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

Calculate the wavelength,

[question] Question. Calculate the wavelength, frequency and wave number of a light wave whose period is $2.0 \times 10^{-10} \mathrm{~s} .$ [/question] [solution] Solution: Frequency $(v)$ of light $=\frac{1}{\text { Period }}$ $=\frac{1}{2.0 \times 10^{-10} \mathrm{~s}}=5.0 \times 10^{9} \mathrm{~s}^{-1}$ Wavelength $(\lambda)$ of light $=\frac{c}{v}$ Where $c=$ velocity of light in vacuum $=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$ Substituting the value in the given expression of $\lambda$ :...

Give the magnitude and direction of the net force acting on

[question] Question. Give the magnitude and direction of the net force acting on (a) a drop of rain falling down with a constant speed, (b) a cork of mass 10 g floating on water, (c) a kite skillfully held stationary in the sky, (d) a car moving with a constant velocity of 30 km/h on a rough road, (e) a high-speed electron in space far from all material objects, and free of electric and magnetic fields. [/question] [solution] solution: (a) Zero net force The rain drop is falling with a constant ...

In figure, $\frac{Q R}{O S}=\frac{Q T}{P R}$ and $\angle 1=\angle 2$.

[question] Question. In figure, $\frac{Q R}{O S}=\frac{Q T}{P R}$ and $\angle 1=\angle 2$. Show that $\Delta P Q S \sim \Delta T Q R .$ [/question] [solution] Solution: In figure, $\angle 1=\angle 2$ (Given) $\Rightarrow \mathrm{PQ}=\mathrm{PR}$ (Sides opposite to equal angles of $\Delta \mathrm{PQR}$ ) We are given that $\frac{Q R}{O S}=\frac{Q T}{P R}$ $\Rightarrow \frac{\mathrm{QR}}{\mathrm{OS}}=\frac{\mathrm{QT}}{\mathrm{PQ}} \quad(\because \mathrm{PQ}=\mathrm{PR}$ proved $)$ $\Rightarrow \f...

(a) Show that for a projectile the angle between the velocity

[question] Question. (a) Show that for a projectile the angle between the velocity and the x-axis as a function of time is given by $\theta(t)=\tan ^{-1}\left(\frac{v_{0 y}-\mathrm{g} t}{v_{0 x}}\right)$ (b) Show that the projection angle $\theta_{0}$ for a projectile launched from the origin is given by $\theta_{0}=\tan ^{-1}\left(\frac{4 h_{m}}{R}\right)$ Where the symbols have their usual meaning. [/question] [solution] solution: (a) Let $v_{0 x}$ and $v_{0 y}$ respectively be the initial com...

Diagonals AC and BD of a trapezium ABCD with AB

[question] Question. Diagonals $\mathrm{AC}$ and $\mathrm{BD}$ of a trapezium $\mathrm{ABCD}$ with $\mathrm{AB} \| \mathrm{DC}$ intersect each other at the point O. Using a similarity criterion for two triangles, show that $\frac{O A}{O C}=\frac{O B}{O D}$. [/question] [solution] Solution: In figure, $\mathrm{AB} \| \mathrm{DC}$ $\Rightarrow \angle 1=\angle 3, \angle 2=\angle 4$ (Alternate interior angles) Also $\angle \mathrm{DOC}=\angle \mathrm{BOA}$ (Vertically opposite angles) $\Rightarrow \...

Find energy of each of the photons which

[question] Question. Find energy of each of the photons which (i)correspond to light of frequency 3× 1015 Hz. (ii)have wavelength of 0.50 Å. [/question [solution] Solution: (i) Energy $(E)$ of a photon is given by the expression, $E=h v$ Where, $h=$ Planck's constant $=6.626 \times 10^{-34} \mathrm{Js}$ $v=$ frequency of light $=3 \times 10^{15} \mathrm{~Hz}$ Substituting the values in the given expression of $E$ : $E=\left(6.626 \times 10^{-34}\right)\left(3 \times 10^{15}\right)$ $E=1.988 \tim...

Define the following terms:

[question] Question. Define the following terms: (a) Aestivation (b) Placentation (c) Actinomorphic (d) Zygomorphic (e) Superior ovary (f) Perigynous flower (g) Epipetalous Stamen [/question] [solution] Solution: (a) Aestivation The term ‘aestivation’ refers to the mode in which sepals or petals are arranged in a floral bud with respect to other floral members. There are four types of aestivation in plants i.e., valvate, twisted, imbricate, and vexillary. (b) Placentation The term ‘placentation’...

In figure, $\Delta \mathrm{ODC} \sim \Delta \mathrm{OBA}, \angle \mathrm{BOC}=125^{\circ}$

[question] Question. In figure, $\triangle \mathrm{ODC} \sim \Delta \mathrm{OBA}, \angle \mathrm{BOC}=125^{\circ}$ and $\angle \mathrm{CDO}=70^{\circ}$. Find $\angle \mathrm{DOC}, \angle \mathrm{DCO}$ and $\angle \mathrm{OAB}$. [/question] [solution] Solution: From figure, $\angle D O C+125^{\circ}=180^{\circ}$ $\Rightarrow \angle \mathrm{DOC}=180^{\circ}-125^{\circ}=55^{\circ}$ $\angle \mathrm{DCO}+\angle \mathrm{CDO}+\angle \mathrm{DOC}=180^{\circ}$ (Sum of three angles of $\Delta \mathrm{ODC}...

Explain with suitable examples the different types of phyllotaxy?

[question] Question. Explain with suitable examples the different types of phyllotaxy? [/question] [solution] Solution: Phyllotaxy refers to the pattern or arrangement of leaves on the stem or branch of a plant. It is of three types, alternate, opposite, and whorled phyllotaxy. In alternate phyllotaxy, a single leaf arises from the node of a branch. This type of phyllotaxy is observed in the sunflower, mustard, and peepal. Plants with opposite phyllotaxy have two leaves arising from the node in ...

Yellow light emitted from a sodium lamp has a wavelength

[question] Question. Yellow light emitted from a sodium lamp has a wavelength (λ) of 580 nm. Calculate the frequency (ν) and wave number $(\bar{v})$ of the yellow light [/question] [solution] Solution: From the expression $\lambda=\frac{\mathrm{c}}{v}$ We get $v=\frac{c}{\lambda}$..........(i) Where, ν= frequency of yellow light $\mathrm{c}=$ velocity of light in vacuum $=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$ $\lambda=$ wavelength of yellow light $=580 \mathrm{~nm}=580 \times 10^{-9} \mathrm...

State which pairs of triangles in figure,

[question] Question. State which pairs of triangles in figure, are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form: [/question] [solution] Solution: (i) Yes. $\angle \mathrm{A}=\angle \mathrm{P}=60^{\circ}, \angle \mathrm{B}=\angle \mathrm{Q}=80^{\circ}$, $\angle \mathrm{C}=\angle \mathrm{R}=40^{\circ}$ Therefore, $\Delta \mathrm{ABC} \sim \Delta \mathrm{PQR}$. By AAA similarity criterion (ii) Yes. ...

How is pinnately compound leaf different from palmately compound leaf?

[question] Question. How is pinnately compound leaf different from palmately compound leaf? [/question] [solution] Solution: [solution]...

Write the complete symbol for the atom with thegiven atomic numbe

[question] Question. Write the complete symbol for the atom with thegiven atomic number (Z) and Atomic mass (A (i)Z = 17, A = 35 (ii)Z = 92, A = 233 (iii)Z = 4, A = 9 [/question] [solution] Solution: (i) ${ }_{17}^{35} \mathrm{Cl}$ (ii) ${ }_{92}^{233} \mathrm{U}$ (iii) ${ }_{4}^{9} \mathrm{Be}$ [/solution]...

How many neutrons and protons are there inthe following nuclei?

[question] Question. How many neutrons and protons are there inthe following nuclei? ${ }_{6}^{13} \mathrm{C}$ ${ }_{8}^{16} \mathrm{O}$ ${ }_{12}^{24} \mathrm{Mg}$ ${ }_{26}^{56} \mathrm{Fe}$ ${ }_{38}^{88} \mathrm{Sr}$ [/question] [solution] Solution: ${ }^{13}{ }_{6} \mathrm{C}:$ Atomic mass $=13$ Atomic number $=$ Number of protons $=6$ Number of neutrons $=$ (Atomic mass) $-$ (Atomic number) $=13-6=7$ ${ }_{8}^{16} \bigcirc$ Atomic mass $=16$ Atomic number $=8$ Number of protons $=8$ Number...

The diagonals of a quadrilateral ABCD intersect

[question] Question. The diagonals of a quadrilateral $\mathrm{ABCD}$ intersect each other at the point $\mathrm{O}$ such that $\frac{\mathrm{AO}}{\mathrm{BO}}=\frac{\mathrm{CO}}{\mathrm{DO}}$. Show that $\mathrm{ABCD}$ is a trapezium. [/question] [solution] Solution: In figure $\frac{A O}{B O}=\frac{C O}{D O}$ $\Rightarrow \frac{A O}{O C}=\frac{B O}{O D} \quad \ldots$ (1) (given) Through $\mathrm{O}$, we draw $\mathrm{OE} \| \mathrm{BA}$ OE meets AD at E. From $\Delta \mathrm{DAB}$, $\mathrm{EO...

Can you associate vectors with (a) the length of a wire bent into a loop,

[question] Question. Can you associate vectors with (a) the length of a wire bent into a loop, (b) a plane area, (c) a sphere? Explain. [/question] [solution] solution: Answer: No; Yes; No (a) One cannot associate a vector with the length of a wire bent into a loop. (b) One can associate an area vector with a plane area. The direction of this vector is normal, inward or outward to the plane area. (c) One cannot associate a vector with the volume of a sphere. However, an area vector can be associ...

A vector has magnitude and direction.

[question] Question. A vector has magnitude and direction. Does it have a location in space? Can it vary with time? Will two equal vectors a and b at different locations in space necessarily have identical physical effects? Give examples in support of your answer. [/question] [solution] solution: Answer: No; Yes; No Generally speaking, a vector has no definite locations in space. This is because a vector remains invariant when displaced in such a way that its magnitude and direction remain the s...

ABCD is a trapezium in which AB

[question] Question. $\mathrm{ABCD}$ is a trapezium in which $\mathrm{AB} \| \mathrm{DC}$ and its diagonals intersect each other at the point $\mathrm{O}$. Show that $\frac{\mathrm{AO}}{\mathrm{BO}}=\frac{\mathrm{CO}}{\mathrm{DO}}$. [/question] [solution] Solution: We draw EOF $\| \mathrm{AB}($ also $\| \mathrm{CD})$ (see figure) In $\Delta \mathrm{ACD}, \quad \mathrm{OE} \| \mathrm{CD}$ $\Rightarrow \frac{A E}{E D}=\frac{A O}{O C} \ldots(1)$ In $\triangle \mathrm{ABD}, \mathrm{OE} \| \mathrm{BA...

An aircraft is flying at a height of 3400 m above the ground.

[question] Question. An aircraft is flying at a height of $3400 \mathrm{~m}$ above the ground. If the angle subtended at a ground observation point by the aircraft positions $10.0 \mathrm{~s}$ apart is $30^{\circ}$, what is the speed of the aircraft? [/question] [solution] solution: The positions of the observer and the aircraft are shown in the given figure. Height of the aircraft from ground, OR = 3400 m Angle subtended between the positions, $\angle \mathrm{POQ}=30^{\circ}$ Time = 10 s In $\t...

Justify the following statements on the basis of external features

[question] Question. Justify the following statements on the basis of external features (i) Underground parts of a plant are not always roots (ii) Flower is a modified shoot [question] [solution] Solution: (i) Various parts of plants are modified into underground structures to perform various functions such as stems, leaves, and even fruits. The stems in ginger and banana are underground and swollen due to storage of food. They are called rhizomes. Similarly, corm is an underground stem in Coloc...

Using Theorem 6.1,

[question] Question. Using Theorem 6.1, prove that a line drawn through the mid-point of one side of a triangle parallel to another side bisects the third side. [/question] [solution] Solution: In $\triangle \mathrm{ABC}, \mathrm{D}$ is mid point of $\mathrm{AB}$ (see figure) i.e., $\frac{A D}{D B}=1$ Straight line $\ell \| \mathrm{BC}$. Line $\ell$ is drawn through $\mathrm{D}$ and it meets $\mathrm{AC}$ at $\mathrm{E}$. By Basic Proportionality Theorem $\frac{A D}{D B}=\frac{A E}{E C} \Rightar...

In figure, A, B and C are points on OP,

[question] Question. In figure, $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are points on $\mathrm{OP}, \mathrm{OQ}$ and $\mathrm{OR}$ respectively such that $\mathrm{AB} \| \mathrm{PQ}$ and $\mathrm{AC}$ $\| \mathrm{PR}$. Show that $\mathrm{BC} \| \mathrm{QR}$. [/question] [solution] Solution: In $\triangle \mathrm{POO}$ AB $\| P Q$ (given) $\frac{\mathrm{OB}}{\mathrm{BQ}}=\frac{\mathrm{OA}}{\mathrm{AP}} \ldots$ (i) (Basic Proportionality Theorem) In $\triangle \mathrm{POR}$ $\mathrm{AC} \| \math...

Read each statement below carefully and state,

[question] Question. Read each statement below carefully and state, with reasons and examples, if it is true or false: A scalar quantity is one that (a) is conserved in a process (b) can never take negative values (c) must be dimensionless (d) does not vary from one point to another in space (e) has the same value for observers with different orientations of axes [/question] [solution] solution: (a) False Despite being a scalar quantity, energy is not conserved in inelastic collisions. (b) False...

Calculate the total number of electrons present in one mole of methane

[question] Question. (i)Calculate the total number of electrons present in one mole of methane (ii) Find (a) the total number and (b) the total mass of neutrons in $7 \mathrm{mg}$ of ${ }^{14} \mathrm{C}$. (Assume that mass of a neutron $=1.675 \times 10^{-27} \mathrm{~kg}$ ). (iii) Find (a) the total number and (b) the total mass of protons in $34 \mathrm{mg}$ of $\mathrm{NH}_{3}$ at STP. Will the answer change if the temperature and pressure are changed? [/question] [solution] Solution: (i) Nu...

What is meant by modification of root? What type of modification of root is found in the

[question] Question. What is meant by modification of root? What type of modification of root is found in the (a) Banyan tree (b) Turnip (c) Mangrove trees [/question] [solution] Solution: Primarily, there are two types of root systems found in plants, namely the tap root system and fibrous root system. The main function of the roots is to absorb water and minerals from the soil. However, roots are also modified to perform various other functions. The roots of some plants act as storage sites fo...

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