Solve this following
Question: Let $A, B$ and $C$ be three events, which are pair-wise independent and $\bar{E}$ denotes the complement of an event E. If $\mathrm{P}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})=0$ and $\mathrm{P}(\mathrm{C})0$, then $\mathrm{P}[(\overline{\mathrm{A}} \cap \overline{\mathrm{B}}) \mid \mathrm{C}]$ is equal to: $P(A)+P(\bar{B})$$P(\bar{A})-P(\bar{B})$$P(\bar{A})-P(B)$$P(\overline{\mathrm{A}})+\mathrm{P}(\overline{\mathrm{B}})$Correct Option: 3, Solution: Solution not required...
Read More →Two reactions
Question: Two reactions $\mathrm{R}_{1}$ and $\mathrm{R}_{2}$ have identical pre-exponential factors. Activation energy of $\mathrm{R}_{1}$ exceeds that of $R_{2}$ by $10 \mathrm{~kJ} \mathrm{~mol}^{-1}$. If $\mathrm{k}_{1}$ and $\mathrm{k}_{2}$ are rate constants for reactions $\mathrm{R}_{1}$ and $\mathrm{R}_{2}$ respectively at $300 \mathrm{~K}$, then $\ln \left(\mathrm{k}_{2} / \mathrm{k}_{1}\right)$ is equal to :- $\left(\mathrm{R}=8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right...
Read More →The octahedral complex of a metal ion
Question: The octahedral complex of a metal ion $\mathrm{M}^{3+}$ with four monodentate ligands $\mathrm{L}_{1}, \mathrm{~L}_{2}, \mathrm{~L}_{3}$ and $\mathrm{L}_{4}$ absorb wavelength in the region of red, green, yellow and blue, respectively. The increasing order of ligand strength of the four ligands is:$\mathrm{L}_{3}\mathrm{L}_{2}\mathrm{L}_{4}\mathrm{L}_{1}$$\mathrm{L}_{1}\mathrm{L}_{2}\mathrm{L}_{4}\mathrm{L}_{3}$$\mathrm{L}_{4}\mathrm{L}_{3}\mathrm{L}_{2}\mathrm{L}_{1}$$\mathrm{L}_{1}\m...
Read More →If two tangents drawn from a point P to the parabola
Question: If two tangents drawn from a point $P$ to the parabola $y^{2}=4 x$ are at right angles then the locus of $P$ is :-x = 12x + 1 = 0x = 12x 1 = 0Correct Option: , 3 Solution: Locus of point of intersection of perpendicular tangent is directrix of the parabola. so $\mathrm{x}=-1$...
Read More →The magnetic moment of the complex anion
Question: The magnetic moment of the complex anion $\left[\mathrm{Cr}(\mathrm{NO})\left(\mathrm{NH}_{3}\right)(\mathrm{CN})_{4}\right]^{2-}$ is :$2.82 \mathrm{BM}$$5.91 \mathrm{BM}$$1.73 \mathrm{BM}$$3.87 \mathrm{BM}$Correct Option: , 3 Solution: Solution not required...
Read More →Decomposition of
Question: Decomposition of $\mathrm{H}_{2} \mathrm{O}_{2}$ follows a first order reaction. In fifty minutes the concentration of $\mathrm{H}_{2} \mathrm{O}_{2}$ decreases from $0.5$ to $0.125 \mathrm{M}$ in one such decomposition. When the concentration of $\mathrm{H}_{2} \mathrm{O}_{2}$ reaches $0.05 \mathrm{M}$, the rate of formation of $\mathrm{O}_{2}$ will be :-$1.34 \times 10^{-2} \mathrm{~mol} \mathrm{~min}{ }^{-1}$$6.93 \times 10^{-2} \mathrm{~mol} \mathrm{~min}{ }^{-1}$$6.93 \times 10^{-...
Read More →Assuming the balls to be identical except for difference in colours, the number
Question: Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is -879880629630Correct Option: 1 Solution:...
Read More →The area under the curve y=|cos x-sin x|,
Question: The area under the curve $y=|\cos x-\sin x|, 0 \leq x \leq \frac{\pi}{2}$, and above $x$-axis is :$2 R_{1}=3 R_{2}$$R_{1}=R_{2}$$3 R_{1}=2 R_{2}$$R_{1}=2 R_{2}$Correct Option: , 4 Solution:...
Read More →A bag contains 4 red and 6 black balls.
Question: A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is:$\frac{2}{5}$$\frac{1}{5}$$\frac{3}{4}$$\frac{3}{10}$Correct Option: 1 Solution:...
Read More →For the equilibrium,
Question: For the equilibrium, $\mathrm{A}(\mathrm{g}) \rightleftharpoons \mathrm{B}(\mathrm{g}), \Delta \mathrm{H}$ is $-40 \mathrm{~kJ} / \mathrm{mol}$. If the ratio of the activation energies of the forward $\left(E_{f}\right)$ and reverse $\left(E_{b}\right)$ reactions is $\frac{2}{3}$ then :-$\mathrm{E}_{\mathrm{f}}=60 \mathrm{~kJ} / \mathrm{mol} ; \mathrm{E}_{\mathrm{b}}=100 \mathrm{~kJ} / \mathrm{mol}$$\mathrm{E}_{\mathrm{f}}=30 \mathrm{~kJ} / \mathrm{mol} ; \mathrm{E}_{\mathrm{b}}=70 \ma...
Read More →There are 10 points in a plane, out of these 6 are collinear.
Question: There are 10 points in a plane, out of these 6 are collinear. If N is the number of triangles formed by joining these points, then :$\mathrm{N}190$$\mathrm{N} \leq 100$$100\mathrm{N} \leq 140$$140\mathrm{N} \leq 190$Correct Option: , 2 Solution:...
Read More →Solve this following
Question: For three events $A, B$ and $C$, $P$ (Exactly one of $\mathrm{A}$ or $\mathrm{B}$ occurs) $=\mathrm{P}($ Exactly one of $\mathrm{B}$ or $\mathrm{C}$ occurs $)$ $=\mathrm{P}($ Exactly one of $\mathrm{C}$ or A occurs $)=\frac{1}{4}$ and $\mathrm{P}($ All the three events occur simultaneously $)=\frac{1}{16}$. Then the probability that at least one of the events occurs, is :-$\frac{3}{16}$$\frac{7}{32}$$\frac{7}{16}$$\frac{7}{64}$Correct Option: , 3 Solution:...
Read More →Solve this
Question: The reaction $2 \mathrm{~N}_{2} \mathrm{O}_{5}(\mathrm{~g}) \rightarrow 4 \mathrm{NO}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g})$ follows first order kinetics. The pressure of a vessel containing only $\mathrm{N}_{2} \mathrm{O}_{5}$ was found to increase from $50 \mathrm{~mm} \mathrm{Hg}$ to $87.5 \mathrm{~mm} \mathrm{Hg}$ in $30 \mathrm{~min}$. The pressure exerted by the gases after $60 \mathrm{~min}$. will be (Assume temperature remains constant)$106.25 \mathrm{~nm} \mathrm{Hg}$$1...
Read More →Let the orthocentre and centroid of a triangle be A(–3, 5) and B(3, 3) respectively.
Question: Let the orthocentre and centroid of a triangle be A(3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter, is:$2 \sqrt{10}$$3 \sqrt{\frac{5}{2}}$$\frac{3 \sqrt{5}}{2}$$\sqrt{10}$Correct Option: , 2 Solution:...
Read More →The area of the region (in sq. units), in the first quadrant,
Question: The area of the region (in sq. units), in the first quadrant, bounded by the parabola $\mathrm{y}=9 \mathrm{x}^{2}$ and the lines $\mathrm{x}=0, \mathrm{y}=1$ and $\mathrm{y}=4$, is :-$7 / 9$$14 / 3$$14 / 9$$7 / 3$Correct Option: , 3 Solution:...
Read More →Which of the following is diamagnetic ?
Question: Which of the following is diamagnetic ?$\left[\mathrm{CoF}_{6}\right]^{3-}$$\left[\mathrm{FeF}_{6}\right]^{3-}$$\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}$$\left[\mathrm{Co}(\mathrm{Ox})_{3}\right]^{3-}$Correct Option: , 4 Solution: Solution not required...
Read More →Statement - 1 : The number of ways of distributing 10 identical balls in 4
Question: Statement - 1 : The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is ${ }^{9} C_{3}$ Statement - 2 : The number of ways of choosing any 3 places from 9 different places is${ }^{9} \mathrm{C}_{3}$Statement-1 is true, Statement-2 is false.Statement-1 is false, Statement-2 is trueStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement- 1Statement-1 is true, Statement-2 is true; Statement-2 is not a corr...
Read More →Higher order
Question: Higher order $(3)$ reactions are rare due to :-shifting of equilibrium towards reactants due to elastic collisionloss of active species on collisionlow probability of simultaneous collision of all the reacting speciesincrease in entropy and activation energy as more molecules are involved.Correct Option: , 3 Solution:...
Read More →Let k be an integer such that triangle with vertices (k, –3k), (5, k) and (–k, 2) has area 28 sq.
Question: Let k be an integer such that triangle with vertices (k, 3k), (5, k) and (k, 2) has area 28 sq. units. Then the orthocentre of this triangle is at the point :$\left(2, \frac{1}{2}\right)$$\left(2,-\frac{1}{2}\right)$$\left(1, \frac{3}{4}\right)$$\left(1,-\frac{3}{4}\right)$Correct Option: 1 Solution:...
Read More →Type of isomerism which exists between
Question: Type of isomerism which exists between $\left[\mathrm{Pd}\left(\mathrm{C}_{6} \mathrm{H}_{5}\right)_{2}(\mathrm{SCN})_{2}\right]$ and $\left[\mathrm{Pd}\left(\mathrm{C}_{6} \mathrm{H}_{5}\right)_{2}(\mathrm{NCS})_{2}\right]$ is :Solvate isomerismIonisation isomerismLinkage isomerismCoordination isomerismCorrect Option: , 3 Solution: Solution not required...
Read More →The area bounded by the curve y = ln (x) and the lines
Question: The area bounded by the curve $\mathrm{y}=\ln (x)$ and the lines $y=0, y=\ln (3)$ and $x=0$ is equal to :$3 \ln (3)-2$32$3 \ln (3)+2$Correct Option: , 3 Solution:...
Read More →If two different numbers are taken from the set
Question: If two different numbers are taken from the set $\{0,1,2,3, \ldots \ldots, 10)$, then the probability that their sum as well as absolute difference are both multiple of 4 , is :-$\frac{7}{55}$$\frac{6}{55}$$\frac{12}{55}$$\frac{14}{45}$Correct Option: , 2 Solution:...
Read More →For the non-stoichiometre
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}]$$\frac{\mathrm{dc}}{\mathrm{dt}}=\mathrm{k}[\mathrm{A}]^{2}[\mathrm{~B}]$Correct Option: , 2 Solut...
Read More →Solve the equation
Question: Let $A(-3,2)$ and $B(-2,1)$ be the vertices of a triangle $A B C$. If the centroid of this triangle lies on the line $3 x+4 y+2=0$, then the vertex $\mathrm{C}$ lies on the line :4x + 3y + 5 = 03x + 4y + 5 = 03x + 4y + 3 = 04x + 3y + 3 = 0Correct Option: , 3 Solution:...
Read More →Which of the following complex species is
Question: Which of the following complex species is not expected to exhibit optical isomerism ?$\left[\mathrm{Co}(\mathrm{en})_{3}\right]^{3+}$$\left[\mathrm{Co}(\mathrm{en})_{2} \mathrm{Cl}_{2}\right]^{+}$$\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\right]$$\left[\mathrm{Co}(\mathrm{en})\left(\mathrm{NH}_{3}\right)_{2} \mathrm{Cl}_{2}\right]^{+}$Correct Option: Solution: Solution not required...
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