eSaral - JEE | NEET | Class 8-10 Exam Prep App

A nucleus is at rest in the laboratory frame of reference.

[question] Question. A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei the products must move in opposite directions. [/question] [solution] solution: Let $m, m_{1}$, and $m_{2}$ be the respective masses of the parent nucleus and the two daughter nuclei. The parent nucleus is at rest. Initial momentum of the system (parent nucleus) $=0$ Let $v_{1}$ and $v_{2}$ be the respective velocities of the daughter nuclei having masses $m_{1}$ ...

PQR is a triangle right angled at P and M is a point on QR

[question] Question. $\mathrm{PQR}$ is a triangle right angled at $\mathrm{P}$ and $\mathrm{M}$ is a point on $\mathrm{QR}$ such that $\mathrm{PM} \perp \mathrm{QR}$. Show that $\mathrm{PM}^{2}=\mathrm{QM} \times \mathrm{MR}$. [/question] [solution] Solution: $\angle 1+\angle 2=\angle 2+\angle 4$ $\left(\mathrm{Each}=90^{\circ}\right)$ $\Rightarrow \angle 1=\angle 4$ Similarly, $\angle 2=\angle 3$. Now, this gives $\Delta \mathrm{QPM} \sim \Delta \mathrm{PRM}$ (AA similarity) $\Rightarrow \frac{...

What is the energy in joules, required to shift the electron of the hydrogen atom

[question] Question. What is the energy in joules, required to shift the electron of the hydrogen atom from the first Bohr orbit to the fifth Bohr orbit and what is the wavelength of the light emitted when the electron returns to the ground state? The ground state electron energy is $-2.18 \times 10^{-11}$ ergs. [/question] [solution] Solution: Energy $(E)$ of the $\mathrm{n}^{\text {th }}$ Bohr orbit of an atom is given by, $E_{n}=\frac{-\left(2.18 \times 10^{-18}\right) \mathrm{Z}^{2}}{n^{2}}$...

Cork cambium forms tissues that form the cork. Do you agree with this statement? Explain.

[question] Question. Cork cambium forms tissues that form the cork. Do you agree with this statement? Explain. [/question] [solution] Solution: When secondary growth occurs in the dicot stem and root, the epidermal layer gets broken. There is a need to replace the outer epidermal cells for providing protection to the stem and root from infections. Therefore, the cork cambium develops from the cortical region. It is also known as phellogen and is composed of thin-walled rectangular cells. It cuts...

Sides of some triangles are given below.

[question] Question. Sides of some triangles are given below. Determine which of them are right triangles. In case of a right triangle, write the length of its hypotenuse. (i) 7 cm, 24 cm, 25 cm (ii) 3 cm, 8 cm, 6 cm (iii) 50 cm, 80 cm, 100 cm (iv) 13 cm, 12 cm, 5 cm [/question] [solution] Solution: (i) $(7)^{2}+(24)^{2}=49+576=625=(25)^{2}$ Therefore, given sides $7 \mathrm{~cm}, 24 \mathrm{~cm}, 25 \mathrm{~cm}$ make a right triangle. (ii) $(6)^{2}+(3)^{2}=36+9=45$ $(8)^{2}=64$ $(6)^{2}+(3)^{2...

State the location and function of different types of meristem.

[question] Question. State the location and function of different types of meristem.\ [/question] [solution] Solution: Meristems are specialised regions of plant growth. The meristems mark the regions where active cell division and rapid division of cells take place. Meristems are of three types depending on their location. Apical meristem It is present at the root apex and the shoot apex. The shoot apical meristem is present at the tip of the shoots and its active division results in the elonga...

Sides of two similar triangles are in the ratio 4 : 9.

[question] Question. Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio (1) 2 : 3 (2) 4 : 9 (3) 81 : 16 (4) 16 : 81 [/question] [solution] Solution: $\frac{\text { area of } 1^{\text {st }} \Delta}{\text { area of } 2^{\text {nd }} \Delta}=\left(\frac{4}{9}\right)^{2}=\frac{16}{81}$ [/solution]...

ABC and BDE are two equilateral triangles such that D is the mid-point of BC.

[question] Question. ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is (1) 2 : 1 (2) 1 : 2 (3) 4 : 1 (4) 1 : 4 [/question] [solution] Solution: $(\because B C=2 B D)$ Since, both are equilateral triangles $\Delta \mathrm{ABC} \sim \Delta \mathrm{EBD}$ $\frac{\operatorname{ar} \Delta \mathrm{ABC}}{\operatorname{ar} \Delta \mathrm{BDE}}=\left(\frac{\mathrm{BC}}{\mathrm{BD}}\right)^{2}=\left(\frac{2}{1}\right)^{2}=4: 1$ [/so...

Calculate the wave number for the longest wavelength transition

[question] Question. Calculate the wave number for the longest wavelength transition in the Balmer series of atomic hydrogen. [/question] [solution] Solution: For the Balmer series, $n_{i}=2$. Thus, the expression of wavenumber $(\bar{v})$ is given by, $\bar{v}=\left[\frac{1}{(2)^{2}}-\frac{1}{n_{\mathrm{f}}^{2}}\right]\left(1.097 \times 10^{7} \mathrm{~m}^{-1}\right)$ Wave number $(\bar{v})$ is inversely proportional to wavelength of transition. Hence, for the longest wavelength transition, $(\...

Prove that the area of an equilateral triangle described on one side

[question] Question. Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals. [/question] [solution] Solution: ABCD is a square having sides of length = a. Then the diagonal $\mathrm{BD}=\mathrm{a} \sqrt{2}$. We construct equilateral $\Delta \mathrm{s}$ PAB and QBD $\Rightarrow \Delta \mathrm{PAB} \sim \Delta \mathrm{QBD}$ (Equilateral triangles are similar) $\Rightarrow \frac{\operat...

Describe the arrangement of floral members in relation to their insertion on thalamus?

[question] Question. Describe the arrangement of floral members in relation to their insertion on thalamus? [/question] [solution] Solution: Based on the position of the calyx, corolla, and androecium (with respect to the ovary on the thalamus), the flowers are described as hypognous, perigynous, and epigynous. In hypogynous flowers, the ovary occupies the highest position on the thalamus while other floral parts are situated below it. In such flowers, the ovary is superior e.g., China rose, mus...

Prove that the ratio of the areas of two similar triangles is equal

[question] Question. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians. [/question] [solution] Solution: In figure, $\mathrm{AD}$ is a median of $\triangle \mathrm{ABC}$ and $\mathrm{PM}$ is a median of $\triangle \mathrm{PQR}$. Here, $\mathrm{D}$ is mid-point of $\mathrm{BC}$ and $M$ is mid-point of $Q R$. Now, we have $\triangle \mathrm{ABC} \sim \triangle \mathrm{PQR}$. $\Rightarrow \angle \mathrm{B}=\angle \mathrm{Q}...

Write the floral formula of an actinomorphic bisexual,

[question] Question. Write the floral formula of an actinomorphic bisexual, hypogynous flower with five united sepals, five free petals. Five free stamens and two united carpals with superior ovary and axile placentation. [question] [solution] Solution: The floral formula of the described flower is represented as: Actinomorphic flowers are represented by the symbol $\oplus$. The calyx contains five united sepals which can be represented as $K_{(5)}$. The corolla consists of five free petals and ...

The energy associated with the first orbit in the hydrogen atom

[question] Question. (i) The energy associated with the first orbit in the hydrogen atom is $-2.18 \times 10^{-18} \mathrm{~J}$ atom $^{-1}$. What is the energy associated with the fifth orbit? (ii) Calculate the radius of Bohr’s fifth orbit for hydrogen atom. [/question] [solution] Solution: (i)Energy associated with the fifth orbit of hydrogen atom is calculated as: $E_{5}=\frac{-\left(2.18 \times 10^{-18}\right)}{(5)^{2}}=\frac{-2.18 \times 10^{-18}}{25}$ $E_{5}=-8.72 \times 10^{-20} \mathrm{...

D, E and F are respectively the mid-points of sides AB,

[question] Question. $\mathrm{D}, \mathrm{E}$ and $\mathrm{F}$ are respectively the mid-points of sides $\mathrm{AB}, \mathrm{BC}$ and $\mathrm{CA}$ of $\triangle \mathrm{ABC}$. Find the ratio of the areas of $\Delta \mathrm{DEF}$ and $\triangle \mathrm{ABC}$. [/question] [solution] Solution: $\mathrm{DF}=\frac{1}{2} \mathrm{BC}, \mathrm{DE}=\frac{1}{2} \mathrm{AC}, \mathrm{EF}=\frac{1}{2} \mathrm{AB}$ [By midpoint theorem] So, $\frac{D F}{B C}=\frac{D E}{A C}=\frac{E F}{A B}=\frac{1}{2}$ $\ther...

Define the term inflorescence. Explain the basis for the different types of inflorescence in flowering plants.

[question] Question. Define the term inflorescence. Explain the basis for the different types of inflorescence in flowering plants. [/question] [solution] Solution: Inflorescence is the manner in which the flowers are arranged on the flowering axis. During the flowering season, the vegetative apex of the stem gets converted into a floral meristem. Based on whether the floral axis continues to grow or end in a flower, inflorescence is classified into racemose and cymose. In racemose inflorescence...

What is the maximum number of emission lines when the excited electron of an H

[question] Question. What is the maximum number of emission lines when the excited electron of an H atom in n = 6 drops to the ground state? [/question] [solution] Solution: When the excited electron of an H atom in n = 6 drops to the ground state, the following transitions are possible: Hence, a total number of (5 + 4 + 3 + 2 + 1) 15 lines will be obtained in the emission spectrum. The number of spectral lines produced when an electron in the $n^{\text {th }}$ level drops down to the ground sta...

How do the various leaf modifications help plants?

[question] Question. How do the various leaf modifications help plants? [/question] [solution] Solution: The main function of the leaves is to carry out the process of photosynthesis. However, in a few plants, leaves are modified to perform different functions. (a) Tendrils: The leaves of a pea plant are modified into tendrils that help the plant in climbing. (b) Spines: The leaves in cactus are modified into sharp spines that act as an organ of defense. (c) Phyllode: The leaves of some Australi...

If the areas of two similar triangles are equal,

[question] Question. If the areas of two similar triangles are equal, prove that they are congruent. [/question] [solution] Solution: Let $\Delta \mathrm{ABC} \sim \Delta \mathrm{PQR}$ and area $(\Delta \mathrm{ABC}) \quad=$ area $(\Delta \mathrm{PQR}) \quad($ Given $)$ i.e., $\frac{\operatorname{area}(\Delta A B C)}{\operatorname{area}(\Delta P O R)}=1$ $\Rightarrow \frac{A B^{2}}{P Q^{2}}=\frac{B C^{2}}{Q R^{2}}=\frac{C A^{2}}{P R^{2}}=1$ $\Rightarrow \mathrm{AB}=\mathrm{PQ}, \mathrm{BC}=\math...

In figure, ABC and DBC are two triangles on the same base BC.

[question] Question. In figure, $\mathrm{ABC}$ and $\mathrm{DBC}$ are two triangles on the same base $\mathrm{BC}$. If $\mathrm{AD}$ intersects $\mathrm{BC}$ at $\mathrm{O}$, show that $\frac{\operatorname{ar}(A B C)}{\operatorname{ar}(D B C)}=\frac{A O}{D O}$.' [/question] [solution] Solution: Draw $\mathrm{AL} \perp \mathrm{BC}$ and $\mathrm{DM} \perp \mathrm{BC}$ (see figure) $\Delta \mathrm{OLA} \sim \Delta \mathrm{OMD}$(AA similarity criterion) $\Rightarrow \frac{A L}{D M}=\frac{A O}{D O}$ ...

How much energy is required to ionise a H atom if the electron occupies n = 5 orbit?

[question] Question. How much energy is required to ionise a H atom if the electron occupies n = 5 orbit? Compare your answer with the ionization enthalpy of H atom (energy required to remove the electron from n =1 orbit). [/question] [solution] Solution: The expression of energy is given by, $E_{n}=\frac{-\left(2.18 \times 10^{-18}\right) Z^{2}}{n^{2}}$ Where, Z = atomic number of the atom n = principal quantum number For ionization from $n_{1}=5$ to $n_{2}=\infty$, $\Delta E=E_{x}-E_{3}$ $=\le...

What is a flower? Describe the parts of a typical angiosperm flower?

[question] Question. What is a flower? Describe the parts of a typical angiosperm flower? [/question] [solution] Solution: A flower can be defined as the reproductive unit of any flowering plant (angiosperms). Flowers carry out sexual reproduction in angiosperms. A typical flower is a modified stem with a condensed axis. A flower has four different parts i.e., the calyx, corolla, androecium, and gynoecium. Androecium and gynoecium represent the male and female reproductive organs of a flower (re...

Diagonals of trapezium ABCD with AB

[question] Question. Diagonals of trapezium $\mathrm{ABCD}$ with $\mathrm{AB} \| \mathrm{DC}$ intersect each other at the point $\mathrm{O}$. If $\mathrm{AB}=2 \mathrm{CD}$, find the ratio of the areas of triangles $\mathrm{AOB}$ and COD. [/question] [solution] Solution: In $\Delta \mathrm{AOB}$ and $\Delta \mathrm{COD}$, $\angle \mathrm{OAB}=\angle \mathrm{OCD}$ (Alternate interior angles) $\angle \mathrm{OBA}=\angle \mathrm{ODC}$ (Alternate interior angles) $\therefore$ By AA, similarity $\Del...

A man of mass 70 kg stands on a weighing scale in a lift which is moving

[question] Question. A man of mass 70 kg stands on a weighing scale in a lift which is moving (a) upwards with a uniform speed of $10 \mathrm{~m} \mathrm{~s}^{-1}$, (b) downwards with a uniform acceleration of $5 \mathrm{~m} \mathrm{~s}^{-2}$, (c) upwards with a uniform acceleration of $5 \mathrm{~m} \mathrm{~s}^{-2}$. What would be the readings on the scale in each case? (d) What would be the reading if the lift mechanism failed and it hurtled down freely under gravity? [/question] [solution] s...

Describe the various types of placentations found in flowering plants.

[question] Question. Describe the various types of placentations found in flowering plants. [/question] [solution] Solution: Placentation refers to the arrangement of ovules inside the ovary. It is of five basic types. (A) Marginal placentation: The ovary in which the placenta forms a ridge along the ventral suture of the ovary and the ovules develop on two separate rows is known to have marginal placentation. This type of placentation is found in peas. (B) Parietal placentation When the ovules ...

All Study Material