In the following reaction the reason why meta-nitro product also formed is:

Question: In the following reaction the reason why meta-nitro product also formed is: Formation of anilinium ion$-\mathrm{NO}_{2}$ substitution always takes place at meta-positionlow temperature$-\mathrm{NH}_{2}$ group is highly meta-directiveCorrect Option: Solution: When light of wavelength $248 \mathrm{~nm}$ falls on a metal of threshold energy $3.0 \mathrm{eV}$, the de-Broglie wavelength of emitted electrons is _______\AA. (Round off to the Nearest Integer). $\left[\right.$ Use: $\sqrt{3}=1....

A cylinder and a cone have equal radii of their bases and equal heights.

Question: A cylinder and a cone have equal radii of their bases and equal heights. If their curved surface areas are in the ratio 8 : 5., show that the radius and height of each has the ratio 3 : 4. Solution: Suppose that the respective radii and height of the cone and the cylinder arerandh.Then ratio of curved surface areas = 8 : 5Let the curved surfaces areas be 8xand 5x. i. e., $2 \pi r h=8 \mathrm{x}$ and $\pi r l=5 \mathrm{x} \Rightarrow \pi r \sqrt{h^{2}+r^{2}}=5 x$ Hence $4 \pi^{2} r^{2} ...

Two cones have their heights in the ratio 1 : 3 and the radii of their bases in the ratio 3 : 1.

Question: Two cones have their heights in the ratio 1 : 3 and the radii of their bases in the ratio 3 : 1. Show that their volumes are in the ratio 3 : 1. Solution: Let the heights of the first and second cones beh and 3h, respectively .Also, let the radius of the first and second cones be 3randr, respectively. $\therefore$ Ratio of volumes of the cones $=\frac{\text { volume of the first cone }}{\text { volume of the second cone }}$ $=\frac{\frac{1}{3} \pi \times(3 \mathrm{r})^{2} \times \mathr...

Let be given as

Question: Let $\mathrm{f}:[-3,1] \rightarrow \mathrm{R}$ be given as $f(x)= \begin{cases}\min \left\{(x+6), x^{2}\right\}, -3 \leq x \leq 0 \\ \max \left\{\sqrt{x}, x^{2}\right\}, 0 \leq x \leq 1\end{cases}$ If the area bounded by $y=f(x)$ and $x$-axis is $\mathrm{A}$, then the value of $6 \mathrm{~A}$ is equal to Solution: $\mathrm{f}:[-3,1] \rightarrow \mathrm{R}$ $f(x)= \begin{cases}\min \left\{(x+6), x^{2}\right\} ,-3 \leq x \leq 0 \\ \max \left\{\sqrt{x}, x^{2}\right\} , 0 \leq x \leq 1\end...

The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength

Question: The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength $491 \mathrm{~nm}$ is $0.710 \mathrm{~V}$. When the incident wavelength is changed to a new value, the stopping potential is $1.43 \mathrm{~V}$. The new wavelength is:(1) $400 \mathrm{~nm}$(2) $382 \mathrm{~nm}$(3) $309 \mathrm{~nm}$(4) $329 \mathrm{~nm}$Correct Option: , 2 Solution: (2) From the photoelectric effect equation $\frac{h c}{\lambda}=\phi+\operatorname{ev}_{s}$ so ...

How many metres of cloth, 2.5 m wide, will be required to make a conical

Question: How many metres of cloth, 2.5 m wide, will be required to make a conical tent whose base radius is 7 m and height 24 metres? Solution: Radius of the conical tent,r =7 mHeight of the conical tent,h= 24 m Now, $l=\sqrt{r^{2}+h^{2}}$ $=\sqrt{49+576}$ $=\sqrt{625}$ $=25 \mathrm{~m}$ Curved surface area of the cone $=\pi r l$ $=\frac{22}{7} \times 7 \times 25$ $=550 \mathrm{~m}^{2}$ Here, area of the cloth $=$ curved surface area of the cone $=550 \mathrm{~m}^{2}$ Width of the cloth = 2.5 m...

Solve this

Question: Note Use $\pi=\frac{22}{7}$, unless stated otherwise. A man uses a piece of canvas having an area of 551 m2, to make a conical tent of base radius 7 m. Assuming that all the stitching margins and wastage incurred while cutting, amount to approximately 1 m2, find the volume of the tent that can be made with it. Solution: Area of the canvas = 551 m2​Area of the canvas used in stitching margins and wastage incurred while cutting = 1 m2 Area of the canvas used in making the tent = 551 1 = ...

Let C1 be the curve obtained by the solution of differential

Question: Let $C_{1}$ be the curve obtained by the solution of differential equation $2 x y \frac{d y}{d x}=y^{2}-x^{2}, x0 \$ Let the curve $C_{2}$ be the solution of $\frac{2 x y}{x^{2}-y^{2}}=\frac{d y}{d x}$ If both the curves pass through $(1,1)$, then the area enclosed by the curves $C_{1}$ and $\mathrm{C}_{2}$ is equal to :(1) $\pi-1$(2) $\frac{\pi}{2}-1$(3) $\pi+1$(4) $\frac{\pi}{4}+1$Correct Option: , 2 Solution: $\frac{d y}{d x}=\frac{y^{2}-x^{2}}{2 x y}, \quad x \in(0, \infty)$ put $y...

In the following reactions, products A and B are:

Question: In the following reactions, products $\mathrm{A}$ and $\mathrm{B}$ are: Correct Option: 1 Solution:...

The wavelength of the photon emitted by a hydrogen atom when

Question: The wavelength of the photon emitted by a hydrogen atom when an electron makes a transition from $n=2$ to $n=1$ state is:(1) $194.8 \mathrm{~nm}$(2) $490.7 \mathrm{~mm}$(3) $913.3 \mathrm{~nm}$(4) $121.8 n m$Correct Option: 4, Solution: (4) $\Delta \mathrm{E}=10.2 \mathrm{eV}$ $\frac{\mathrm{he}}{\lambda}=10.2 \mathrm{ev}$ $\lambda=\frac{h c}{(10.2) e}$ $=\frac{12400}{10.2} \mathrm{~A}$ $=121.56 \mathrm{~nm}$ $\simeq 121.8 \mathrm{~nm}$...

In the following reactions, products $mathrm{A}$ and $mathrm{B}$ are:

Question: In the following reactions, products $\mathrm{A}$ and $\mathrm{B}$ are: Correct Option: 1 Solution:...

A heap of wheat is in the form of a cone of diameter 9 m and height 3.5 m.

Question: A heap of wheat is in the form of a cone of diameter 9 m and height 3.5 m. Find its volume. How much canvas cloth is required to just cover the heap? (Use = 3.14). Solution: Radius of the heap, $r=\frac{9}{2} \mathrm{~m}=4.5 \mathrm{~m}$ Height of the heap,h = 3.5 m $\therefore$ Volume of the heap of wheat $=\frac{1}{3} \pi r^{2} h=\frac{1}{3} \times 3.14 \times(4.5)^{2} \times 3.5=74.1825 \mathrm{~m}^{3}$ Now, Slant height of the heap, $l=\sqrt{r^{2}+h^{2}}=\sqrt{(4.5)^{2}+(3.5)^{2}}=...

Solve this

Question: Note Use $\pi=\frac{22}{7}$, unless stated otherwise. A conical pit of diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?HINT1 m3= 1 kilolitre. Solution: Radius of the conical pit, $r=\frac{3.5}{2} \mathrm{~m}$ Depth of the conical pit,h = 12 m $\therefore$ Capacity of the conical pit $=\frac{1}{3} \pi r^{2} h=\frac{1}{3} \times \frac{22}{7} \times\left(\frac{3.5}{2}\right)^{2} \times 12=38.5 \mathrm{~m}^{3}=38.5 \mathrm{~kL} \quad\left(1 \mathrm{~m}^{3}=1\right.$ kilolit...

Let the curve

Question: Let the curve $y=y(x)$ be the solution of the differential equation, $\frac{\mathrm{dy}}{\mathrm{dx}}=2(\mathrm{x}+1)$. If the numerical value of area bounded by the curve $\mathrm{y}=\mathrm{y}(\mathrm{x})$ and $\mathrm{x}$-axis is $\frac{4 \sqrt{8}}{3}$, then the value of $\mathrm{y}(1)$ is equal to Solution: $\frac{d y}{d x}=2(x+1)$ $\Rightarrow \quad \int d y=\int 2(x+1) d x$ $\Rightarrow y(x)=x^{2}+2 x+C$ Area $=\frac{4 \sqrt{8}}{3}$ $-1+\sqrt{1-\mathrm{C}}$ $\Rightarrow \quad 2 \...

An

Question: An $\alpha$ particle and a proton are accelerated from rest by a potential difference of $200 \mathrm{~V}$. After this, their de Broglie wavelengths are $\lambda_{\alpha}$ and $\lambda_{\mathrm{p}}$ respectively. The ratio $\frac{\lambda_{\mathrm{p}}}{\lambda_{\alpha}}$ is :(1) 8(2) $2.8$(3) $3.8$(4) $7.8$ Correct Option: 2, Solution: (2) $\lambda=\frac{h}{p}=\frac{h}{\sqrt{2 m q v}}$ $\frac{\lambda_{p}}{\lambda_{\alpha}}=\sqrt{\frac{m_{\alpha} q_{\alpha}}{m_{p} q_{p}}}=\sqrt{\frac{4 \...

Find the volume, curved surface area and the total surface area of a cone

Question: Find the volume, curved surface area and the total surface area of a cone whose height and slant height are 6 cm and 10 cm respectively. Solution: Height of the cone,h= 6 cmSlant height of the cone,l= 10 cm Radius, $r=\sqrt{l^{2}-h^{2}}=\sqrt{100-36}=\sqrt{64}=8 \mathrm{~cm}$ Volume of the cone $=\pi r^{2} h$ $=\frac{1}{3} \times 3.14 \times 8^{2} \times 6$ $=401.92 \mathrm{~cm}^{3}$ Curved surface area of the cone $=\pi r l$ $=3.14 \times 8 \times 10$ $=251.2 \mathrm{~cm}^{2}$ $\there...

Solve the following

Question: $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COCH}_{3}+\mathrm{PhMgX}$$\mathrm{PhCOCH}_{2} \mathrm{CH}_{3}+\mathrm{CH}_{3} \mathrm{MgX}$$\mathrm{PhCOCH}_{3}+\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{MgX}$$\mathrm{HCHO}+\mathrm{PhCH}\left(\mathrm{CH}_{3}\right) \mathrm{CH}_{2} \mathrm{MgX}$Correct Option: , 4 Solution: Tertiary alcohol is prepared by the reaction of Grignard reagent with a ketone (formaldehyde is used to prepare primary alcohol)....

Question: An $\alpha$ particle and a proton are accelerated from rest by a potential difference of $200 \mathrm{~V}$. After this, their de Broglie wavelengths are $\lambda_{\alpha}$ and $\lambda_{\mathrm{p}}$ respectively. The ratio $\frac{\lambda_{\mathrm{p}}}{\lambda_{\alpha}}$ is :(1) 8(2) $2.8$(3) $3.8$(4) $7.8$Correct Option: Solution: (2) $\lambda=\frac{h}{p}=\frac{h}{\sqrt{2 m q v}}$ $\frac{\lambda_{p}}{\lambda_{\alpha}}=\sqrt{\frac{m_{\alpha} q_{\alpha}}{m_{p} q_{p}}}=\sqrt{\frac{4 \time...

Solve this

Question: Note Use $\pi=\frac{22}{7}$, unless stated otherwise. Find the volume, curved surface area and the total surface area of a cone having base radius 35 cm and height is 12 cm. Solution: Radius of the cone,r= 35 cmHeight of the cone,h = 12 cm $\therefore$ Slant height of the cone, $l=\sqrt{r^{2}+h^{2}}=\sqrt{35^{2}+12^{2}}=\sqrt{1225+144}=\sqrt{1369}=37 \mathrm{~cm}$ (i) Volume of the cone $=\frac{1}{3} \pi r^{2} h=\frac{1}{3} \times \frac{22}{7} \times(35)^{2} \times 12=15400 \mathrm{~cm...

The de Broglie wavelength of a proton

Question: The de Broglie wavelength of a proton and $\alpha$-particle are equal. The ratio of their velocities is :(1) $4: 2$(2) $4: 1$(3) $1: 4$(4) $4: 3$Correct Option: , 2 Solution: (2) From De-broglie's wavelength : $\lambda=\frac{h}{m v}$ Given $\lambda_{\mathrm{p}}=\lambda_{\alpha}$ $v \alpha \frac{1}{m}$ $\frac{\mathrm{v}_{\mathrm{p}}}{\mathrm{v}_{\alpha}}=\frac{\mathrm{m}_{\alpha}}{\mathrm{m}_{p}}=\frac{4 \mathrm{~m}_{\mathrm{p}}}{\mathrm{m}_{\mathrm{p}}}=\frac{4}{1}$...

A bus stop is barricated from the remaining part of the road by using 50 hollow cones made of recycled cardboard.

Question: A bus stop is barricated from the remaining part of the road by using 50 hollow cones made of recycled cardboard. Each one has a base diameter of $40 \mathrm{~cm}$ and height $1 \mathrm{~m}$. If the outer side of each of the cones is to be painted and the cost of painting is $₹ 25$ per $\mathrm{m}^{2}$, what will be the cost of painting all these cones? (Use $\pi=3.14$ and $\sqrt{1.04}=1.02$ ). Solution: Radius of each cone, $r=\frac{40}{2}=20 \mathrm{~cm}=0.2 \mathrm{~m} \quad(1 \math...

The major product of the following reaction is:

Question: The major product of the following reaction is: Correct Option: , 3 Solution: DIBAL-H will reduce cyanides and esters to aldehydes....

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Question: Note Use $\pi=\frac{22}{7}$, unless stated otherwise. A conical tent is $10 \mathrm{~m}$ high and the radius of its base is $24 \mathrm{~m}$. Find the slant height of the tent. If the cost of $1 \mathrm{~m}^{2}$ canvas is $₹ 70$, find the cost of canvas required to make the tent. Solution: Radius of the conical tent,r= 24 mHeight of the conical tent,h= 10 m $\therefore$ Slant height of the conical tent, $l=\sqrt{r^{2}+h^{2}}=\sqrt{24^{2}+10^{2}}=\sqrt{576+100}=\sqrt{676}=26 \mathrm{~m}...

According to Bohr atom model, in which of the following transitions will the frequency be maximum?

Question: According to Bohr atom model, in which of the following transitions will the frequency be maximum?(1) $n=2$ to $n=1$(2) $n=4$ to $n=3$(3) $n=5$ to $\mathrm{n}=4$(4) $n=3$ to $n=2$Correct Option: 1 Solution: $\mathrm{f}$ is more for transition from $\mathrm{n}=2$ to $\mathrm{n}=1$. JEE Main previous year Questions Paper- Atomic Physics...

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Question: Note Use $\pi=\frac{22}{7}$, unless stated otherwise. The slant height and base diameter of a conical tomb are 25 m and 14 m respectively. Find the cost of whitewashing its curved surface at the rate of ₹ 12 per m2. Solution: Slant height of the conical tomb,l = 25 m Radius of the conical tomb, $r=\frac{14}{2}=7 \mathrm{~m}$ $\therefore$ Curved surface area of the conical tomb $=\pi r l=\frac{22}{7} \times 7 \times 25=550 \mathrm{~m}^{2}$ Rate of whitewashing = ₹12 per m2 Cost of white...