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Question: Note Use $\pi=\frac{22}{7}$, unless stated otherwise. The curved surface area of a cone is 308 cm2and its slant height is 14 cm. Find the radius of the base and total surface area of the cone. Solution: Slant height,l= 14 cmLet the radius of the base bercm.Curved surface area of the cone =308 cm2 (Given) $\therefore \pi r l=308$ $\Rightarrow \frac{22}{7} \times r \times 14=308$ $\Rightarrow r=\frac{308 \times 7}{22 \times 14}$ $\Rightarrow r=7 \mathrm{~cm}$ $\therefore$ Total surface a...

The increasing order of the reactivity of the following

Question: The increasing order of the reactivity of the following with $\mathrm{LiAlH}_{4}$ is : $(B)(A)(C)(D)$$(B)(A)(D)(C)$$(\mathrm{A})(\mathrm{B})(\mathrm{D})(\mathrm{C})$$(A)(B)(C)(D)$Correct Option: , 3 Solution: The reactivity order of carboxylic acid derivatives depends on the electrophilicity of the carbonyl carbon and Leaving ability of the four groups is...

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Question: Note Use $\pi=\frac{22}{7}$, unless stated otherwise. A joker's cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps. Solution: Radius of the cone,r= 7 cmHeight of the cone,h= 24 cm $\therefore$ Slant height of the cone, $l=\sqrt{r^{2}+h^{2}}=\sqrt{7^{2}+24^{2}}=\sqrt{49+576}=\sqrt{625}=25 \mathrm{~cm}$ Area of the sheet required to make one cap = Curved surface area of the cone $=\pi r l=\frac{22}{7}...

In the given figure, the energy levels of hydrogen atom have been shown along

Question: In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ and $\mathrm{E}$. The transitions $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ respectively represents - (1) The series limit of Lyman series, third member of Balmer series and second member of Paschen series(2) The first member of the Lyman series, third member of Balmer series and second member of Paschen series(3) The ionization pot...

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Question: Note Use $\pi=\frac{22}{7}$, unless stated otherwise. Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m. Solution: Slant height,l= 21 m Radius of the base, $r=\frac{24}{2}=12 \mathrm{~m}$ $\therefore$ Total surface area of the cone $=\pi r(r+l)=\frac{22}{7} \times 12 \times(12+21)=\frac{22}{7} \times 12 \times 33=\frac{8712}{7} \mathrm{~cm}^{2}$ Thus, the total surface area of the cone is $\frac{8712}{7} \mathrm{~cm}^{2}$....

The aldehydes which will not form Grignard product with one equivalent Grignard reagents are :

Question: The aldehydes which will not form Grignard product with one equivalent Grignard reagents are : (B), (D)(B), (C)(B), (C), (D)(C),(D)Correct Option: 1 Solution: Grignard reagent will not react with aldehydes if it has a functional group which contains acidic hydrogen. Thus options (B) and(D) have - $\mathrm{COOH}$ and $-\mathrm{CH}_{2} \mathrm{OH}$ respectively which contain acidic $\mathrm{H}$-atom. Therefore, acid-base reaction occurs....

Note Use π=227, unless stated otherwise.

Question: Note Use $\pi=\frac{22}{7}$, unless stated otherwise. Find the curved surface area of a cone with base radius 5.25 cm and slant height 10 cm. Solution: Radius of the base,r= 5.25 cmSlant height,l= 10 cm $\therefore$ Curved surface area of the cone $=\pi r l=\frac{22}{7} \times 5.25 \times 10=165 \mathrm{~cm}^{2}$ Thus, the curved surface area of the cone is165 cm2....

If the function f given by

Question: If the function $f$ given by $f(x)=x^{3}-3(a-2) x^{2}+3 a x+7$, for some $\mathrm{a} \in \mathrm{R}$ is increasing in $(0,1]$ and decreasing in $[1,5)$, then a root of the equation, $\frac{f(x)-14}{(x-1)^{2}}=0(x \neq 1)$ is (1) $-7$(2) 5(3) 7(4) 6Correct Option: , 3 Solution: $f(x)=x^{3}-3(a-2) x^{2}+3 a x+7, f(0)=7$ $\Rightarrow \quad f^{\prime}(x)=3 x^{2}-6(a-2) x+3 a$ $f^{\prime}(1)=0$ $\Rightarrow \quad 1-2 a+4+a=0$ $\Rightarrow \quad a=5$ Then, $f(x)=x^{3}-9 x^{2}+15 x+7$ Now, $\...

A rectangular sheet of paper 30 cm × 18 cm can be transformed into the curved surface of a right circular cylinder in two ways namely,

Question: A rectangular sheet of paper 30 cm 18 cm can be transformed into the curved surface of a right circular cylinder in two ways namely, either by rolling the paper along its length or by rolling it along its breadth. Find the ratio of the volumes of the two cylinders, thus formed. Solution: The dimensions of the rectangular sheet of paper are30 cm 18 cm.LetV1andV2be the volumes of the cylinders formed by rolling the rectangular sheet of paper along its length (i.e. 30 cm) and breadth (i.e...

The major product of the following reaction is :

Question: The major product of the following reaction is : Correct Option: , 2 Solution:...

The major product of the following reaction is :

Question: The major product of the following reaction is : Correct Option: , 2 Solution:...

A proton and an $lpha$-particle, having kinetic energies

Question: A proton and an $\alpha$-particle, having kinetic energies $\mathrm{K}_{\mathrm{p}}$ and $\mathrm{K}_{\alpha}$, respectively, enter into a magnetic field at right angles. The ratio of the radii of trajectory of proton to that of $\alpha$-particle is $2: 1$. The ratio of $\mathrm{K}_{\mathrm{p}}: \mathrm{K}_{\alpha}$ is :(1) $1: 8$(2) $8: 1$(3) $1: 4$(4) $4: 1$Correct Option: , 4 Solution: $(4)$ $\mathrm{r}=\frac{\mathrm{mv}}{\mathrm{qB}}=\frac{\mathrm{p}}{\mathrm{qB}} \quad \frac{\math...

The difference between inside and outside surfaces of a cylindrical tube 14 cm long, is 88 cm2.

Question: The difference between inside and outside surfaces of a cylindrical tube 14 cm long, is 88 cm2. If the volume of the tube is 176 cm3, find the inner and outer radii of the tube. Solution: Let the inner and outer radii of the tube bercm andRcm, respectively.Length of the cylindrical tube,h= 14 cmOuter curved surface of the cylinder Inner curved surface of the cylinder = 88 cm2 (Given) $\therefore 2 \pi R h-2 \pi r h=88$ $\Rightarrow 2 \times \frac{22}{7} \times 14 \times(R-r)=88$ $\Righ...

If a curve passes through the point (1,-2)

Question: If a curve passes through the point $(1,-2)$ and has slope of the tangent at any point $(x, y)$ on it as $\frac{x^{2}-2 y}{x}$, then the curve also passes through the point :(1) $(3,0)$(2) $(\sqrt{3}, 0)$(3) $(-1,2)$(4) $\quad(-\sqrt{2}, 1)$Correct Option: , 2 Solution: $\because$ Slope of the tangent $=\frac{x^{2}-2 y}{x}$ $\because \quad \frac{d y}{d x}=\frac{x^{2}-2 y}{x}$ $\frac{d y}{d x}+\frac{2}{x} y=x$ I.F, $=e^{\int^{\frac{1}{4 x}}}=e^{2 \ln x}=x^{2}$ Solution of equation $y \c...

The major product obtained in the following conversion is:

Question: The major product obtained in the following conversion is: Correct Option: 1 Solution:...

Question: A particle is travelling 4 times as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is $2: 1$, the mass of the particle is :-(1) $\frac{1}{16}$ times the mass of e-(2) 8 times the mass of $\mathrm{e}^{-}$(3) 16 times the mass of $\mathrm{e}^{-}$(4) $\frac{1}{8}$ times the mass of e-Correct Option: , 4 Solution: (4) $\lambda=\frac{\mathrm{h}}{\mathrm{p}}$ $\frac{\lambda_{\mathrm{p}}}{\lambda_{\mathrm{e}}}=\frac{\mathrm{P}_{\mathrm{e}}}{...

It costs ₹ 3300 to paint the inner curved surface of a cylindrical vessel 10 m deep at the rate of Rs 30 per m2. Find the

Question: It costs ₹ 3300 to paint the inner curved surface of a cylindrical vessel 10 m deep at the rate of Rs 30 per m2. Find the(i) inner curved surface area of the vessel,(ii) inner radius of the base, and(iii) capacity of the vessel. Solution: Total cost of paining the inner curved surface of the cylinderical vassel =₹ 3,300Rate of painting =₹ 30 per m2(i) Inner curved surface area of the vassel $=\frac{\text { Total cost of painting the inner curved surface of the cylindrical vassel }}{\te...

Which of the following compounds reacts

Question: Which of the following compounds reacts with ethylmagnesium bromide and also decolourizes bromine water solution?Correct Option: , 4 Solution:...

Imagine that the electron in a hydrogen atom is replaced by a muon

Question: Imagine that the electron in a hydrogen atom is replaced by a muon $(\mu)$ The mass of muon particle is 207 times that of an electron and charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be :-(1) $13.6 \mathrm{eV}$(2) $2815.2 \mathrm{eV}$(3) $331.2 \mathrm{eV}$(4) $27.2 \mathrm{eV}$Correct Option: , 2 Solution: (2) $\mathrm{E} \propto \frac{1}{\mathrm{r}} \quad \mathrm{r} \propto \frac{1}{\mathrm{~m}}$ $\mathrm{E} \propto \mathrm{m}$ Ion...

and $d$ are non-zero real constants. Then :

Question: Let $f(x)=\frac{x}{\sqrt{\mathrm{a}^{2}+x^{2}}}-\frac{\mathrm{d}-x}{\sqrt{\mathrm{b}^{2}+(\mathrm{d}-x)^{2}}}, x \in \mathbf{R}$ where $\mathrm{a}, \mathrm{b}$ and $d$ are non-zero real constants. Then :(1) $f$ is an increasing function of $x$(2) $f$ is a decreasing function of $x$(3) $f^{\prime}$ is not a continuous function of $x$(4) $f$ is neither increasing nor decreasing function of $x$Correct Option: 1, 2 Solution: $f(x)=\frac{x}{\sqrt{a^{2}+x^{2}}}-\frac{(d-x)}{\sqrt{b^{2}+(d-x)...

The major product of the following reaction is :

Question: The major product of the following reaction is : Correct Option: , 3 Solution:...

Find the length of 13.2 kg of copper wire of diameter 4 mm,

Question: Find the length of 13.2 kg of copper wire of diameter 4 mm, when 1 cubic centimetre of copper weighs 8.4 g. Solution: Mass of copper wire = 13.2 kg = 13.2 1000 = 13200 g (1 kg = 1000 g)Volume of 8.4 g of copper wire = 1 cm3 $\therefore$ Volume of $13200 \mathrm{~g}$ (or $13.2 \mathrm{~kg}$ ) of copper wire $=\frac{13200}{8.4} \mathrm{~cm}^{3}$ Let the length of the copper wire bel cm. Radius of the copper wire, $r=\frac{4}{2}=2 \mathrm{~mm}=0.2 \mathrm{~cm} \quad(1 \mathrm{~cm}=10 \mat...

An oil drop of radius

Question: An oil drop of radius $2 \mathrm{~mm}$ with a density $3 \mathrm{~g}$ $\mathrm{cm}^{-3}$ is held stationary under a constant electric field $3.55 \times 10^{5} \mathrm{~V} \mathrm{~m}^{-1}$ in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess? (consider $\mathrm{g}=9.81 \mathrm{~m} / \mathrm{s}^{2}$ )(1) $48.8 \times 10^{11}$(2) $1.73 \times 10^{10}$(3) $17.3 \times 10^{10}$(4) $1.73 \times 10^{12}$Correct Option: , 2 Solution: (2...

The major product of the following reaction is :

Question: The major product of the following reaction is : Correct Option: , 4 Solution:...

Themaximum value of the function

Question: Themaximum value of the function $f(x)=3 x^{3}-18 x^{2}+27 x-40$ on the set $\mathrm{S}=\left\{x \in R: x^{2}+30 \leq 11 x\right\}$ is :(1) $-122$(2) $-222$(3) 122(4) 222Correct Option: 3, Solution: Consider the function, $f(x)=3 x(x-3)^{2}-40$ Now $S=\left\{x \in R: x^{2}+30 \leq 11 x\right\}$ So $x^{2}-11 x+30 \leq 0$ $\Rightarrow \quad x \in[5,6]$ $\therefore f(x)$ will have maximum value for $x=6$ The maximum value of function is, $f(6)=3 \times 6 \times 3 \times 3-40=122$...