If the line
Question: If the line $2 \mathrm{x}+\mathrm{y}=\mathrm{k}$ passes through the point which divides the line segment joining the points $(1,1)$ and $(2,4)$ in the ratio $3: 2$, then $\mathrm{k}$ equals :$\frac{11}{5}$$\frac{29}{5}$56Correct Option: Solution: $\Rightarrow \quad k=6$...
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Question: Let $S=\left\{t \in R: f(x)=|x-\pi| \cdot\left(e^{|x|}-1\right) \sin |x|\right.$ is not differentiable at $\left.t\right\}$. Then the set $S$ is equal to:$\{0\}$$\{\pi\}$$\{0, \pi\}$$\phi$ (an empty set)Correct Option: , 4 Solution:...
Read More →If z is a complex number
Question: If $z$ is a complex number such that $|z| \geq 2$, then the minimum value of $\left|z+\frac{1}{2}\right|$ :is equal to $\frac{5}{2}$lies in the interval (1, 2)is strictly greater than $\frac{5}{2}$is strictly greater than $\frac{3}{2}$ but less thanCorrect Option: , 2 Solution:...
Read More →The molecule having smallest bond angle is :-
Question: The molecule having smallest bond angle is :-$\mathrm{PCl}_{3}$$\mathrm{NCl}_{3}$$\mathrm{AsCl}_{3}$$\mathrm{SbCl}_{3}$Correct Option: , 4 Solution:...
Read More →A line is drawn through the point
Question: A line is drawn through the point $(1,2)$ to meet the coordinate axes at $P$ and $Q$ such that it forms a triangle $\mathrm{OPQ}$, where $\mathrm{O}$ is the origin. If the area of the triangle $\mathrm{OPQ}$ is least, then the slope of the line $P Q$ is :$-\frac{1}{2}$$-\frac{1}{4}$$-4$$-2$Correct Option: , 4 Solution: Let the equationof line be $\frac{x}{a}+\frac{y}{b}=1$ It passes through $(1,2)$...
Read More →The number of types
Question: The number of types of bonds between two carbon atoms in calcium carbide is :-One sigma, two piOne sigma, one piTwo sigma, one piTwo sigma, two piCorrect Option: 1 Solution:...
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Question: If the vectors $\overrightarrow{\mathrm{AB}}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{AC}}=5 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}$ are the sides of a triangle $\mathrm{ABC}$, then the length of the median through $\mathrm{A}$ is :$\sqrt{18}$$\sqrt{72}$$\sqrt{33}$$\sqrt{45}$Correct Option: , 3 Solution:...
Read More →If z is a complex number of unit modulus
Question: If $\mathrm{z}$ is a complex number of unit modulus and argument $\theta$, then $\arg \left(\frac{1+\mathrm{z}}{1+\overline{\mathrm{z}}}\right)$ equals$-\theta$$\frac{\pi}{2}-\theta$$\theta$$\pi-\theta$Correct Option: , 3 Solution:...
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Question: For $x \in R, f(x)=|\log 2-\sin x|$ and $g(x)=f(f(x))$, then :$\mathrm{g}$ is differentiable at $\mathrm{x}=0$ and $\mathrm{g}^{\prime}(0)=-\sin (\log 2)$$\mathrm{g}$ is not differentiable at $\mathrm{x}=0$$\mathrm{g}^{\prime}(0)=\cos (\log 2)$$g^{\prime}(0)=-\cos (\log 2)$Correct Option: , 3 Solution:...
Read More →In the chemical reactions,
Question: In the chemical reactions, Nitrobenzene and chlorobenzeneNitrobenzene and fluorobenzenePhenol and benzeneBenzene diazonium chloride and fluorobenzeneCorrect Option: , 4 Solution: Solution not required...
Read More →Which of the following
Question: Which of the following has maximum number of lone pairs associated with Xe$\mathrm{XeO}_{3}$$\mathrm{XeF}_{4}$$\mathrm{XeF}_{6}$$\mathrm{XeF}_{2}$Correct Option: , 4 Solution:...
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Question: If $\mathrm{z} \neq 1$ and $\frac{\mathrm{z}^{2}}{\mathrm{z}-1}$ is real, then the point represented by the complex number $\mathrm{z}$ lies :on the imaginary axis.either on the real axis or on a circle passing through the origin.on a circle with centre at the origin.either on the real axis or on a circle not passing through the origin.Correct Option: , 2 Solution:...
Read More →The lines
Question: The lines $x+y=|a|$ and $a x-y=1$ intersect each other in the first quadrant. Then the set of all possible values of a is the interval:(1, 1]$(0, \infty)$$[1, \infty)$$(-1, \infty)$Correct Option: , 3 Solution:...
Read More →Let f: R → R be a function such that
Question: Let $f: R \rightarrow R$ be a function such that $|f(x)| \leq x^{2}$, for all $x \in R$. Then, at $x=0, f$ is:Neither continuous nor differentiabledifferentiable but not continuouscontinuous as well as differentiablecontinuous but not differentiableCorrect Option: , 3 Solution:...
Read More →Among the following
Question: Among the following the maximum covalent character is shown by the compound :-$\mathrm{AlCl}_{3}$$\mathrm{MgCl}_{2}$$\mathrm{FeCl}_{2}$$\mathrm{SnCl}_{2}$Correct Option: 1 Solution:...
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Question: If $\omega(\neq 1)$ is a cube root of unity, and $(1+\omega)^{7}=\mathrm{A}+\mathrm{B} \omega$. Then $(\mathrm{A}, \mathrm{B})$ equals :-(1, 0)(1, 1)(0, 1)(1, 1)Correct Option: , 4 Solution:...
Read More →The structure of
Question: The structure of $\mathrm{IF}_{7}$ is :-octahedralpentagonal bipyramidsquare pyramidtrigonal bipyramidCorrect Option: , 2 Solution:...
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Question: Let $\mathrm{ABCD}$ be a parallelogram such that $\overrightarrow{\mathrm{AB}}=\overrightarrow{\mathrm{q}}, \overrightarrow{\mathrm{AD}}=\overrightarrow{\mathrm{p}}$ and $\angle \mathrm{BAD}$ be an acute angle. If $\overrightarrow{\mathrm{r}}$ is the vector that coincides with the altitude directed from the vertex $\mathrm{B}$ to the side $\mathrm{AD}$, then $\overrightarrow{\mathrm{r}}$ is given by :$\overrightarrow{\mathrm{r}}=-3 \overrightarrow{\mathrm{q}}+\frac{3(\overrightarrow{\m...
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Question: Let $\alpha, \beta$ be real and $z$ be a complex number. If $z^{2}+\alpha z+\beta=0$ has two distinct roots on the line $\operatorname{Re} z=1$, then it is necessary that :-$|\beta|=1$$\beta \in(1, \infty)$$\beta \in(0,1)$$\beta \in(-1,0)$Correct Option: , 2 Solution:...
Read More →The hybridisation of orbitals of
Question: The hybridisation of orbitals of $\mathrm{N}$ atom in $\mathrm{NO}_{3}^{-}, \mathrm{NO}_{2}^{+}$and $\mathrm{NH}_{4}^{+}$are respectively:-$s p, s p^{3}, s p^{2}$$s p^{2}, s p^{3}, s p$$s p, s p^{2}, s p^{3}$$\mathrm{sp}^{2}, \mathrm{sp}, \mathrm{sp}^{3}$Correct Option: , 4 Solution:...
Read More →Using MO theory
Question: Using MO theory predict which of the following species has the shortest bond length ?$\mathrm{O}_{2}^{-}$$\mathrm{O}_{2}^{2-}$$\mathrm{O}_{2}^{2+}$$\mathrm{O}_{2}^{+}$Correct Option: , 3 Solution:...
Read More →The lines
Question: The lines $\mathrm{L}_{1}: \mathrm{y}-\mathrm{x}=0$ and $\mathrm{L}_{2}: 2 \mathrm{x}+\mathrm{y}=0$ intersect the line $\mathrm{L}_{3}: \mathrm{y}+2=0$ at $\mathrm{P}$ and $\mathrm{Q}$ respectively. The bisector of the acute angle between $L_{1}$ and $L_{2}$ intersects $L_{3}$ at $R$. Statement - 1 : The ratio PR : RQ equals $2 \sqrt{2}: \sqrt{5}$ Statement - 2 : In any triangle, bisector of an angle divides the triangle into two similar triangles.Statement-1 is true, Statement-2 is fa...
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Question: Let $\hat{a}$ and $\hat{b}$ be two unit vectors. If the vectors $\vec{c}=\hat{a}+2 \hat{b}$ and $\vec{d}=5 \hat{a}-4 \hat{b}$ are perpendicular to each other, then the angle between $\hat{a}$ and $\hat{b}$ is :$\frac{\pi}{4}$$\frac{\pi}{6}$$\frac{\pi}{2}$$\frac{\pi}{3}$Correct Option: , 4 Solution:...
Read More →Let f, g: R → R be two functions defined by
Question: Let $f, g: R \rightarrow R$ be two functions defined byf $(x)=$ $\left\{\begin{array}{l}x \sin \left(\frac{1}{x}\right), x \neq 0 \\ 0 \quad, x=0\end{array}\right.$, and $g(x)=x f(x):-$ Statement I : $\mathrm{f}$ is a continuous function at $\mathrm{x}=0$. Statement II : $\mathrm{g}$ is a differentiable function at $\mathrm{x}=0$.Statement I is false and statement II is trueStatement I is true and statement II is falseBoth statement I and II are trueBoth statements I and II are falseCo...
Read More →Phenol reacts with methyl chloroformate in
Question: Phenol reacts with methyl chloroformate in the presence of $\mathrm{NaOH}$ to form product $\mathrm{A}$. A reacts with $\mathrm{Br}_{2}$ to form product B. A and $\mathrm{B}$ are respectively :Correct Option: , 2 Solution:...
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