A person is to count 4500 currency notes.
Question: A person is to count 4500 currency notes. Let $a_{n}$ denote the number of notes he counts in the $\mathrm{n}^{\text {th }}$ minute. If $\mathrm{a}_{1}=\mathrm{a}_{2}=\ldots=\mathrm{a}_{10}=150$ and $\mathrm{a}_{10}, \mathrm{a}_{11}, \ldots .$ are in an AP with common difference 2 , then the time taken by him to count all notes is :-24 minutes34 minutes125 minutes135 minutesCorrect Option: , 2 Solution:...
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^{-4} \ma...
Read More →In allene
Question: In allene $\left(\mathrm{C}_{3} \mathrm{H}_{4}\right)$, the type(s) of hybridization of the carbon atoms is (are):only $\mathrm{sp}^{2}$$\mathrm{sp}^{2}$ and $\mathrm{sp}$$s p$ and $\mathrm{sp}^{3}$$\mathrm{sp}^{2}$ and $\mathrm{sp}^{3}$Correct Option: , 2 Solution:...
Read More →Let [.] denote the greatest integet function then the value
Question: Let [.] denote the greatest integet function then the value of $\int_{0}^{1.5} \mathrm{x}\left[\mathrm{x}^{2}\right]_{\mathrm{dx}}$ is :-$\frac{5}{4}$0$\frac{3}{2}$\frac{3}{4}$Correct Option: 4, Solution:...
Read More →Two sets A and B are as under
Question: Two sets $A$ and $B$ are as under $\mathrm{A}=\{(\mathrm{a}, \mathrm{b}) \in \mathrm{R} \times \mathrm{R}:|\mathrm{a}-5|1$ and $|\mathrm{b}-5|1\}$ $\mathrm{B}=\left\{(\mathrm{a}, \mathrm{b}) \in \mathrm{R} \times \mathrm{R}: 4(\mathrm{a}-6)^{2}+9(\mathrm{~b}-5)^{2} \leq 36\right\} .$ Then :- $A \subset B$$A \cap B=\phi($ an empty set $)$neither $\mathrm{A} \subset \mathrm{B}$ nor $\mathrm{B} \subset \mathrm{A}$$\mathrm{B} \subset \mathrm{A}$Correct Option: 1 Solution:...
Read More →Let the equations of two ellipses be
Question: Let the equations of two ellipses be $E_{1}: \frac{x^{2}}{3}+\frac{y^{2}}{2}=1$ and $E_{2}: \frac{x^{2}}{16}+\frac{y^{2}}{b^{2}}=1$. If the product of their eccentricities is $\frac{1}{2}$, then the length of the minor axis of ellipse $E_{2}$ is :-9824Correct Option: , 4 Solution:...
Read More →The sum to infinity of the series
Question: The sum to infinity of the series $1+\frac{2}{3}+\frac{6}{3^{2}}+\frac{10}{3^{3}}+\frac{14}{3^{4}}+\ldots$ is :-4623Correct Option: , 4 Solution:...
Read More →Which of the following has unpaired electron(s) ?
Question: Which of the following has unpaired electron(s) ?$\mathrm{O}_{2}^{-}$$\mathrm{N}_{2}^{2+}$$\mathrm{O}_{2}^{2-}$$\mathrm{N}_{2}$Correct Option: 1 Solution:...
Read More →For the compounds
Question: For the compounds $\mathrm{CH}_{3} \mathrm{Cl}, \mathrm{CH}_{3} \mathrm{Br}, \mathrm{CH}_{3} \mathrm{I}$ and $\mathrm{CH}_{3} \mathrm{~F}$, the correct order of increasing $\mathrm{C}$-halogen bond length is :$\mathrm{CH}_{3} \mathrm{~F}\mathrm{CH}_{3} \mathrm{Br}\mathrm{CH}_{3} \mathrm{Cl}\mathrm{CH}_{3} \mathrm{I}$$\mathrm{CH}_{3} \mathrm{~F}\mathrm{CH}_{3} \mathrm{Cl}\mathrm{CH}_{3} \mathrm{Br}\mathrm{CH}_{3} \mathrm{I}$$\mathrm{CH}_{3} \mathrm{Cl}\mathrm{CH}_{3} \mathrm{Br}\mathrm{...
Read More →Equation of the line passing through the points of intersection
Question: Equation of the line passing through the points of intersection of the parabola $x^{2}=8 y$ and the ellipse $\frac{x^{2}}{3}+y^{2}=1$ is :-y + 3 = 03y + 1 = 03y 1 = 0y 3 = 0Correct Option: , 3 Solution:...
Read More →Solve this following
Question: If $A, B$ and $C$ are three sets such that $A \cap B=A \cap C$ and $A \cup B=A \cup C$, then :- $B=C$$A \cap B=\phi$$A=B$$A=C$Correct Option: 1 Solution:...
Read More →The number and type
Question: The number and type of bonds in $\mathrm{C}_{2}^{2-}$ ion in $\mathrm{CaC}_{2}$ are:Two $\sigma$ bonds and one $\pi-$ bondTwo $\sigma$ bonds and two $\pi$ - bondsOne $\sigma$ bond and two $\pi$-bondsOne $\sigma$ bond and one $\pi$ - bondCorrect Option: , 3 Solution: The number and type...
Read More →The value of
Question: The value of $\int_{0}^{1} \frac{8 \log (1+x)}{1+x^{2}} d x$ is :-$\frac{\pi}{2} \log 2$$\log 2$$\pi \log 2$$\frac{\pi}{8} \log 2$Correct Option: 3, Solution:...
Read More →For which of the following
Question: For which of the following molecule significant $\mu \neq 0$ Only (3)(3) and (4)Only (1)(1) and (2)Correct Option: , 2 Solution:...
Read More →If a and c are positive real number and the ellipse
Question: If $\mathrm{a}$ and $\mathrm{c}$ are positive real number and the ellipse $\frac{\mathrm{x}^{2}}{4 \mathrm{c}^{2}}+\frac{\mathrm{y}^{2}}{\mathrm{c}^{2}}=1$ has four distinct points in common with the circle $x^{2}+y^{2}=9 a^{2}$, then$6 a c+9 a^{2}-2 c^{2}0$$6 a c+9 a^{2}-2 c^{2}0$$9 a c-9 a^{2}-2 c^{2}0$$9 a c-9 a^{2}-2 c^{2}0$Correct Option: , 4 Solution:...
Read More →Let p(x) be a function defined on R such that
Question: Let $\mathrm{p}(\mathrm{x})$ be a function defined on $\mathrm{R}$ such that $\mathrm{p}^{\prime}(\mathrm{x})=\mathrm{p}^{\prime}(1-\mathrm{x})$, for all $\mathrm{x} \in[0,1], \mathrm{p}(0)=1$ and $p(1)=41$. Then $\int_{0}^{1} p(x) d x$ equals :-$\sqrt{41}$214142Correct Option: , 2 Solution:...
Read More →The mean and the standard deviation(s.d.) of five observations are 9 and 0, respectively.
Question: The mean and the standard deviation(s.d.) of five observations are 9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is :0142Correct Option: , 4 Solution: Solution not requierd...
Read More →Which one of the following
Question: Which one of the following properties is not shown by NO ?It combines with oxygen to form nitrogen dioxideIt's bond order is $2.5$It is diamagnetic in gaseous stateIt is a neutral oxideCorrect Option: , 3 Solution:...
Read More →The equation of the circle passing through the foci of the ellipse
Question: The equation of the circle passing through the foci of the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{9}=1$ and having centre at $(0,3)$ is :$x^{2}+y^{2}-6 y-7=0$$x^{2}+y^{2}-6 y+7=0$$x^{2}+y^{2}-6 y-5=0$$x^{2}+y^{2}-6 y+5=0$Correct Option: 1 Solution:...
Read More →If the mean of the data : 7,8,9,7,8,7,
Question: If the mean of the data : $7,8,9,7,8,7, \lambda, 8$ is 8 , then the variance of this data is :-2$\frac{7}{8}$$\frac{9}{8}$1Correct Option: , 4 Solution: Solution not requierd...
Read More →Solve this following Question
Question: $\int_{0}^{\pi}[\cot x] \mathrm{dx}$, where $[\cdot]$ denotes the greatest integer function, is equal to -$-1$$-\frac{\pi}{2}$$\frac{\pi}{2}$1Correct Option: 1 Solution:...
Read More →The internuclear distances
Question: The internuclear distances in $\mathrm{O}-\mathrm{O}$ bonds for $\mathrm{O}_{2}^{+}, \mathrm{O}_{2}, \mathrm{O}_{2}^{-}$and $\mathrm{O}_{2}^{2-}$ respectively are :Correct Option: , 3 Solution:...
Read More →The mean of a set of 30 observations is 75 .
Question: The mean of a set of 30 observations is 75 . If each observation is multiplied by a non-zero number $\lambda$ and then each of them is decreased by 25 , their mean remains the same. Then $\lambda$ is equal to$\frac{2}{3}$$\frac{10}{3}$$\frac{1}{3}$$\frac{4}{3}$Correct Option: , 4 Solution: Solution not requierd...
Read More →Statement–1 : An equation of a common tangent
Question: Statement-1 : An equation of a common tangent to the parabola $y^{2}=16 \sqrt{3} x$ and the ellipse $2 x^{2}+y^{2}=4$ is $y=2 x+2 \sqrt{3}$ Statement-2 : If the line $y=m x+\frac{4 \sqrt{3}}{m},(m \neq 0)$ is a common tangent to the parabola $y^{2}$ $16 \sqrt{3} \mathrm{x}$ and the ellipse $2 \mathrm{x}^{2}+\mathrm{y}^{2}=4$, then $\mathrm{m}$ satisfies $\mathrm{m}^{4}+2 \mathrm{~m}^{2}=24$Statement1 : An equation of a common tangentStatement1 is false, Statement2 is true.Statement1 is...
Read More →In which of the following sets,
Question: In which of the following sets, all the given species are isostructural ?$\mathrm{BF}_{3}, \mathrm{NF}_{3}, \mathrm{PF}_{3}, \mathrm{AlF}_{3}$$\mathrm{PCl}_{3}, \mathrm{AlCl}_{3}, \mathrm{BCl}_{3}, \mathrm{SbCl}_{3}$$\mathrm{BF}_{4}^{-}, \mathrm{CCl}_{4}, \mathrm{NH}_{4}^{+}, \mathrm{PCl}_{4}^{+}$$\mathrm{CO}_{2}, \mathrm{NO}_{2}, \mathrm{ClO}_{2}, \mathrm{SiO}_{2}$Correct Option: , 3 Solution:...
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