What is the work function of the metal if the light of wavelength

Question: What is the work function of the metal if the light of wavelength $4000 \AA$ generates photoelectrons of velocity $6 \times 10^{5} \mathrm{~ms}^{-1}$ from it? (Mass of electron $=9 \times 10^{-31} \mathrm{~kg}$ Velocity of light $=3 \times 10^{8} \mathrm{~ms}^{-1}$ Planck's constant $=6.626 \times 10^{-34} \mathrm{Js}$ Charge of electron $=1.6 \times 10^{-19} \mathrm{JeV}^{-1}$ )$0.9 \mathrm{eV}$$3.1 \mathrm{eV}$$2.1 \mathrm{eV}$$4.0 \mathrm{eV}$Correct Option: , 3 Solution: $E=h v=\fr...

Solve this

Question: A $5 \mu \mathrm{F}$ capacitor is charged fully by a $220 \mathrm{~V}$ supply. It is then disconnected from the supply and is connected in series to another uncharged $2.5 \mu \mathrm{F}$ capacitor. If the energy change during the charge redistribution is $\frac{X}{100} \mathrm{~J}$ then value of $X$ to the nearest integer is Solution: Given, $C_{1}=5 \mu \mathrm{F}$ and $V_{1}=220$ Volt When capacitor $C_{1}$ fully charged it is disconnected from the supply and connected to uncharged ...

Draw a histogram for the frequency distribution of the following data.

Question: Draw a histogram for the frequency distribution of the following data. Solution: The given frequency distribution is in exclusive form.We will represent the class intervals along thex-axis the corresponding frequencies along they-axis.The scale is as follows:Onx-axis: 1 big division = 5 unitsOny-axis: 1 big division = 50 unitsBecause the scale on thex-axis starts at 8, a kink, i.e., a break, is indicated near the origin to signify that the graph is drawn with a scale beginning at 8and ...

The following table gives the lifetimes of 400 neon lamps:

Question: The following table gives the lifetimes of 400 neon lamps: (i) Represent the given information with the help of a histogram.(ii) How many lamps have a lifetime of more than 700 hours? Solution: (i) (ii) Lamps with lifetime more than 700 hours = 74 + 62 + 48 = 184...

If the de Broglie wavelength of the electron in

Question: If the de Broglie wavelength of the electron in $\mathrm{n}^{\text {th }}$ Bohr orbit in a hydrogenic atom is equal to $1.5 \pi \mathrm{a}_{0}\left(\mathrm{a}_{0}\right.$ is Bohr radius), then the value of $\mathrm{n} / \mathrm{z}$ is :$0.40$$1.50$$1.0$$0.75$Correct Option: , 4 Solution: Given $\lambda=1.5 \pi a_{0}$ $n \lambda=2 \pi r$ ...(i) Radii of stationary states $(r)$ is expressed as: $r=a_{0} \frac{n^{2}}{z}$ ...(ii) From eqn (i) and (ii) $n \lambda=\frac{2 \pi a_{0} n^{2}}{z}...

27 similar drops of mercury are maintained

Question: 27 similar drops of mercury are maintained at $10 \mathrm{~V}$ each. All these spherical drops combine into a single big drop. The potential energy of the bigger drop is _____ times that of a smaller drop. Solution: (243) For self energy of sphere (conducting) $U=\frac{k q^{2}}{2 r}$ For small drop $\rightarrow U_{i}=\frac{k q^{2}}{2 r}$ ......(1) After combine small drops volume remains same as bigger drop $\therefore \quad \frac{4}{3} \pi r^{3} \times n=\frac{4}{3} \pi R^{3}$ $\mathr...

The de Broglie wavelength

Question: The de Broglie wavelength $(\lambda)$ associated with a photoelectron varies with the frequency $(v)$ of the incident radiation as, $\left[v_{0}\right.$ is threshold frequency $]$ :$\lambda \propto \frac{1}{\left(v-v_{0}\right)}$$\lambda \propto \frac{1}{\left(v-v_{0}\right) \frac{1}{4}}$$\lambda \propto \frac{1}{\left(v-v_{0}\right)^{\frac{3}{2}}}$$\lambda \propto \frac{1}{\left(v-v_{0}\right)^{\frac{1}{2}}}$Correct Option: , 4 Solution: According to de-Broglie wavelength equation, $\...

Question: The de Broglie wavelength $(\lambda)$ associated with a photoelectron varies with the frequency $(v)$ of the incident radiation as, $\left[v_{0}\right.$ is threshold frequency $]$ :$\lambda \propto \frac{1}{\left(v-v_{0}\right)}$$\lambda \propto \frac{1}{\left(v-v_{0}\right) \frac{1}{4}}$$\lambda \propto \frac{1}{\left(v-v_{0}\right)^{\frac{3}{2}}}$$\lambda \propto \frac{1}{\left(v-v_{0}\right)^{\frac{1}{2}}}$Correct Option: , 4 Solution: According to de-Broglie wavelength equation, $\...

Choose the correct statement about two

Question: Choose the correct statement about two circles whose equations are given below: $x^{2}+y^{2}-10 x-10 y+41=0$ $x^{2}+y^{2}-22 x-10 y+137=0$ (1) circles have same centre(2) circles have no meeting point(3) circles have only one meeting point(4) circles have two meeting pointsCorrect Option: , 3 Solution: $x^{2}+y^{2}-10 x-10 y+41=0$ $\mathrm{~A}(5,5), \mathrm{R}_{1}=3$ $x^{2}+y^{2}-22 x-10 y+137=0$ $\mathrm{B}(11,5), \mathrm{R}_{2}=3$ $\mathrm{AB}=6=\mathrm{R}_{1}+\mathrm{R}_{2}$ Touch e...

Two tangents are drawn from a point

Question: Two tangents are drawn from a point $\mathrm{P}$ to the circle $x^{2}+y^{2}-2 x-4 y+4=0$, such that the angle between these tangents is $\tan ^{-1}\left(\frac{12}{5}\right)$, where $\tan ^{-1}\left(\frac{12}{5}\right) \in(0, \pi)$. If the centre of the circle is denoted by $\mathrm{C}$ and these tangents touch the circle at points $\mathrm{A}$ and $\mathrm{B}$, then the ratio of the areas of $\Delta \mathrm{PAB}$ and $\triangle \mathrm{CAB}$ is :(1) $11: 4$(2) 9: 4(3) 3: 1(4) $2: 1$Cor...

Consider the combination of 2 capacitors

Question: Consider the combination of 2 capacitors $C_{1}$ and $C_{2}$, with $C_{2}C_{1}$, when connected in parallel, the equivalent capacitance is $\frac{15}{4}$ times the equivalent capacitance of the same connected in series. Calculate the ratio of capacitors, $\frac{\mathrm{C}_{2}}{\mathrm{C}_{1}}$ Note: NTA has dropped this question in the final official answer key.(1) $\frac{15}{11}$(2) $\frac{29}{15}$(3) $\frac{15}{4}$(4) None of the aboveCorrect Option: , 4 Solution: (4) $C_{1}+C_{2}=\f...

Heat treatment of muscular pain involves radiation of wavelength of about 900 nm .

Question: Heat treatment of muscular pain involves radiation of wavelength of about $900 \mathrm{~nm}$. Which spectral line of H-atom is suitable for this purpose ? $\left[\mathrm{R}_{\mathrm{H}}=1 \times 10^{5} \mathrm{~cm}^{-1} \cdot \mathrm{h}=6.6 \times 10^{-34} \mathrm{Js}, \mathrm{c}=3 \times 10^{8} \mathrm{~ms}^{-1}\right]$Paschen, $\infty \rightarrow 3$Paschen, $5 \rightarrow 3$Balmer, $\infty \rightarrow 2$Lyman, $\infty \rightarrow 1$Correct Option: 1 Solution: $\frac{1}{\lambda}=\math...

The minimum distance between any two points

Question: The minimum distance between any two points $P_{1}$ and $P_{2}$ while considering point $P_{1}$ on one circle and point $\mathrm{P}_{2}$ on the other circle for the given circles' equations $x^{2}+y^{2}-10 x-10 y+41=0$ $x^{2}+y^{2}-24 x-10 y+160=0$ Solution: Given $\mathrm{C}_{1}(5,5), \mathrm{r}_{1}=3$ and $\mathrm{C}_{2}(12,5), \mathrm{r}_{2}=3$ Now, $\mathrm{C}_{1} \mathrm{C}_{2}\mathrm{r}_{1}+\mathrm{r}_{2}$ Thus, $\left(\mathrm{P}_{1} \mathrm{P}_{2}\right)_{\min }=7-6=1$...

The heights of 75 students in a school are given below:

Question: The heights of 75 students in a school are given below: Draw a histogram to represent the above data. Solution: The given frequency distribution is in exclusive form.We will represent the class intervals [heights (in cm)] along thex-axis the corresponding frequencies [number of students ] along they-axis.The scale is as follows:Onx-axis: 1 big division = 6 cmOny-axis: 1 big division = 2 studentsBecause the scale on thex-axis starts at 130, a kink, i.e., a break, is indicated near the o...

An electron with kinetic energy

Question: An electron with kinetic energy $K_{1}$ enters between parallel plates of a capacitor at an angle ' $\alpha$ ' with the plates, It leaves the plates at angle ' $\beta^{\prime}$ with kinetic energy $K_{2}$. Then the ratio of kinetic energies $K_{1}: K_{2}$ will be:(1) $\frac{\sin ^{2} \beta}{\cos ^{2} \alpha}$(2) $\frac{\cos ^{2} \beta}{\cos ^{2} \alpha}$(3) $\frac{\cos \beta}{\sin \alpha}$(4) $\frac{\cos \beta}{\cos \alpha}$Correct Option: , 2 Solution: (2) $\because v_{1} \cos \alpha=...

The following table shows the average daily earnings of 40 general stores in a market, during a certain week.

Question: The following table shows the average daily earnings of 40 general stores in a market, during a certain week. Draw a histogram to represent the above data. Solution: The given frequency distribution is in exclusive form.We will represent the class intervals [daily earnings (in rupees)] along thex-axis the corresponding frequencies [number of stores] along they-axis.The scale is as follows:Onx-axis: 1 big division = 50 rupeesOny-axis: 1 big division = 1 storeBecause the scale on thex-ax...

The ground state energy of hydrogen atom is

Question: The ground state energy of hydrogen atom is $-13.6 \mathrm{eV}$. The energy of second excited state of $\mathrm{He}^{+}$ion in $\mathrm{eV}$ is:$-54.4$$-3.4$$-6.04$$-27.2$Correct Option: , 3 Solution: According to Bohr's model energy in $n^{\text {th }}$ state $=-13.6 \times \frac{Z^{2}}{n^{2}} \mathrm{eV}$ For second excited state, of $\mathrm{He}^{+}, n=3$ $\therefore E_{3}\left(\mathrm{He}^{+}\right)=-13.6 \times \frac{2^{2}}{3^{2}} \mathrm{eV}=-6.04 \mathrm{eV}$...

Choose the incorrect statement about the

Question: Choose the incorrect statement about the two circles whose equations are given below: $x^{2}+y^{2}-10 x-10 y+41=0$ and $x^{2}+y^{2}-16 x-10 y+80=0$ (1) Distance between two centres is the average of radii of both the circles.(2) Both circles' centres lie inside region of one another.(3) Both circles pass through the centre of each other.(4) Circles have two intersection points.Correct Option: , 2 Solution: $\mathrm{r}_{1}=3, \mathrm{c}_{1}(5,5)$ $\mathrm{r}_{2}=3, \mathrm{c}_{2}(8,5)$ ...

The daily wages of 50 workers in a factory are given below:

Question: The daily wages of 50 workers in a factory are given below: Construct a histogram to represent the above frequency distribution. Solution: The given frequency distribution is in exclusive form.We will represent the class intervals [daily wages (in rupees)] along thex-axis the corresponding frequencies [number of workers] along they-axis.The scale is as follows:Onx-axis: 1 big division = 40 rupeesOny-axis: 1 big division = 2 workersBecause the scale on thex-axis starts at 340, a kink, i...

Which of the graphs shown below does not represent the

Question: Which of the graphs shown below does not represent the relationship between incident light and the electron ejected from metal surface?Correct Option: , 3 Solution: K.E. $=\mathrm{h} v-\mathrm{hv}_{0}$ where, $v=$ Frequency of incident radiation $v_{0}=$ Threshold frequency KE is independent of intensity, it depends on frequency of light. Intensity is directly proportional to the no, of electrons emitted....

The line

Question: The line $2 \mathrm{x}-\mathrm{y}+1=0$ is a tangent to the circle at the point $(2,5)$ and the centre of the circle lies on $x-2 y=4$. Then, the radius of the circle is:(1) $3 \sqrt{5}$(2) $5 \sqrt{3}$(3) $5 \sqrt{4}$(4) $4 \sqrt{5}$Correct Option: 1 Solution: $\left.\begin{array}{l}\left(\frac{\mathrm{h}-\frac{(\mathrm{h}-\mathrm{i})}{2}}{2-\mathrm{h}}\right)(2)--1 \\ \mathrm{~h}=8\end{array}\right)$ center $(8,2)$ Radius $\left.=\sqrt{(8-2)^{2}+(2-5)^{2}}=3 \sqrt{5}\right)$...

Look at the bar graph given below.

Question: Look at the bar graph given below. Read it carefully and answer the following questions.(i) What information does the bar graph give?(ii) In which subject is the student very good?(iii) In which subject is he poor?(iv) What is the average of his marks? Solution: (i) The bar graph shows the marks obtained by a student in various subjects in an examination.(ii) The student scores very good in mathematics, as the height of the corresponding bar is the highest.(iii) The student scores bad ...

Two equal capacitors are first connected in series and then in parallel.

Question: Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities capacities in the two cases will be -(1) $2: 1$(2) $1: 4$(3) $4: 1$(4) $1: 2$Correct Option: , 2 Solution: (2) Given that first connection $\Rightarrow \frac{1}{C_{12}}=\frac{1}{C}+\frac{1}{C} \Rightarrow C_{12}=\frac{C}{2}$ Second connection $C_{34}=C+C=2 C$ Now, the ratio of equivalent capacities in the two cases will be $\Rightarrow \frac{C_{12}}{C_{34}}=\frac{C / 2}{2 C} ...

Various modes of transport used by 1850 students of a school are given below.

Question: Various modes of transport used by 1850 students of a school are given below. Draw a bar graph to represent the above data. Solution:...

Let the lengths of intercepts on

Question: Let the lengths of intercepts on $x$-axis and $y$-axis made by the circle $x^{2}+y^{2}+a x+2 a y+c=0$ $(a0)$ be $2 \sqrt{2}$ and $2 \sqrt{5}$, respectively. Then the shortest distance from origin to a tangent to this circle which is perpendicular to the line $\mathrm{x}+2 \mathrm{y}=0$, is euqal to : (1) $\sqrt{11}$(2) $\sqrt{7}$(3) $\sqrt{6}$(4) $\sqrt{10}$Correct Option: , 3 Solution: $x^{2}+y^{2}+a x+2 a y+c=0$ $2 \sqrt{\mathrm{g}^{2}-\mathrm{c}}=2 \sqrt{\frac{\mathrm{a}^{2}}{4}-\ma...