Which of the following has an optical isomer?
Question: Which of the following has an optical isomer?$\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}(\mathrm{en})\right]^{3+}$$\left[\mathrm{Co}(\mathrm{en})_{2}\left(\mathrm{NH}_{3}\right)_{2}\right]^{3+}$$\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}\right]^{+}$$\left[\mathrm{Co}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2}\right]^{2+}$Correct Option: , 2 Solution: Solution not required...
Read More →For the reaction
Question: For the reaction $\mathrm{SO}_{2(\mathrm{~g})}+\frac{1}{2} \mathrm{O}_{2(\mathrm{~g})} \rightleftharpoons \mathrm{SO}_{3(\mathrm{~g})}$, if $\mathrm{K}_{\mathrm{p}}=\mathrm{K}_{\mathrm{C}}(\mathrm{RT})^{\mathrm{x}}$ where the symbols have usual meaning then the value of $x$ is :(assuming ideality)$\frac{1}{2}$1$-1$$-\frac{1}{2}$Correct Option: , 4 Solution:...
Read More →A tangent to the hyperbola
Question: A tangent to the hyperbola $\frac{x^{2}}{4}-\frac{y^{2}}{2}=1$ meets $x$-axis at $P$ and $y$-axis at $Q$. Lines $P R$ and $Q R$ are drawn such that OPRQ is a rectangle (where $\mathrm{O}$ is the origin). Then $\mathrm{R}$ lies on :$\frac{2}{x^{2}}-\frac{4}{y^{2}}=1$$\frac{4}{x^{2}}-\frac{2}{y^{2}}=1$$\frac{4}{x^{2}}+\frac{2}{y^{2}}=1$$\frac{2}{x^{2}}+\frac{4}{y^{2}}=1$Correct Option: , 2 Solution:...
Read More →Solve this following
Question: If $C$ and $D$ are two events such that $C \subset D$ and $P(D) \neq 0$, then the correct statement among the following is :-$\mathrm{P}(\mathrm{C} \mid \mathrm{D})\mathrm{P}(\mathrm{C})$$P(C \mid D)=\frac{P(D)}{P(C)}$$\mathrm{P}(\mathrm{C} \mid \mathrm{D})=\mathrm{P}(\mathrm{C})$$\mathrm{P}(\mathrm{C} \mid \mathrm{D}) \geq \mathrm{P}(\mathrm{C})$Correct Option: , 4 Solution:...
Read More →Which of the following pairs represents linkage isomers ?
Question: Which of the following pairs represents linkage isomers ?$\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{NO}_{3}\right] \mathrm{SO}_{4}$ and $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{SO}_{4}\right] \mathrm{NO}_{3}$$\left[\mathrm{PtCl}_{2}\left(\mathrm{NH}_{3}\right)_{4}\right] \mathrm{Br}_{2}$ and $\left[\mathrm{PtBr}_{2}\left(\mathrm{NH}_{3}\right)_{4}\right] \mathrm{Cl}_{2}$$\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]\left[\mathrm{PtCl}_{4}\ri...
Read More →In reaction
Question: In reaction $\mathrm{A}+2 \mathrm{~B} \rightleftharpoons 2 \mathrm{C}+\mathrm{D}$, initial concentration of $\mathrm{B}$ was $1.5$ times of $|\mathrm{A}|$, but at equilibrium the concentrations of $\mathrm{A}$ and $\mathrm{B}$ became equal. The equilibrium constant for the reaction is :46128Correct Option: 1, Solution:...
Read More →Solve this following Question
Question: Let $f(x)= \begin{cases}(x-1)^{\frac{1}{2-x}}, x1, x \neq 2 \\ k , x=2\end{cases}$ The value of $k$ for which $f$ is continuous at $x=2$ is :$\mathrm{e}^{-1}$$\mathrm{e}$$\mathrm{e}^{-2}$1Correct Option: 1 Solution: Solution Not Requird...
Read More →The equation of the hyperbola whose foci are
Question: The equation of the hyperbola whose foci are (2,0) and (2, 0) and eccentricity is 2 is given by :$-3 x^{2}+y^{2}=3$$x^{2}-3 y^{2}=3$$3 x^{2}-y^{2}=3$$-x^{2}+3 y^{2}=3$Correct Option: , 3 Solution:...
Read More →Solve this
Question: $\mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_{3}(\mathrm{~g}), \mathrm{K}_{1} \quad$ (A) $\mathrm{N}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g}), \mathrm{K}_{2}$ $\mathrm{H}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(\mathrm{g}), \mathrm{K}_{3}$ The equation for the equilibrium constant of the reaction $2 \mathrm{NH}_{3}(\mathrm{~g})+\f...
Read More →Four numbers are chosen at random
Question: Four numbers are chosen at random (without replacement) from the set $(1,2,3, \ldots .20)$. Statement-1 : The probability that the chosen numbers when arranged in some order will form an $\mathrm{AP}$ is $\frac{1}{85}$ Statement-2 : In the four chosen numbers form an AP, then the set of all possible values of common difference is $\{\pm 1, \pm 2, \pm 3, \pm 4, \pm 5\}$. Statement-1 is true, Statement $-2$ is true; Statement- 2 is a correct explanation for Statement$1 .$Statement-1 is t...
Read More →One mole of
Question: One mole of $\mathrm{O}_{2}(\mathrm{~g})$ and two moles of $\mathrm{SO}_{2}(\mathrm{~g})$ were heated in a closed vessel of one litre capacity at $1098 \mathrm{~K}$. At equilibrium $1.6$ moles of $\mathrm{SO}_{3}(\mathrm{~g})$ were found. The equilibrium constant $\mathrm{K}_{\mathrm{C}}$ of the reaction would be :-60803040Correct Option: , 2 Solution:...
Read More →If the function f defined as f(x)
Question: If the function $\mathrm{f}$ defined as $\mathrm{f}(\mathrm{x})=\frac{1}{\mathrm{x}}-\frac{\mathrm{k}-1}{\mathrm{e}^{2 \mathrm{x}}-1}, \mathrm{x} \neq 0$, is continuous at $\mathrm{x}=0$, then the ordered pair $(k, f(0))$ is equal to :$\left(\frac{1}{3}, 2\right)$$(3,2)$$(2,1)$$(3,1)$Correct Option: 4, Solution: Solution Not Required...
Read More →An urn contains nine balls of which three are red, four are blue and two are green.
Question: An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have difference colours is :-$\frac{1}{3}$$\frac{2}{7}$$\frac{1}{21}$$\frac{2}{23}$Correct Option: , 2 Solution:...
Read More →Solve this
Question: $\mathrm{K}_{1}, \mathrm{~K}_{2}$ and $\mathrm{K}_{3}$ are the equilibrium constants of the following reactions (I), (II) and (III), respectively (I) $\mathrm{N}_{2}+2 \mathrm{O}_{2} \rightleftharpoons 2 \mathrm{NO}_{2}$ (II) $2 \mathrm{NO}_{2} \rightleftharpoons \mathrm{N}_{2}+2 \mathrm{O}_{2}$ (III) $\mathrm{NO}_{2} \rightleftharpoons \frac{1}{2} \mathrm{~N}_{2}+\mathrm{O}_{2}$ The correct relation from the following is:$K_{1}=\sqrt{K_{2}}=K_{3}$$\mathrm{K}_{1}=\frac{1}{\mathrm{~K}_{...
Read More →Solve the equation
Question: Let $A$ be the sum of the first 20 terms and B be the sum of the first 40 terms of the series $1^{2}+2 \cdot 2^{2}+3^{2}+2 \cdot 4^{2}+5^{2}+2 \cdot 6^{2}+\ldots \ldots \ldots$ If $\mathrm{B}-2 \mathrm{~A}=100 \lambda$, then $\lambda$ is equal to :248464496232Correct Option: 1 Solution:...
Read More →PQR is a triangular park with PQ = PR = 200 m. A T.V.
Question: PQR is a triangular park with $P Q=P R=200 \mathrm{~m}$. A T.V. tower stands at the mid-point of $Q R$. If the angles of elevation of the top of the tower at $P, Q$ and $R$ are respectively $45^{\circ}$, $30^{\circ}$ and $30^{\circ}$, then the height of the tower (in m) is-50$100 \sqrt{3}$$50 \sqrt{2}$100Correct Option: , 4 Solution:...
Read More →If the function f(x)=
Question: If the function $f(x)= \begin{cases}\frac{\sqrt{2+\cos x}-1}{(\pi-x)^{2}}, x \neq \pi \\ k \quad, x=\pi\end{cases}$ is continuous at $x=\pi$, then $\mathrm{k}$ equals:-$\frac{1}{4}$$\frac{1}{2}$20Correct Option: 1 Solution:...
Read More →Solve the equation
Question: Let $\mathrm{a}_{1}, \mathrm{a}_{2}, \mathrm{a}_{3}, \ldots . . \mathrm{a}_{49}$ be in A.P. such that $\sum_{\mathrm{k}=0} \mathrm{a}_{4 \mathrm{k}+1}=416$ and $\mathrm{a}_{9}+\mathrm{a}_{43}=66$. If $\mathrm{a}_{1}^{2}+\mathrm{a}_{2}^{2}+\ldots \ldots+\mathrm{a}_{17}^{2}$ $=140 \mathrm{~m}$, then $\mathrm{m}$ is equal to-68343366Correct Option: , 2 Solution:...
Read More →Let a vertical tower AB have its end A on the level ground
Question: Let a vertical tower $\mathrm{AB}$ have its end $\mathrm{A}$ on the level ground. Let $\mathrm{C}$ be the mid-point $\tan \beta$ is equal to :-$\frac{4}{9}$$\frac{6}{7}$$\frac{1}{4}$$\frac{2}{9}$Correct Option: , 4 Solution:...
Read More →In a binomial distribution
Question: In a binomial distribution $\mathrm{B} \mid \mathrm{f}, \mathrm{p}=\frac{1}{4} \mathrm{~h}$, if the probability of at least one success is greater than or equal to $\frac{9}{10}$, then $\mathrm{n}$ is greater than$\frac{9}{\log _{10} 4-\log _{10} 3}$$\frac{4}{\log _{10} 4-\log _{10} 3}$$\frac{1}{\log _{10} 4-\log _{10} 3}$$\frac{1}{\log _{10} 4+\log _{10} 3}$Correct Option: , 3 Solution:...
Read More →The value of
Question: The value of $\mathrm{Kp}$ for the equilibrium reaction $\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NO}_{2}(\mathrm{~g})$ is 2 . The percentage dissociation of $\mathrm{N}_{2} \mathrm{O}_{4}(\mathrm{~g})$ at a pressure of $0.5 \mathrm{~atm}$ is71508825Correct Option: 1 Solution:...
Read More →If f(x) is continuous and f(9/2)=2/9, then
Question: If $f(x)$ is continuous and $f(9 / 2)=2 / 9$, then $\lim _{x \rightarrow 0} f\left(\frac{1-\cos 3 x}{x^{2}}\right)$ is equal to:$9 / 2$0$2 / 9$$2 / 9$Correct Option: , 3 Solution:...
Read More →Solve the equation
Question: Let $a, b, c \in R$. If $f(x)=a x^{2}+b x+c$ is such that $a+b+c=3$ and $f(x+y)=f(x)+f(y)+$ $x y, \forall x, y \in R$, then $\sum_{n=1}^{10} f(n)$ is equal to :255330165190Correct Option: Solution:...
Read More →Solve this
Question: $8 \mathrm{~mol}$ of $\mathrm{AB}_{3}(\mathrm{~g})$ are introduced into a $1.0 \mathrm{dm}^{3}$ vessel. If it dissociates as $2 \mathrm{AB}_{3}(\mathrm{~g}) \rightleftharpoons \mathrm{A}_{2}(\mathrm{~g})+3 \mathrm{~B}_{2}(\mathrm{~g})$ At equilibrium, $2 \mathrm{~mol}$ of $\mathrm{A}_{2}$ are found to be present. The equilibrium constant of this reaction is :-363272Correct Option: , 3 Solution:...
Read More →A man is walking towards a vertical pillar in a straight path
Question: A man is walking towards a vertical pillar in a straight path, at a uniform speed. Then the time taken (in minutes) by him, form B to reach the pillar, is :561020Correct Option: 1 Solution:...
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