Find the surface area of a sphere whose volume is 606.375 m3.
Question: Find the surface area of a sphere whose volume is 606.375 m3. Solution: Volume of the sphere = 606.375 m3 Then $\frac{4}{3} \pi r^{3}=606.375$ $\Rightarrow r^{3}=\frac{606.375 \times 3 \times 7}{4 \times 22}=144.703$ $\Rightarrow r=5.25 \mathrm{~m}$ $\therefore$ Surface area $=4 \pi r^{2}$ $=4 \times \frac{22}{7} \times 5.25 \times 5.25$ $=346.5 \mathrm{~m}^{2}$...
Read More →In the following reaction sequence the major products A and B are :
Question: In the following reaction sequence the major products A and $\mathrm{B}$ are : Correct Option: Solution: Given below are two statements: Statement I : Bohr's theory accounts for the stability and line spectrum of $\mathrm{Li}^{+}$ion. Statement II : Bohr's theory was unable to explain the splitting of spectral lines in the presence of a magnetic field. In the light of the above statements, choose the most appropriate answer from the options given below: (1) Both statement I and stateme...
Read More →The volume of a sphere is 38808 cm3.
Question: The volume of a sphere is 38808 cm3. Find its radius and hence its surface area. Solution: Volume of the sphere = 38808 cm3 Supposethatrcm is the radius of the given sphere. $\therefore \frac{4}{3} \pi r^{3}=38808$ $\Rightarrow r^{3}=\frac{38808 \times 3 \times 7}{4 \times 22}=9261$ $\Rightarrow r=\sqrt[3]{9261}=21 \mathrm{~cm}$ $\therefore$ Surface area of the sphere $=4 \pi r^{2}$ $=4 \times \frac{22}{7} \times 21 \times 21$ $=5544 \mathrm{~cm}^{2}$...
Read More →The graphs of sine and cosine functions,
Question: The graphs of sine and cosine functions, intersect each other at a number of points and between two consecutive points of intersection, the two graphs enclose the same area $A$. Then $A^{4}$ is equal to Solution: $ Required area $=2 \int_{0}^{\sqrt{3}}\left(2 x^{2}+9-5 x^{2}\right) d x$ $=2 \int_{0}^{\sqrt{3}}\left(9-3 x^{2}\right) d x$ $=2\left|9 x-x^{3}\right|_{0}^{\sqrt{3}}=12 \sqrt{3}$...
Read More →Solve the following
Question: [P] on treatment with $\mathrm{Br}_{2} / \mathrm{FeBr}_{3}$ in $\mathrm{CCl}_{4}$ produced a single isomer $\mathrm{C}_{8} \mathrm{H}_{7} \mathrm{O}_{2} \mathrm{Br}$ while heating $[\mathrm{P}]$ with sodalime gave toluene. The compound [P] is :Correct Option: Solution: A certain orbital has no angular nodes and two radial nodes. The orbital is: (1) $2 \mathrm{~s}$ (2) $3 \mathrm{~s}$ (3) $3 \mathrm{p}$ (4) $2 \mathrm{p}$...
Read More →Two stream of photons, possessing energies equal to twice and ten times the work function of metal are incident on the
Question: Two stream of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons emitted in the two respective cases is $\mathrm{x}: \mathrm{y}$. The value of $\mathrm{x}$ is Solution: (1) Forphotoelectric effectk. $\mathrm{E}_{\max }=\mathrm{E}-\phi$ $\mathrm{E}_{1}=2 \phi_{r} \quad \mathrm{k}_{1}=\phi$ $\mathrm{E}_{2}=10 \phi_{r} \quad \mathrm{k}_{2}=9 \phi...
Read More →The major product of the following reaction is :
Question: The major product of the following reaction is : Correct Option: Solution: In the ground state of atomic $\mathrm{Fe}(\mathrm{Z}=26)$, the spin-only magnetic moment is _________ $\times 10^{-1} \mathrm{BM}$. (Round off to the Nearest Integer). $[$ Given $: \sqrt{3}=1.73, \sqrt{2}=1.41]$...
Read More →Find the volume and surface area of a sphere whose radius is:
Question: Find the volume and surface area of a sphere whose radius is:(i) 3.5 cm(ii) 4.2 cm(iii) 5 m Solution: (i) Radius of the sphere = 3.5 cm Now, volume $=\frac{4}{2} \pi r^{3}$ $=\frac{4}{3} \times \frac{22}{7} \times 3.5 \times 3.5 \times 3.5$ $=179.67 \mathrm{~cm}^{3}$ $\therefore$ Surface area $=4 \pi r^{2}$ $=4 \times \frac{22}{7} \times 3.5 \times 3.5$ $=154 \mathrm{~cm}^{2}$ (ii) Radius of the sphere=4.2 cm Now, volume $=\frac{4}{3} \pi r^{3}$ $=\frac{4}{3} \times \frac{22}{7} \times...
Read More →The recoil speed of a hydrogen atom after it emits a photon in going from
Question: The recoil speed of a hydrogen atom after it emits a photon in going from $\mathrm{n}=5$ state to $\mathrm{n}=1$ state will be:(1) $4.17 \mathrm{~m} / \mathrm{s}$(2) $4.34 \mathrm{~m} / \mathrm{s}$(3) $219 \mathrm{~m} / \mathrm{s}$(4) $3.25 \mathrm{~m} / \mathrm{s}$Correct Option: Solution: (1) momentum $(P)=\frac{\Delta E}{C}=\frac{(13.6-0.54) \mathrm{eV}}{3 \times 10^{8}}$ $\mathrm{mv}=\frac{(13.06) \times 1.6 \times 10^{-19}}{3 \times 10^{8}}$ $\mathrm{v}=\frac{(13.06) \times 1.6 \t...
Read More →The area (in sq. units) of the part of the circle
Question: The area (in sq. units) of the part of the circle $x^{2}+y^{2}=36$, which is outside the parabola $y^{2}=9 x$, is : (1) $24 \pi+3 \sqrt{3}$(2) $12 \pi+3 \sqrt{3}$(3) $12 \pi-3 \sqrt{3}$(4) $24 \pi-3 \sqrt{3}$Correct Option: , 4 Solution: The curves intersect at point $(3, \pm 3 \sqrt{3})$ Required area $=\pi r^{2}-2\left[\int_{0}^{3} \sqrt{9 x} d x+\int_{3}^{6} \sqrt{36-x^{2}} d x\right]$ $=36 \pi-12 \sqrt{3}-2\left(\frac{x}{2} \sqrt{36-x^{2}}+18 \sin ^{-1}\left(\frac{x}{6}\right)\righ...
Read More →The correct sequence of reagents used in the preparation
Question: The correct sequence of reagents used in the preparation of 4 -bromo-2-nitroethyl benzene from benezene is :$\mathrm{CH}_{3} \mathrm{COCl} / \mathrm{AlCl}_{3}, \mathrm{Br}_{2} / \mathrm{AlBr}_{3}, \mathrm{HNO}_{3} / \mathrm{H}_{2} \mathrm{SO}_{4}, \mathrm{Zn} / \mathrm{HCl}$$\mathrm{CH}_{3} \mathrm{COCl} / \mathrm{AlCl}_{3}, \mathrm{Zn}-\mathrm{Hg} / \mathrm{HCl}, \mathrm{Br}_{2} / \mathrm{AlBr}_{3}, \mathrm{HNO}_{3} / \mathrm{H}_{2} \mathrm{SO}_{4}$$\mathrm{Br}_{2} / \mathrm{AlBr}_{3}...
Read More →Solve this
Question: Note Use $\pi=\frac{22}{7}$, unless stated otherwise. A cloth having an area of $165 \mathrm{~m}^{2}$ is shaped into the form of a conical tent of radius $5 \mathrm{~m}$. (i) How many students can sit in the tent if a student, on an average, iccupies $\frac{5}{7} \mathrm{~m}^{2}$ on the ground? (ii) Find the volume of the cone. Solution: Radius of the conical tent,r= 5 m Area of the base of the conical tent $=\pi r^{2}=\frac{22}{7} \times 5^{2}=\frac{550}{7} \mathrm{~m}^{2}$ Average ar...
Read More →The major product of the following reaction is :
Question: The major product of the following reaction is : Correct Option: Solution: What is the spin-only magnetic moment value (BM) of a divalent metal ion with atomic number 25 , in it's aqueous solution? (1) $5.92$ (2) 5 (3) zero (4) $5.26$...
Read More →Let y=y(x) be the solution of the differential
Question: Let $y=y(x)$ be the solution of the differential equation $x d y=y d x=\sqrt{\left(x^{2}-y^{2}\right)} d x, x \geq 1$, with $y(1)=0 .$ If the area bounded by the line $x=1, x=e^{\pi}, y=0$ and $y=y(x)$ is $\alpha \mathrm{e}^{2 \pi}+\beta$, then the value of $10(\alpha+\beta)$ is equal to_________ Solution: $x d y-y d x=\sqrt{x^{2}-y^{2}} d x$ $\Rightarrow \frac{x d y-y d x}{x^{2}}=\frac{1}{x} \sqrt{1-\frac{y^{2}}{x^{2}}} d x$ $\Rightarrow \int \frac{d\left(\frac{y}{x}\right)}{\sqrt{1-\...
Read More →Let y=y(x) be the solution of the differential
Question: Let $y=y(x)$ be the solution of the differential equation $x d y=y d x=\sqrt{\left(x^{2}-y^{2}\right)} d x, x \geq 1$, with $y(1)=0 .$ If the area bounded by the line $x=1, x=e^{\pi}, y=0$ and $y=y(x)$ is $\alpha \mathrm{e}^{2 \pi}+\beta$, then the value of $10(\alpha+\beta)$ is equal to_________ Solution: $x d y-y d x=\sqrt{x^{2}-y^{2}} d x$ $\Rightarrow \frac{x d y-y d x}{x^{2}}=\frac{1}{x} \sqrt{1-\frac{y^{2}}{x^{2}}} d x$ $\Rightarrow \int \frac{d\left(\frac{y}{x}\right)}{\sqrt{1-\...
Read More →Compound(s) which will liberate carbon dioxide with sodium bicarbonate solution is/are:
Question: Compound(s) which will liberate carbon dioxide with sodium bicarbonate solution is/are: $\mathrm{B}$ and $\mathrm{C}$ onlyB only$A$ and $B$ only$C$ onlyCorrect Option: Solution: The number of orbitals with $\mathrm{n}=5, \mathrm{~m}_{1}=+2$ is_____________ (Round off to the Nearest Integer)....
Read More →if
Question: If $\lambda_{1}$ and $\lambda_{2}$ are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of $\lambda_{1}: \lambda_{2}$ is :(1) $1: 3$(2) $1: 9$(3) $7: 135$(4) 7:108Correct Option: , 3 Solution: (3) For Lyman series $n_{1}=1, \quad n_{2}=4$ $\frac{1}{\lambda_{1}}=R z^{2}\left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right)$ $\frac{1}{\lambda_{1}}=\mathrm{Rz}^{2}\left(\frac{1}{1_{1}^{2}}-\frac{1}{4^{2}}\right)$ $\frac{1}{\lamb...
Read More →Water flows at the rate of 10 metres per minute through a cylindrical pipe 5 mm in diameter.
Question: Water flows at the rate of 10 metres per minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter art the surface 40 cm and depth 24 cm? Solution: Radius of the cylindrical pipe = 2.5 mm = 0.25 cmWater flowing per minute = 10 m = 1000 cm Volume of water flowing per minute through the cylindrical pipe $=\pi(0.25)^{2} 1000 \mathrm{~cm}^{3}=196.4 \mathrm{~cm}^{3}$ Radius of the the conical vessel = 40 cmDepth of the vessel = 24 cm ...
Read More →The correct order of the following compounds showing increasing tendency towards nucleophilic substitution reaction is :
Question: The correct order of the following compounds showing increasing tendency towards nucleophilic substitution reaction is : $(i v)(i)(i i i)(i i)$$(\mathrm{i} v)(\mathrm{i})(\mathrm{ii})(\mathrm{iii})$$(i)(i i)(i i i)(i v)$(iv) $$ (iii) $$ (ii) $$ (i)Correct Option: Solution: Arrange the following metal complex/ compounds in the increasing order of spin only magnetic moment. Presume all the three, high spin system. (Atomic numbers $\mathrm{Ce}=58, \mathrm{Gd}=64$ and $\mathrm{Eu}=63 .)$ (...
Read More →From a solid right circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and base is removed.
Question: From a solid right circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and base is removed. Find the volume of the remaining solid. Solution: Height of the cylinder = 10 cmRadius of the cylinder = 6 cmThe respective heights and radii of the cone and the cylinder are the same. Volume of the remaining solid = volume of the cylinder volume of the cone $=\pi r^{2} h-\frac{1}{3} \pi r^{2} h$ $=\frac{2}{3} \pi r^{2} h$ $=\frac{2}{3} \time...
Read More →An electron of mass
Question: An electron of mass $m_{e}$ and a proton of mass $m_{p}=1836 m_{e}$ are moving with the same speed. The ratio of their de Broglie wavelength $\frac{\lambda_{\text {himene }}}{\lambda_{\text {temown }}}$ will be:(1) 918(2) 1836(3) $\frac{1}{1836}$(4) 1Correct Option: , 2 Solution: (2) Given mass of electron $=\mathrm{m}_{e}$ Mass of proton $=\mathrm{m}_{\mathrm{p}}$ $\therefore$ given $m_{p}=1836 \mathrm{~m}_{\mathrm{e}}$ From de-Broglie wavelength $\lambda=\frac{h}{p}=\frac{h}{m v}$ $\...
Read More →An iron pillar consists of a cylindrical portion 2.8 m high and 20 cm in diameter and a cone 42 cm high is surmounting it.
Question: An iron pillar consists of a cylindrical portion 2.8 m high and 20 cm in diameter and a cone 42 cm high is surmounting it. Find the weight of the pillar, given that 1 cm3of iron weights 7.5 g. Solution: Height of the cylindrical portion of the iron pillar,h= 2.8 m = 280 cmRadius of the cylindrical portion of the iron pillar,r= 20 cmHeight of the cone which is surmounted on the cylindrical portion,H= 42 cmNow, volume of the pillar = volume of the cylindrical portion + volume of the coni...
Read More →The area bounded by the curve
Question: The area bounded by the curve $4 y^{2}=x^{2}(4-x)(x-2)$ is equal to:(1) $\frac{\pi}{8}$(2) $\frac{3 \pi}{8}$(3) $\frac{3 \pi}{2}$(4) $\frac{\pi}{16}$Correct Option: , 3 Solution: $4 y^{2}=x^{2}(4-x)(x-2)$ $|y|=\frac{|x|}{2} \sqrt{(4-x)(x-2)}$ $\Rightarrow y_{1}=\frac{x}{2} \sqrt{(4-x)(x-2)}$ and $y_{2}=\frac{-x}{2} \sqrt{(4-x)(x-2)}$ $\mathrm{D}: \mathrm{x} \in[2,4]$ Required Area $=\int_{2}^{4}\left(y_{1}-y_{2}\right) d x=\int_{2}^{4} x \sqrt{(4-x)(x-2)} d x \ldots(1)$ Applying $\int_...
Read More →A circus tent is cylindrical to a height of 3 metres and conical above it.
Question: A circus tent is cylindrical to a height of 3 metres and conical above it. If its diameter is 105 m and the slant height of the conical portion is 53 m, calculate the length of the canvas 5 m wide to make the required tent. Solution: Radius of the tent,r= 52.5 mHeight of the cylindrical portion of the tent,H= 3 mSlant height of the conical portion of the tent,l= 53 mThe tent is a combination of a cylindrical and a conical portion.i.e., area of the canvas = curved surface area of the co...
Read More →A right circular cone is 3.6 cm high and the radius of its base is 1.6 cm.
Question: A right circular cone is 3.6 cm high and the radius of its base is 1.6 cm. It is melted and recast into a right circular cone having base radius 1.2 cm. Find its height. Solution: Let the cone which is being melted be denoted by cone 1 and let the cone into which cone 1 is being melted be denoted by cone 2.Height of cone 1 = 3.6 cmRadius of the base of cone 1 = 1.6 cmRadius of the base of cone 2 = 1.2 cmLethcm be the height of cone 2.The volumes of both the cones should be equal i. e.,...
Read More →