A spherical iron ball of
Question: A spherical iron ball of $10 \mathrm{~cm}$ radius is coated with a layer of ice of uniform thickness the melts at a rate of $50 \mathrm{~cm}^{3} / \mathrm{min}$. When the thickness of ice is $5 \mathrm{~cm}$, then the rate (in $\mathrm{cm} / \mathrm{min}$.) at which of the thickness of ice decreases, is :$\frac{1}{36 \pi}$$\frac{5}{6 \pi}$$\frac{1}{18 \pi}$$\frac{1}{54 \pi}$Correct Option: , 3 Solution:...
Read More →The decreasing order of basicity of the following amines is:
Question: The decreasing order of basicity of the following amines is: (I) $($ III $)($ IV $)($ II $)$$(\mathrm{II})(\mathrm{I})(\mathrm{II})(\mathrm{IV})$$(\mathrm{III})(\mathrm{II})(\mathrm{I})(\mathrm{IV})$$(\mathrm{II})(\mathrm{III})(\mathrm{IV})(\mathrm{I})$Correct Option: , 3 Solution: (III) $(\mathrm{II})(\mathrm{I})(\mathrm{IV})$...
Read More →In the figure shown below reactant
Question: In the figure shown below reactant $A$ (represented by square) is in equilibrium with product B (represented by circle). The equilibrium constant is : 2184Correct Option: 1 Solution:...
Read More →Which of the following has the shortest
Question: Which of the following has the shortest $\mathrm{C}-\mathrm{Cl}$ bond? $\mathrm{Cl}-\mathrm{CH}=\mathrm{CH}-\mathrm{OCH}_{3}$$\mathrm{Cl}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_{3}$$\mathrm{C} 1-\mathrm{CH}=\mathrm{CH}_{2}$$\mathrm{C} 1-\mathrm{CH}=\mathrm{CH}-\mathrm{NO}_{2}$Correct Option: , 4 Solution: Due to $-\mathrm{M}$ effect of $-\mathrm{NO}_{2}$ and $+\mathrm{M}$ effect of $\mathrm{Cl}$ more D.B. character between $\mathrm{C}-\mathrm{Cl}$ bond. So shortest bond length....
Read More →Amongst the following, the form of water with the lowest ionic conductance
Question: Amongst the following, the form of water with the lowest ionic conductance at $298 \mathrm{~K}$ is:distilled waterwater from a wellsaline water used for intravenous injectionsea waterCorrect Option: 1 Solution: Distilled water have lowest ionic conductance....
Read More →Among the statements (a)-(d) the correct ones are:
Question: Among the statements (a)-(d) the correct ones are: (a) Lithium has the highest hydration enthalpy among the alkali metals. (b) Lithium chloride is insoluble in pyridine. (c) Lithium cannot form ethynide upon its reaction with ethyne. (d) Both lithium and magnesium react slowly with $\mathrm{H}_{2} \mathrm{O}$. (a), (b) and (d) only(b) and (c) only(a), (c) and (d) only(a) and (d) onlyCorrect Option: , 3 Solution: Lithium has highest hydration enthalpy among alkali metals due to its smal...
Read More →Biochemical Oxygen Demand (BOD) is the amount of oxygen required (in ppm):
Question: Biochemical Oxygen Demand (BOD) is the amount of oxygen required (in ppm): by anaerobic bacteria to breakdown inorganic waste present in a water body.for the photochemical breakdown of waste present in $1 \mathrm{~m}^{3}$ volume of a water body.by bacteria to break-down organic waste in a certain volume of a water sample.for sustaining life in a water body.Correct Option: , 3 Solution: Biochemical oxygen demand (BOD) is amount of oxygen required by bacteria to break down organic waste ...
Read More →Which polymer has 'chiral' monomer(s) ?
Question: Which polymer has 'chiral' monomer(s) ? Buna-NNylon 6,6NeoprenePHBVCorrect Option: , 4 Solution:...
Read More →Solve this following
Question: A mixture of gases $\mathrm{O}_{2}, \mathrm{H}_{2}$ and $\mathrm{CO}$ are taken in a closed vessel containing charcoal. The graph that represents the correct behaviour of pressure with time is:Correct Option: , 4 Solution: Adsorption of Gases will decreases...
Read More →In the following reaction
Question: In the following reaction $\mathrm{A}$ is : Correct Option: , 3 Solution:...
Read More →Which of the following reactions will not produce a racemic product ?
Question: Which of the following reactions will not produce a racemic product ?Correct Option: 1 Solution: (No chiral centre, so no racemisation possible)...
Read More →The first and second ionisation enthalpies of a metal are 496
Question: The first and second ionisation enthalpies of a metal are 496 and $4560 \mathrm{~kJ} \mathrm{~mol}^{-1}$, respectively. How many moles of $\mathrm{HCl}$ and $\mathrm{H}_{2} \mathrm{SO}_{4}$, respectively, will be needed to react completely with 1 mole of the metal hydroxide ?1 and $0.5$2 and $0.5$1 and 11 and 2Correct Option: 1 Solution:...
Read More →Prove the following
Question: Let $X=\{n \in N: 1 \leq n \leq 50\}$. If $A=\{n \in X: n$ is a multiple of 2$\}$ and $\mathrm{B}=\{\mathrm{n} \in \mathrm{X}: \mathrm{n}$ is a multiple of 7$\}$, then the number of elements in the smallest subset of $\mathrm{X}$ containing both $A$ and $B$ is_________. Solution:...
Read More →If the foot of the perpendicular drawn from
Question: If the foot of the perpendicular drawn from the point $(1,0,3)$ on a line passing through $(\alpha, 7,1)$ is $\left(\frac{5}{3}, \frac{7}{3}, \frac{17}{3}\right)$, then $\alpha$ is equal to________ Solution:...
Read More →If the mean and variance of eight numbers
Question: If the mean and variance of eight numbers $3,7,9,12,13,20, x$ and $y$ be 10 and 25 respectively, then $x \cdot y$ is equal to______ Solution:...
Read More →If the function
Question: If the function $\mathrm{f}$ defined on $\left(-\frac{1}{3}, \frac{1}{3}\right)$ by $f(x)= \begin{cases}\frac{1}{x} \log _{e}\left(\frac{1+3 x}{1-2 x}\right) \text {, when } x \neq 0 \\ k , \text { when } x=0\end{cases}$ is continuous, then $\mathrm{k}$ is equal to___________ Solution: $k=\lim _{x \rightarrow 0}\left(\frac{\ell n(1+3 x)}{x}-\frac{\ell n(1-2 x)}{x}\right)$ $k=3+2=5$...
Read More →If the system of linear equations,
Question: If the system of linear equations, $x+y+z=6$ $x+2 y+3 z=10$ $3 x+2 y+\lambda z=\mu$ has more two solutions, then $\mu-\lambda^{2}$ is equal to_________. Solution:...
Read More →Let the tangents drawn from the origin to the circle,
Question: Let the tangents drawn from the origin to the circle, $x^{2}+y^{2}-8 x-4 y+16=0$ touch it at the points $A$ and $B$. The $(A B)^{2}$ is equal to :$\frac{52}{5}$$\frac{32}{5}$$\frac{56}{5}$$\frac{64}{5}$Correct Option: , 4 Solution:...
Read More →In a workshop,
Question: In a workshop, there are five machines and the probability of any one of them to be out of service on a day is $\frac{1}{4}$. If the probability that at most two machines will be out of service on the same day is $\left(\frac{3}{4}\right)^{3} \mathrm{k}$, then $\mathrm{k}$ is equal to :$\frac{17}{2}$4$\frac{17}{8}$$\frac{17}{4}$Correct Option: , 3 Solution:...
Read More →Let f(x) be a polynomial of degree 5 such
Question: Let $f(x)$ be a polynomial of degree 5 such that $x=\pm 1$ are its critical points. If $\lim _{x \rightarrow 0}\left(2+\frac{f(x)}{x^{3}}\right)=4$, then which one of the following is not true? $f$ is an odd function$x=1$ is a point of minima and $x=-1$ is a point of maxima of $f$.$x=1$ is a point of maxima and $x=-1$ is a point of minimum of $f$.$f(1)-4 f(-1)=4$Correct Option: , 2 Solution:...
Read More →Let y=y(x) be the solution curve of the
Question: Let $y=y(x)$ be the solution curve of the differential cquation, $\quad\left(\mathrm{y}^{2}-\mathrm{x}\right) \frac{\mathrm{dy}}{\mathrm{dx}}=1$, satisfying $\mathrm{y}(0)=1$. This curve intersects the $x$-axis at a point whose abscissa is :$2+\mathrm{e}$2$2-\mathrm{e}$$-\mathrm{e}$Correct Option: , 3 Solution:...
Read More →Prove the following
Question: If $\frac{3+i \sin \theta}{4-i \cos \theta}, \theta \in[0,2 \pi]$, is a real number, then an argument of $\sin \theta+i \cos \theta$ is :$-\tan ^{-1}\left(\frac{3}{4}\right)$$\tan ^{-1}\left(\frac{4}{3}\right)$$\pi-\tan ^{-1}\left(\frac{4}{3}\right)$$\pi-\tan ^{-1}\left(\frac{3}{4}\right)$Correct Option: , 3 Solution:...
Read More →The locus of the mid-points of the perpendiculars
Question: The locus of the mid-points of the perpendiculars drawn from points on the line, $x=2 y$ to the line $x=y$ is :$2 x-3 y=0$$7 x-5 y=0$$5 x-7 y=0$$3 x-2 y=0$Correct Option: , 3 Solution:...
Read More →Let alpha and beta be the roots of the equation
Question: Let $\alpha$ and $\beta$ be the roots of the equation $\mathrm{x}^{2}-\mathrm{x}-1=0$. If $\mathrm{p}_{\mathrm{k}}=(\alpha)^{\mathrm{k}}+(\beta)^{\mathrm{k}}, \mathrm{k} \geq 1$, then which one of the following statements is not true ?$\left(\mathrm{p}_{1}+\mathrm{p}_{2}+\mathrm{p}_{3}+\mathrm{p}_{4}+\mathrm{p}_{5}\right)=26$$\mathrm{p}_{5}=11$$\mathrm{p}_{3}=\mathrm{p}_{5}-\mathrm{p}_{4}$$\mathrm{p}_{5}=\mathrm{p}_{2} \cdot \mathrm{p}_{3}$Correct Option: , 4 Solution:...
Read More →The correct order of the spin-only magnetic moments of the following complexes is :
Question: The correct order of the spin-only magnetic moments of the following complexes is : (I) $\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right] \mathrm{Br}_{2}$ (II) $\mathrm{Na}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]$ (III) $\mathrm{Na}_{3}\left[\mathrm{Fe}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]\left(\Delta_{0}\mathrm{P}\right)$ (IV) $\left(\mathrm{Et}_{4} \mathrm{~N}\right)_{2}\left[\mathrm{CoCl}_{4}\right]$(III) $$ (I) $$ (II) $$ (IV)(I) $(\mathrm{IV}...
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