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...

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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:...

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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:...

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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:...

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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...

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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:...

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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...

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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:...

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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...

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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...

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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:...

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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...

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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:...

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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}_{...

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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:...

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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:...

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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:...

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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:...

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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:...

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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:...

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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:...

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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:...

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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:...

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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:...

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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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