Solve this following
Question: If the angle between the lines, $\frac{x}{2}=\frac{y}{2}=\frac{z}{1}$ and $\frac{5-x}{-2}=\frac{7 y-14}{p}=\frac{z-3}{4}$ is $\cos ^{-1}\left(\frac{2}{3}\right)$, then $p$ is equal to:$-\frac{4}{7}$$\frac{7}{2}$$-\frac{7}{4}$$\frac{2}{7}$Correct Option: , 2 Solution: Solution not required...
Read More →Bond order normally gives
Question: Bond order normally gives idea of stability of a molecular species. All the molecules viz. $\mathrm{H}_{2}$, $\mathrm{Li}_{2}$ and $\mathrm{B}_{2}$ have the same bond order yet they are not equally stable. Their stability order is:$\mathrm{Li}_{2}\mathrm{H}_{2}\mathrm{B}_{2}$$\mathrm{H}_{2}\mathrm{B}_{2}\mathrm{Li}_{2}$$\mathrm{B}_{2}\mathrm{H}_{2}\mathrm{Li}_{2}$$\mathrm{Li}_{2}\mathrm{B}_{2}\mathrm{H}_{2}$Correct Option: , 2 Solution:...
Read More →If S is the set of distinct values of 'b' for which
Question: If $S$ is the set of distinct values of ' $b$ ' for which the following system of linear equations $x+y+z=1$ $x+a y+z=1$ $a x+b y+z=0$ has no solution, then $S$ is :a singletonan empty setan infinite seta finite set containing two or more elementsCorrect Option: 1 Solution:...
Read More →If the mean deviation about the median of the numbers a,
Question: If the mean deviation about the median of the numbers a, 2a, .........., 50a is 50, then |a| equals:4523Correct Option: 1 Solution:...
Read More →For the non-stoichiometre reaction
Question: For the non-stoichiometre reaction $2 \mathrm{~A}+\mathrm{B} \rightarrow \mathrm{C}+\mathrm{D}$, the following kinetic data were obtained in three separate experiments, all at $298 \mathrm{~K}$. $\frac{\mathrm{dc}}{\mathrm{dt}}=\mathrm{k}[\mathrm{A}][\mathrm{B}]^{2}$$\frac{\mathrm{dc}}{\mathrm{dt}}=\mathrm{k}[\mathrm{A}]$$\frac{\mathrm{dc}}{\mathrm{dt}}=\mathrm{k}[\mathrm{A}][\mathrm{B}]$$\frac{\mathrm{dc}}{\mathrm{dt}}=\mathrm{k}[\mathrm{A}]^{2}[\mathrm{~B}]$Correct Option: , 2 Soluti...
Read More →For two data sets each of size is 5,
Question: For two data sets each of size is 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4 respectively, then the variance of the combined data set is :-$\frac{5}{2}$$\frac{11}{2}$6$\frac{13}{2}$Correct Option: , 2 Solution:...
Read More →Oxidation state of sulphur
Question: Oxidation state of sulphur in anions $\mathrm{SO}_{3}^{2-}, \mathrm{S}_{2} \mathrm{O}_{4}^{2-}$ and $\mathrm{S}_{2} \mathrm{O}_{6}^{2-}$ increases in the orders :$\mathrm{S}_{2} \mathrm{O}_{6}^{2-}\mathrm{S}_{2} \mathrm{O}_{4}^{2-}\mathrm{SO}_{3}^{2-}$$\mathrm{SO}_{3}^{2-}\mathrm{S}_{2} \mathrm{O}_{4}^{2-}\mathrm{S}_{2} \mathrm{O}_{6}^{2-}$$\mathrm{S}_{2} \mathrm{O}_{4}^{2-}\mathrm{SO}_{3}^{2-}\mathrm{S}_{2} \mathrm{O}_{6}^{2-}$$\mathrm{S}_{2} \mathrm{O}_{4}^{2-}\mathrm{S}_{2} \mathrm{...
Read More →Solve the following
Question: If $5\left(\tan ^{2} x-\cos ^{2} x\right)=2 \cos 2 x+9$, then the value of $\cos 4 x$ is :-$-\frac{7}{9}$$-\frac{3}{5}$$\frac{1}{3}$$\frac{2}{9}$Correct Option: 1 Solution:...
Read More →Solve this following
Question: If $\vec{a}, \vec{b}$, and $\vec{c}$ are unit vectors such that $\vec{a}+2 \vec{b}+2 \vec{c}=\overrightarrow{0}$, then $|\vec{a} \times \vec{c}|$ is equal to : $\frac{1}{4}$$\frac{\sqrt{15}}{16}$$\frac{15}{16}$$\frac{\sqrt{15}}{4}$Correct Option: , 4 Solution: Solution not required...
Read More →The rate of a reaction doubles when its temperature
Question: The rate of a reaction doubles when its temperature changes from $300 \mathrm{~K}$ to $310 \mathrm{~K}$. Activation energy of such a reaction will be $\left(\mathrm{R}=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right.$ and $\left.\log 2=0.301\right)$$53.6 \mathrm{~kJ} \mathrm{~mol}^{-1}$$48.6 \mathrm{~kJ} \mathrm{~mol}^{-1}$$58.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$$60.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$Correct Option: 1 Solution:...
Read More →Statement-1 : The variance of first n even natural numbers is
Question: Statement-1 : The variance of first $n$ even natural numbers is $\frac{n^{2}-1}{4}$ Statement-2 : The sum of first n natural numbers is $\frac{n(n+1)}{2}$ and the sum of squares of first $n$ natural numbers is $\frac{\mathrm{n}(\mathrm{n}+1)(2 \mathrm{n}+1)}{6}$.Statement1 is true, Statement2 is false.Statement1 is false, Statement2 is true.Statement1 is true, Statement2 is true ; Statement2 is a correct explanation for Statement1.Statement1 is true, Statement2 is true ; Statement2 is ...
Read More →The system of linear equations
Question: The system of linear equations $x+\lambda y-z=0$ $\lambda x-y-z=0$ $x+y-\lambda z=0$ has a non-trivial solution for :exactly three values of $\lambda$.infinitely many values of $\lambda$.exactly one value of $\lambda$.exactly two values of $\lambda$.Correct Option: 1, Solution:...
Read More →Which one of the following molecules is polar?
Question: Which one of the following molecules is polar?$\mathrm{CF}_{4}$$\mathrm{SbF}_{5}$$\mathrm{IF}_{5}$$\mathrm{XeF}_{4}$Correct Option: , 3 Solution:...
Read More →Solve the following
Question: Let $f_{K}(x)=\frac{1}{k}\left(\sin ^{k} x+\cos ^{k} x\right)$ where $x \in R$ and $k \geq 1 .$ Then $f_{4}(x)-f_{6}(x)$ equals :$\frac{1}{6}$$\frac{1}{3}$$\frac{1}{4}$$\frac{1}{12}$Correct Option: , 4 Solution:...
Read More →Solve this following
Question: If the position vectors of the vertices $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ of a $\triangle \mathrm{ABC}$ are respectively $4 \hat{\mathrm{i}}+7 \hat{\mathrm{j}}+8 \hat{\mathrm{k}}, 2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}$ and $2 \hat{\mathrm{i}}+5 \hat{\mathrm{j}}+7 \hat{\mathrm{k}}$, then the position vector of the point, where the bisector of $\angle \mathrm{A}$ meets $\mathrm{BC}$ is :- $\frac{1}{2}(4 \hat{i}+8 \hat{j}+11 \hat{k})$$\frac{1}{3}(6 \hat{\mathrm{...
Read More →The set of all values of
Question: The set of all values of $\lambda$ for which the system of linear equations: $2 x_{1}-2 x_{2}+x_{3}=\lambda x_{1}$ $2 x_{1}-3 x_{2}+2 x_{3}=\lambda x_{2}$ $-\mathrm{x}_{1}+2 \mathrm{x}_{2}=\lambda \mathrm{x}_{3}$ has a non-trivial solutioncontains two elementscontains more than two elementsis an empty setis a singletonCorrect Option: 1 Solution:...
Read More →In which of the following
Question: In which of the following ionization processes the bond energy has increased and also the magnetic behaviour has changed from paramagnetic to diamagnetic ?$\mathrm{NO} \rightarrow \mathrm{NO}^{+}$$\mathrm{O}_{2} \rightarrow \mathrm{O}_{2}^{+}$$\mathrm{N}_{2} \rightarrow \mathrm{N}_{2}^{+}$$\mathrm{C}_{2} \rightarrow \mathrm{C}_{2}^{+}$Correct Option: 1 Solution:...
Read More →If the mean deviation of the numbers 1,
Question: If the mean deviation of the numbers 1, 1 + d, 1 + 2d, ..., 1 + 100d from their mean is 255, then that d is equal to-10.120.210.020.0Correct Option: 1 Solution:...
Read More →Solve this following Question
Question: If $\alpha, \beta \neq 0$, and $f(\mathrm{n})=\alpha^{\mathrm{n}}+\beta^{\mathrm{n}}$ and $\left|\begin{array}{ccc}3 1+f(1) 1+f(2) \\ 1+f(1) 1+f(2) 1+f(3) \\ 1+f(2) 1+f(3) 1+f(4)\end{array}\right|=\mathrm{K}(1-\alpha)^{2}(1-\beta)^{2}(\alpha-\beta)^{2}$ then $\mathrm{K}$ is equal to :$\alpha \beta$$\frac{1}{\alpha \beta}$1-1Correct Option: , 3 Solution:...
Read More →24. Trigonal bipyramidal geometry is shown by:
Question: 24. Trigonal bipyramidal geometry is shown by:$\mathrm{XeO}_{3} \mathrm{~F}_{2}$$\mathrm{XeOF}_{2}$$\left[\mathrm{XeF}_{8}\right]^{2-}$$\mathrm{FXeOSO}_{2} \mathrm{~F}$Correct Option: 1 Solution:...
Read More →Stability of the species
Question: Stability of the species $\mathrm{Li}_{2}, \mathrm{Li}_{2}^{-}$and $\mathrm{Li}_{2}^{+}$increases in the order of :-$\mathrm{Li}_{2}\mathrm{Li}_{2}^{+}\mathrm{Li}_{2}^{-}$$\mathrm{Li}_{2}^{-}\mathrm{Li}_{2}^{+}\mathrm{Li}_{2}$$\mathrm{Li}_{2}\mathrm{Li}_{2}^{-}\mathrm{Li}_{2}^{+}$$\mathrm{Li}_{2}^{-}\mathrm{Li}_{2}\mathrm{Li}_{2}^{+}$Correct Option: , 2 Solution:...
Read More →Solve this following
Question: Let $\overrightarrow{\mathrm{a}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}$. Let $\overrightarrow{\mathrm{c}}$ be a vector such that $|\overrightarrow{\mathrm{c}}-\overrightarrow{\mathrm{a}}|=3,|(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}) \times \overrightarrow{\mathrm{c}}|=3$ and the angle between $\overrightarrow{\mathrm{c}}$ and $\overrightarrow{\mathrm{a}} \times \overrightarrow{\m...
Read More →ABCD is a trapezium such that AB and CD
Question: $\mathrm{ABCD}$ is a trapezium such that $\mathrm{AB}$ and $C D$ are parallel and $\mathrm{BC} \perp \mathrm{CD}$. If $\angle \mathrm{ADB}=\theta, \mathrm{BC}$ $=\mathrm{p}$ and $\mathrm{CD}=\mathrm{q}$, then $\mathrm{AB}$ is equal to$\frac{\left(p^{2}+q^{2}\right) \sin \theta}{p \cos \theta+q \sin \theta}$$\frac{p^{2}+q^{2} \cos \theta}{p \cos \theta+q \sin \theta}$$\frac{\mathrm{p}^{2}+\mathrm{q}^{2}}{\mathrm{p}^{2} \cos \theta+\mathrm{q}^{2} \sin \theta}$$\frac{\left(p^{2}+q^{2}\rig...
Read More →Two sides of a rhombus are along the lines,
Question: Two sides of a rhombus are along the lines, x y + 1 = 0 and 7x y 5 = 0. If its diagonals intersect at (1, 2), then which one of the following is a vertex of this rhombus ?$\left(-\frac{10}{3},-\frac{7}{3}\right)$$(-3,-9)$$(-3,-8)$$\left(\frac{1}{3},-\frac{8}{3}\right)$Correct Option: , 4 Solution: Clearly $\left(\frac{1}{3},-\frac{8}{3}\right)$ lies on (1)...
Read More →In which of the following pairs
Question: In which of the following pairs of molecules/ions, both the species are not likely to exist ?$\mathrm{H}_{2}^{+}, \mathrm{He}_{2}^{2-}$$\mathrm{H}_{2}^{-}, \mathrm{He}_{2}^{2-}$$\mathrm{H}_{2}^{2+}, \mathrm{He}_{2}$$\mathrm{H}_{2}^{-}, \mathrm{He}_{2}^{2+}$Correct Option: , 3 Solution:...
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