-\mathrm{F}$ is :-Significant $\mathrm{p} \pi-\mathrm{p} \pi$ interaction between $\mathrm{B}$ and $\mathrm{F}$ in $\mathrm{BF}_{3}$ whereas there is not po...
Read More →Solve this following
Question: Let $\vec{a}, \vec{b}, \vec{c}$ be three non-zero vectors which are pairwise non-collinear. If $\vec{a}+3 \vec{b}$ is collinear with $\overrightarrow{\mathrm{c}}$ and $\overrightarrow{\mathrm{b}}+2 \overrightarrow{\mathrm{c}}$ is colliner with $\overrightarrow{\mathrm{a}}$, then $\overrightarrow{\mathrm{a}}+3 \overrightarrow{\mathrm{b}}+6 \overrightarrow{\mathrm{c}}$ is:$\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{c}}$$\vec{a}$$\overrightarrow{\mathrm{C}}$$\overrightarrow{0}$Co...
Read More →The line L given by
Question: The line $L$ given by $\frac{x}{5}+\frac{y}{b}=1$ passes through the point $(13,32)$. The line $K$ is parallel to$L$ and has the equation $\frac{x}{c}+\frac{y}{3}=1$. Then the distance between $L$ and $K$ is :$\frac{23}{\sqrt{15}}$$\sqrt{17}$$\frac{17}{\sqrt{15}}$$\frac{23}{\sqrt{17}}$Correct Option: , 4 Solution:...
Read More →Solve the following
Question: If $\left|Z-\frac{4}{Z}\right|=2$, then the maximum value of $|Z|$ is equal to :-2$2+\sqrt{2}$$\sqrt{3}+1$$\sqrt{5}+1$Correct Option: , 4 Solution:...
Read More →Solve this following
Question: If $\vec{a}=\frac{1}{\sqrt{10}}(3 \hat{i}+\hat{k})$ and $\vec{b}=\frac{1}{7}(2 \hat{i}+3 \hat{j}-6 \hat{k})$, then the value of $(2 \vec{a}-\vec{b}) \cdot[(\vec{a} \times \vec{b}) \times(\vec{a}+2 \vec{b})]$ is l:53$-5$$-3$Correct Option: , 3 Solution: $=(2 \vec{a}-\vec{b}) \cdot(\vec{b}-2 \vec{a})$...
Read More →Which compound would
Question: Which compound would give 5-keto-2-methyl hexanal upon ozonlysis? []Correct Option: , 4 Solution: Solution not required...
Read More →In the reaction sequence
Question: In the reaction sequence $\mathrm{CH}_{3}-\mathrm{CH}=\mathrm{CH}-\mathrm{CHO}$$\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{3}$$\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{OH}$Correct Option: 1 Solution: Solution not required...
Read More →Let f(x)=x|x|, g(x)=sin x and h(x)
Question: Let $f(x)=x|x|, g(x)=\sin x$ and $h(x)=$ $(g o f)(x)$. Then$h^{\prime}(x)$ is differentiable at $x=0$$h^{\prime}(x)$ is continuous at $x=0$ but is not differentiable at $x=0$$\mathrm{h}(\mathrm{x})$ is differentiable at $\mathrm{x}=0$ but $\mathrm{h}^{\prime}(\mathrm{x})$ is not continuous at $\mathrm{x}=0$$\mathrm{h}(\mathrm{x})$ is not differentiable at $\mathrm{x}=0$Correct Option: 2, Solution:...
Read More →A compound
Question: A compound $\mathrm{A}$ with molecular formula $\mathrm{C}_{10} \mathrm{H}_{13} \mathrm{Cl}$ gives a white precipitate on adding silver nitrate solution. A on reacting with alcoholic $\mathrm{KOH}$ gives compound $\mathrm{B}$ as the main product. B on ozonolysis gives C and D. C gives Cannizaro reaction but not aldol condensation. D gives aldol condensation but not Cannizaro reaction. A is :$\mathrm{C}_{6} \mathrm{H}_{5}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\...
Read More →The lines p
Question: The lines $p\left(p^{2}+1\right) x-y+q=0$ and $\left(p^{2}+1\right)^{2} x+\left(p^{2}+1\right) y+2 q=0$ are Perpendicular to a common line for :Exactly two values of pMore than two values of pNo value of pExactly one value of pCorrect Option: , 4 Solution:...
Read More →Solve this following
Question: The vectors $\vec{a}$ and $\vec{b}$ are not perpendicular and $\vec{c}$ and $\vec{d}$ are two vectors satisfying : $\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{d}}$ and $\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{d}}=0$. Then the vector $\overrightarrow{\mathrm{d}}$ is equal to :-$\overrightarrow{\mathrm{b}}+\left(\frac{\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathrm{c}}}{\overrightar...
Read More →Phenol on treatment with
Question: Phenol on treatment with $\mathrm{CO}_{2}$ in the presence of $\mathrm{NaOH}$ followed by acidification produces compound $\mathrm{X}$ as the major product. $\mathrm{X}$ on treatment with $\left(\mathrm{CH}_{3} \mathrm{CO}\right)_{2} \mathrm{O}$ in the presence of catalytic amount of $\mathrm{H}_{2} \mathrm{SO}_{4}$ produces :Correct Option: Solution:...
Read More →Consider the function,
Question: Consider the function, $f(x)=|x-2|+|x-5|, x \in R$ Statement-1: $\mathrm{f}^{\prime}(4)=0$. Statement-2 : $\mathrm{f}$ is continuous in $[2,5]$, differentiable in $(2,5)$ and $f(2)=f(5)$.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 $1 .$Statement-1 is true, Statement-2 is true ; Statement-2 is not a correct explanation for Statementl.Correct Option: , 4 S...
Read More →The most suitable reagent
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}$$\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}$Correct Option: 2, Solution:...
Read More →If the tangent at (1, 7) to the curve
Question: If the tangent at $(1,7)$ to the curve $x^{2}=y-6$ touches the circle $x^{2}+y^{2}+16 x+12 y+c=0$ then the value of $\mathrm{c}$ is:1858595195Correct Option: , 3 Solution:...
Read More →The major organic compound
Question: The major organic compound formed by the reaction of $1,1,1$-trichloroethane with silver powder is :-2-Butyne2 -ButeneAcetylenEtheneCorrect Option: 1 Solution:...
Read More →If sum of all the solutions of the equation
Question: If sum of all the solutions of the equation $8 \cos x \cdot\left(\cos \left(\frac{\pi}{6}+x\right) \cdot \cos \left(\frac{\pi}{6}-x\right)-\frac{1}{2}\right)=1$ in $[0, \pi]$ is $\mathrm{k} \pi$, then $\mathrm{k}$ is equal to :$\frac{13}{9}$$\frac{8}{9}$$\frac{20}{9}$$\frac{2}{3}$Correct Option: 1 Solution:...
Read More →Solve this following
Question: Let $\overrightarrow{\mathrm{a}}=\hat{\mathrm{j}}-\hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{c}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}}$. Then the vector $\overrightarrow{\mathrm{b}}$ satisfying $\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}+\overrightarrow{\mathrm{c}}=\overrightarrow{0}$ and $\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}=3$ is : $-\hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$$2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+...
Read More →If function f(x) is differentiable at x=a then
Question: If function $f(x)$ is differentiable at $x=a$ then $\lim _{x \rightarrow a} \frac{x^{2} f(a)-a^{2} f(x)}{x-a}$$2 a f(a)+a^{2} f^{\prime}(a)$$-\mathrm{a}^{2} \mathrm{f}^{\prime}$ (a)$a f(a)-a^{2} f^{\prime}(a)$$2 a f(a)-a^{2} f^{\prime}(a)$Correct Option: , 4 Solution:...
Read More →A compound with molecular mass
Question: A compound with molecular mass 180 is acylated with $\mathrm{CH}_{3} \mathrm{COCl}$ to get a compound with molecular mass 390 . The number of amino groups present per molecule of the former compound is :-2546Correct Option: , 2 Solution:...
Read More →Solve the equation
Question: If $0 \leq x2 \pi$, then the number of real values of $x$, which satisfy the equation $\cos x+\cos 2 x+\cos 3 x+\cos 4 x=0$, is :-9357Correct Option: , 4 Solution:...
Read More →The centres of those circles which touch the circle
Question: The centres of those circles which touch the circle, $x^{2}+y^{2}-8 x-8 y-4=0$, externally and also touch the x-axis, lie on :-A parabolaA circleAn ellipse which is not a circleA hyperbolaCorrect Option: 1 Solution:...
Read More →Solve this following
Question: If $\overrightarrow{\mathrm{u}}, \overrightarrow{\mathrm{v}}, \overrightarrow{\mathrm{w}}$ are non-coplanar vectors and $\mathrm{p}, \mathrm{q}$ are real numbers, then the equality $[3 \overrightarrow{\mathrm{u}} \mathrm{p} \overrightarrow{\mathrm{v}} \mathrm{p} \overrightarrow{\mathrm{w}}]-[\mathrm{p} \overrightarrow{\mathrm{v}} \overrightarrow{\mathrm{w}} \mathrm{q} \overrightarrow{\mathrm{u}}]-[2 \overrightarrow{\mathrm{w}} \mathrm{q} \overrightarrow{\mathrm{v}} \mathrm{qu}]=0$ hold...
Read More →The structure of the products
Question: The structure of the products $\mathbf{Q}$ and $\mathbf{R}$, respectively, areCorrect Option: 1 Solution: Solution not required...
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