Let $\triangle \mathrm{ABC} \sim \Delta \mathrm{DEF}$ and their areas be $64 \mathrm{~cm}^{2}$ and $121 \mathrm{~cm}^{2}$ respectively.
[question] Question. Let $\triangle \mathrm{ABC} \sim \Delta \mathrm{DEF}$ and their areas be $64 \mathrm{~cm}^{2}$ and $121 \mathrm{~cm}^{2}$ respectively. If $\mathrm{EF}=15.4 \mathrm{~cm}$, find BC. [/question] [solution] Solution: $\triangle \mathrm{ABC} \sim \Delta \mathrm{DEF}($ Given $)$ $\Rightarrow \frac{\operatorname{ar}(A B C)}{\operatorname{ar}(D E F)}=\frac{B C^{2}}{E F^{2}}$ (By theorem 6.7) $\Rightarrow \frac{64}{121}=\frac{B C^{2}}{E F^{2}} \quad \Rightarrow\left\{\frac{B C}{E F}...
Read More →What is the wavelength of light emitted
[question] Question. What is the wavelength of light emitted when the electron in a hydrogen atom undergoes transition from an energy level with n = 4 to an energy level with n = 2? [/question] [solution] Solution: The ni = 4 to nf = 2 transition will give rise to a spectral line of the Balmer series. The energy involved in the transition is given by the relation, $E=2.18 \times 10^{-18}\left[\frac{1}{n_{i}^{2}}-\frac{1}{n_{j}^{2}}\right]$ Substituting the values in the given expression of E $E=...
Read More →If AD and PM are medians of triangles ABC and PQR,
[question] Question. If $A D$ and $P M$ are medians of triangles $A B C$ and $P Q R$, respectively where $\Delta A B C \sim \Delta P Q R$, prove that $\frac{A B}{P Q}=\frac{A D}{P M}$. [/question] [solution] Solution: $\Delta \mathrm{ABC} \sim \Delta \mathrm{PQR}$ (Given) $\Rightarrow \frac{A B}{P Q}=\frac{B C}{Q R}=\frac{A C}{P R}$ $\angle \mathrm{A}=\angle \mathrm{P}, \angle \mathrm{B}=\angle \mathrm{Q}, \angle \mathrm{C}=\angle \mathrm{R}$ ...(1) Now, $\quad B D=C D=\frac{1}{2} B C$ and $\qua...
Read More →Take one flower each of families Fabaceae and Solanaceae
[question] Question. Take one flower each of families Fabaceae and Solanaceae and write its semi-technical description. Also draw their floral diagrams after studying them. [/question] [solution] Solution: 1) Family Fabaceae/Papilionaceae (pea plant) Fabaceae/Papilionaceae is a sub-family of the Leguminoseae family. Vegetative features: Habit: Pinnately compound, alternately arranged with leaf tendrils with the pulvinus present at the leaf base along folacious stipules. Root: Tap root system wit...
Read More →Electrons are emitted with zero velocity from a metal surface
[question] Question. Electrons are emitted with zero velocity from a metal surface when it is exposed to radiation of wavelength 6800 Å. Calculate threshold frequency $\left(\begin{array}{ll}v_{0} & )\end{array}\right.$ and work function (W0) of the metal. [/question] [solution] Solution: Threshold wavelength of radiation $\left(\lambda_{0}\right)=6800 =6800 \times 10^{-10} \mathrm{~m}$ Threshold frequency $\left(v_{0}\right)$ of the metal $=\frac{c}{\lambda_{0}}=\frac{3 \times 10^{8} \mathrm{~m...
Read More →A vertical stick of length 6 m casts a shadow 4 m long
[question] Question. A vertical stick of length $6 \mathrm{~m}$ casts a shadow $4 \mathrm{~m}$ long on the ground and at the same time a tower casts a shadow $28 \mathrm{~m}$ long. Find the height of the tower. [/question] [solution] Solution: $\triangle \mathrm{ABC} \sim \triangle \mathrm{PQR}$ $\therefore \quad \frac{\mathrm{AB}}{\mathrm{PQ}}=\frac{\mathrm{BC}}{\mathrm{QR}}$ $\frac{6}{x}=\frac{4}{28}$ $\Rightarrow x=42 \mathrm{~m}$ [/solution]...
Read More →$\mathrm{D}$ is a point on the side $\mathrm{BC}$ of a triangle $\mathrm{ABC}$ such that $\angle \mathrm{ADC}=\angle \mathrm{BAC}$.
[question] Question. $\mathrm{D}$ is a point on the side $\mathrm{BC}$ of a triangle $\mathrm{ABC}$ such that $\angle \mathrm{ADC}=\angle \mathrm{BAC}$. Show that $\mathrm{CA}^{2}=$ CB. CD. [/question] [solution] Solution: For $\triangle \mathrm{ABC}$ and $\triangle \mathrm{DAC}$, We have $\angle \mathrm{BAC}=\angle \mathrm{ADC} \quad($ Given $)$ and $\angle \mathrm{ACB}=\angle \mathrm{DCA} \quad($ Each $=\angle \mathrm{C})$ $\Rightarrow \Delta \mathrm{ABC} \sim \Delta \mathrm{DAC} \quad$ (AA si...
Read More →A 25 watt bulb emits monochromatic yellow light of wavelength of 0.57μm.
[question] Question. A 25 watt bulb emits monochromatic yellow light of wavelength of 0.57μm. Calculate the rate of emission of quanta per second [/question] [solution] Solution: Power of bulb, $P=25 \mathrm{Watt}=25 \mathrm{~J} \mathrm{~s}^{-1}$ Energy of one photon, $E=h v=\frac{h c}{\lambda}$ Substituting the values in the given expression of $E$ : $E=\frac{\left(6.626 \times 10^{-34}\right)\left(3 \times 10^{8}\right)}{\left(0.57 \times 10^{-6}\right)}=34.87 \times 10^{-20} \mathrm{~J}$ $\le...
Read More →A rocket with a lift-off mass 20,000 kg is blasted upwards
[question] Question. A rocket with a lift-off mass $20,000 \mathrm{~kg}$ is blasted upwards with an initial acceleration of $5.0 \mathrm{~m} \mathrm{~s}^{-2}$. Calculate the initial thrust (force) of the blast. [/question] [solution] solution: Mass of the rocket, m = 20,000 kg Initial acceleration, $a=5 \mathrm{~m} / \mathrm{s}^{2}$ Acceleration due to gravity, $g=10 \mathrm{~m} / \mathrm{s}^{2}$ Using Newton’s second law of motion, the net force (thrust) acting on the rocket is given by the rel...
Read More →Describe modifications of stem with suitable examples
[question] Question. Describe modifications of stem with suitable examples [/question] [solution] Solution: Stems of various plants have undergone modifications to perform different functions. Underground stems or storage stems: Examples: Rhizomes, Corms, tubers In ginger and banana, the underground stem is called a rhizome. The underground stem in Colocasia (arvi) is known as corm. Rhizomes and corms are underground stems, modified for the storage of food. Also, these stems help in vegetative r...
Read More →Electromagnetic radiation of wavelength 242 nm is just sufficient to ionise the sodium atom.
[question] Question. Electromagnetic radiation of wavelength $242 \mathrm{~nm}$ is just sufficient to ionise the sodium atom. Calculate the ionisation energy of sodium in $\mathrm{kJ} \mathrm{mol}^{-1}$. [/question] [solution] Solution: Energy of sodium $(E)=\frac{N_{\Lambda} h c}{\lambda}$ $=\frac{\left(6.023 \times 10^{23} \mathrm{~mol}^{-1}\right)\left(6.626 \times 10^{-34} \mathrm{Js}\right)\left(3 \times 10^{8} \mathrm{~ms}^{-1}\right)}{242 \times 10^{-9} \mathrm{~m}}$ $=4.947 \times 10^{5}...
Read More →A body of mass 5 kg is acted upon by two perpendicular forces 8 N and 6 N.
[question] Question. A body of mass 5 kg is acted upon by two perpendicular forces 8 N and 6 N. Give the magnitude and direction of the acceleration of the body. [/question] [solution] solution: $2 \mathrm{~m} / \mathrm{s}^{2}$, at an angle of $37^{\circ}$ with a force of $8 \mathrm{~N}$ Mass of the body, $m=5 \mathrm{~kg}$ The given situation can be represented as follows: The resultant of two forces is given as: $R=\sqrt{(8)^{2}+(-6)^{2}}=\sqrt{64+36}=10 \mathrm{~N}$ $\theta$ is the angle made...
Read More →A photon of wavelength $4 \times 10^{-7} \mathrm{~m}$ strikes on metal surface,
[question] Question. A photon of wavelength $4 \times 10^{-7} \mathrm{~m}$ strikes on metal surface, the work function of the metal being $2.13 \mathrm{eV}$. Calculate (i) the energy of the photon (ev), (ii) the kinetic energy of the emission, and (iii) the velocity of the photoelectron $\left(1 \mathrm{eV}=1.6020 \times 10^{-19} \mathrm{~J}\right)$. [/question] [solution] Solution: (i) Energy (E) of a photon $=h v=\frac{h c}{\lambda}$ Where, $\mathrm{h}=$ Planck's constant $=6.626 \times 10^{-3...
Read More →In figure, $\mathrm{ABC}$ and $\mathrm{AMP}$ are two right triangles,
[question] Question. In figure, $\mathrm{ABC}$ and $\mathrm{AMP}$ are two right triangles, right angled at $\mathrm{B}$ and $\mathrm{M}$ respectively. Prove that: (i) $\triangle \mathrm{ABC} \sim \triangle \mathrm{AMP}$ (ii) $\frac{\mathrm{CA}}{\mathrm{PA}}=\frac{\mathrm{BC}}{\mathrm{MP}}$ [/question] [solution] Solution: (i) In $\Delta \mathrm{ABC}$ and $\Delta \mathrm{AMP}$ $\angle \mathrm{CAB}=\angle \mathrm{PAM}($ common $)$ $\angle \mathrm{ABC}=\angle \mathrm{AMP}=90^{\circ}$ $\therefore$ B...
Read More →A constant retarding force of 50 N is applied to a body of mass
[question] Question. A constant retarding force of $50 \mathrm{~N}$ is applied to a body of mass $20 \mathrm{~kg}$ moving initially with a speed of $15 \mathrm{~ms}^{-1}$. How long does the body take to stop? [/question] [solution] solution: Retarding force, $F=-50 \mathrm{~N}$ Mass of the body, $m=20 \mathrm{~kg}$ Initial velocity of the body, $u=15 \mathrm{~m} / \mathrm{s}$ Final velocity of the body, $v=0$ Using Newton's second law of motion, the acceleration (a) produced in the body can be c...
Read More →$\mathrm{E}$ is a point on the side $\mathrm{AD}$ produced of a parallelogram $\mathrm{ABCD}$ and $\mathrm{BE}$ intersects $\mathrm{CD}$ at $\mathrm{F}$.
[question] Question. $\mathrm{E}$ is a point on the side $\mathrm{AD}$ produced of a parallelogram $\mathrm{ABCD}$ and $\mathrm{BE}$ intersects $\mathrm{CD}$ at $\mathrm{F}$. Show that $\triangle \mathrm{ABE} \sim \triangle \mathrm{CFB}$ [/question] [solution] Solution: In $\Delta \mathrm{ABE}$ and $\Delta \mathrm{CFB}$, $\angle \mathrm{EAB}=\angle \mathrm{BCF}$ (opp. angles of parallelogram) $\angle \mathrm{AEB}=\angle \mathrm{CBF}$ (Alternate interior angles, $\mathrm{As} \mathrm{AE} \| \mathr...
Read More →One end of a string of length l is connected to a particle
[question] Question. One end of a string of length l is connected to a particle of mass m and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed v the net force on the particle (directed towards the centre) is: (i) $T$, (ii) $T-\frac{m v^{2}}{l}$ (iii) $T+\frac{m v^{2}}{l}$ (iv) 0 T is the tension in the string. [Choose the correct alternative]. [/question] [solution] solution: Answer: (i) When a particle connected to a string revolves in a circul...
Read More →In figure, altitudes $\mathrm{AD}$ and $\mathrm{CE}$ of $\triangle \mathrm{ABC}$ intersect each other at the point $\mathrm{P}$.
[question] Question. In figure, altitudes $\mathrm{AD}$ and $\mathrm{CE}$ of $\triangle \mathrm{ABC}$ intersect each other at the point $\mathrm{P}$. Show that : (i) $\triangle \mathrm{AEP} \sim \Delta \mathrm{CDP}$ (ii) $\triangle \mathrm{ABD} \sim \Delta \mathrm{CBE}$ (iii) $\triangle \mathrm{AEP} \sim \triangle \mathrm{ADB}$ (iv) $\Delta \mathrm{PDC} \sim \Delta \mathrm{BEC}$ [/question] [solution] Solution: (i) In $\triangle \mathrm{AEP}$ and $\triangle \mathrm{CDP}$, $\angle \mathrm{APE}=\a...
Read More →What is the number of photons of light with a wavelength
[question] Question. What is the number of photons of light with a wavelength of 4000 pm that provide 1 J of energy? [/question] [solution] Solution: Energy $(E)$ of a photon $=h v$ Energy $\left(E_{n}\right)$ of ' $n$ ' photons $=n h v$ $\Rightarrow n=\frac{E_{n} \lambda}{\text { hc }}$ Where, $\lambda=$ wavelength of light $=4000 \mathrm{pm}=4000$ $\times 10^{-12} \mathrm{~m} \mathrm{c}=$ velocity of light in vacuum $=3 \times 10^{8}$ $\mathrm{m} / \mathrm{s} \mathrm{h}=$ Planck's constant $=6...
Read More →Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg,
[question] Question. Give the magnitude and direction of the net force acting on a stone of mass 0.1 kg, (a) just after it is dropped from the window of a stationary train, (b) just after it is dropped from the window of a train running at a constant velocity of 36 km/h, (c) just after it is dropped from the window of a train accelerating with $1 \mathrm{~m} \mathrm{~s}^{-2}$, (d) Iying on the floor of a train which is accelerating with $1 \mathrm{~m} \mathrm{~s}^{-2}$, the stone being at rest r...
Read More →Draw the labelled diagram of the following:
[question] Question. Draw the labelled diagram of the following: (i) Gram seed (ii) V.S. of maize seed [/question] [solution] Solution: [/solution]...
Read More →In figure, if $\triangle \mathrm{ABE}$
[question] Question. In figure, if $\triangle \mathrm{ABE} \cong \triangle \mathrm{ACD}$, show that $\triangle \mathrm{ADE} \sim \triangle \mathrm{ABC}$. [/question] [solution] Solution: In figure, $\Delta \mathrm{ABE} \cong \triangle \mathrm{ACD}$(Given) $\Rightarrow \mathrm{AB}=\mathrm{AC}$ and $\mathrm{AE}=\mathrm{AD} \quad(\mathrm{CPCT})$ $\Rightarrow \frac{A B}{A C}=1$ and $\frac{A D}{A E}=1$ $\Rightarrow \frac{A B}{A C}=\frac{A D}{A E} \quad(E a c h=1)$ Now, in $\triangle \mathrm{ADE}$ and...
Read More →A pebble of mass 0.05 kg is thrown vertically upwards.
[question] Question. A pebble of mass 0.05 kg is thrown vertically upwards. Give the direction and magnitude of the net force on the pebble, (a) during its upward motion, (b) during its downward motion, (c) at the highest point where it is momentarily at rest. Do your answers change if the pebble was thrown at an angle of $45^{\circ}$ with the horizontal direction? Ignore air resistance. [/question] [solution] solution: 0.5 N, in vertically downward direction, in all cases Acceleration due to gr...
Read More →Differentiate between
[question] Question. Differentiate between (a) Racemose and cymose inflorescence (b) Fibrous roots and adventitious roots (c) Apocarpous and syncarpous ovary [/question] [solution] Solution: [/solution]...
Read More →$\mathrm{S}$ and $\mathrm{T}$ are points on sides $\mathrm{PR}$ and $\mathrm{QR}$ of $\triangle \mathrm{PQR}$ such that $\angle \mathrm{P}=\angle \mathrm{RTS}$.
[question] Question. $\mathrm{S}$ and $\mathrm{T}$ are points on sides $\mathrm{PR}$ and $\mathrm{QR}$ of $\triangle \mathrm{PQR}$ such that $\angle \mathrm{P}=\angle \mathrm{RTS}$. Show that $\triangle \mathrm{RPQ} \sim$ $\triangle \mathrm{RTS}$. [/question] [solution] Solution: In figure, We have RPQ and RTS in which $\angle \mathrm{RPQ}=\angle \mathrm{RTS}$ (Given) $\angle \mathrm{PRQ}=\angle \mathrm{SRT}(\mathrm{Each}=\angle \mathrm{R})$ Then by AA similarity criterion, we have $\Delta \ma...
Read More →