The first term of an AP is 5,
[question] Question. The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference. [/question] [solution] Solution: $a=5$, last term $t_{n}=45$ and $S_{n}=400$ $\mathrm{S}_{\mathrm{n}}=400 \Rightarrow \frac{\mathrm{n}}{2}\left\{\mathrm{t}_{1}+\mathrm{t}_{\mathrm{n}}\right\}=400$ $\Rightarrow \frac{n}{2}\{5+45\}=400 \Rightarrow \frac{n}{2} \times 50=400$ $\Rightarrow \mathrm{n}=16$ Now, $\mathrm{t}_{\mathrm{n}}=45 \quad \Rightarrow \math...
Read More →Establish the following vector inequalities geometrically or otherwise:
[question] Question. Establish the following vector inequalities geometrically or otherwise: (a) $|\mathbf{a}+\mathbf{b}| \leq|\mathbf{a}|+|\mathbf{b}|$ (b) $|\mathbf{a}+\mathbf{b}| \geq\|\mathbf{a}|-| \mathbf{b}\|$ (c) $|\mathbf{a}-\mathbf{b}| \leq|\mathbf{a}|+|\mathbf{b}|$ (d) $|\mathbf{a}-\mathbf{b}| \geq|| \mathbf{a}|-| \mathbf{b}||$ When does the equality sign above apply? [/question] [solution] solution: (a) Let two vectors $\vec{a}$ and $\vec{b}$ be represented by the adjacent sides of a ...
Read More →How many terms of the AP :
[question] Question. How many terms of the AP : 9, 17, 25,.... must be taken to give a sum of 636? [/question] [solution] Solution: $a=9, d=8$ Let $S_{n}=636$ $\Rightarrow \frac{n}{2}[2 a+(n-1) d]=636$ $\Rightarrow \frac{n}{2}\{2 \times 9+(n-1)(8)\}=636$ $\Rightarrow \frac{n}{2}\{18+8 n-8\}=636$ $\Rightarrow \frac{n}{2}\{8 n+10\}=636 \Rightarrow n(4 n+5)=636$ $\Rightarrow 4 n^{2}+5 n-636=0$ $\Rightarrow \mathrm{n}=\frac{-5 \pm \sqrt{25+10176}}{8}=\frac{-5 \pm \sqrt{10201}}{8}$ $=\frac{-5 \pm 101...
Read More →What are the difficulties that you would face in classification of animals,
[question] Question. What are the difficulties that you would face in classification of animals, if common fundamental features are not taken into account? [/question] [solution] Solution: For the classification of living organisms, common fundamental characteristics are considered. If we consider specific characteristics, then each organism will be placed in a separate group and the entire objective of classification would not be achieved. Classification of animals is also important in comparin...
Read More →What will be the mass of one ${ }^{12} \mathrm{C}$ atom in $\mathrm{g}$ ?
[question] Question. What will be the mass of one ${ }^{12} \mathrm{C}$ atom in $\mathrm{g}$ ? [/question] [solution] Solution: 1 mole of carbon atoms $=6.023 \times 10^{23}$ atoms of carbon $=12 \mathrm{~g}$ of carbon $\therefore$ Mass of one ${ }^{12} \mathrm{C}$ atom $=\frac{12 \mathrm{~g}}{6.022 \times 10^{23}}$ $=1.993 \times 10^{-23} \mathrm{~g}$ [/solution]...
Read More →In an AP :
[question] Question. In an AP : (1) Given $a=5, d=3, a_{n}=50$, find $n$ and $S_{n}$. (ii) Given $\mathrm{a}=7, \mathrm{a}_{13}=35$, find $\mathrm{d}$ and $\mathrm{S}_{13}$. (iii) Given $\mathrm{a}_{12}=37, \mathrm{~d}=3$, find a and $\mathrm{S}_{12}$. (iv) Given $a_{3}=15, S_{10}=125$, find $d$ and $a_{10}$. (v) Given $\mathrm{d}=5, \mathrm{~S}_{9}=75$, find a and $\mathrm{a}_{9}$. (vi) Given $\mathrm{a}=2, \mathrm{~d}=8, \mathrm{~S}_{\mathrm{n}}=90$, find $\mathrm{n}$ and $\mathrm{a}_{\mathrm{...
Read More →Calculate the molarity of a solution of ethanol in water
[question] Question. Calculate the molarity of a solution of ethanol in water in which the mole fraction of ethanol is 0.040 (assume the density of water to be one) [/question] [solution] Solution: Mole fraction of $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}=\frac{\text { Number of moles of } \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}}{\text { Number of moles of solution }}$ $0.040=\frac{n_{\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{OH}}}{n_{\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{OH}}+n_{\mathrm{H}_{2} ...
Read More →Which of the following are sets? Justify our answer.
[question] Question Which of the following are sets? Justify our answer. (i) The collection of all months of a year beginning with the letter J. (ii) The collection of ten most talented writers of India. (iii) A team of eleven best-cricket batsmen of the world. (iv) The collection of all boys in your class. (v) The collection of all natural numbers less than 100. (vi) A collection of novels written by the writer Munshi Prem Chand. (vii) The collection of all even integers. (viii) The collection ...
Read More →Describe the important characteristics of gymnosperms.
[question] Question. Describe the important characteristics of gymnosperms. [/question] [solution] Solution: Important features of gymnosperms: 1. The term gymnosperm refers to plants with naked seeds (gymnos – naked, sperma – seeds), i.e., the seeds of these plants are not enclosed in fruits. 2. The plant-body ranges from medium to tall trees and shrubs. The giant redwood tree Sequoia is one of the tallest trees in the world. 3. The root system consists of tap roots. The coralloid roots present...
Read More →Match the followings (column I with column II)
[question] Question. Match the followings (column I with column II) [/question] [solution] Solution: [/solution]...
Read More →How would you distinguish monocots from dicots?
[question] Question. How would you distinguish monocots from dicots? [question] [solution] Solution: Monocots and dicots can be differentiated through their morphological and anatomical characteristics. [solution]...
Read More →Which one of the following will have largest number of atoms
[question] Question. Which one of the following will have largest number of atoms? (i)1 g Au (s) (ii)1 g Na (s) (iii)1 g Li (s) (iv)1 g of Cl2(g) [/question] [solution] Solution: (i). $1 \mathrm{~g}$ of $\mathrm{Au}(\mathrm{s})=\frac{1}{197} \mathrm{~mol}$ of $\mathrm{Au}(\mathrm{s})$ $=\frac{6.022 \times 10^{23}}{197}$ atoms of $A u(s)$ $=3.06 \times 10^{21}$ atoms of $A u(s)$ (ii). $1 \mathrm{~g}$ of $\mathrm{Na}(\mathrm{s})=\frac{1}{23}$ $\mathrm{mol}$ of $\mathrm{Na}(\mathrm{s})$ $=\frac{6.0...
Read More →Differentiate between the following:
[question] Question. Differentiate between the following:- (i)red algae and brown algae (ii) liverworts and moss (iii) homosporous and heterosporous pteridophyte (iv) syngamy and triple fusion [/question] [solution] Solution: (i) Red algae and brown algae <img src="/media/uploads/2021/12/i-Red-algae-and-brown-algae12.png" alt="(i) Red algae and brown algae12" (ii) Liverworts and moss (iii) Homosporous and heterosporous pteridophyte (iv) Syngamy and triple fusion [/solution]...
Read More →Pick out the only vector quantity in the following list: Temperature, pressure,
[question] Question. Pick out the only vector quantity in the following list: Temperature, pressure, impulse, time, power, total path length, energy, gravitational potential, coefficient of friction, charge. [/question] [solution] solution: Impulse Impulse is given by the product of force and time. Since force is a vector quantity, its product with time (a scalar quantity) gives a vector quantity. [/solution]...
Read More →Find the sums given below :
[question] Question. Find the sums given below : (i) $7+10 \frac{1}{2}+14+\ldots+84$ (ii) 34 + 32 + 30 + ... + 10 (iii) – 5 + (– 8) + (– 11) +...+ (– 230). [/question] [solution] Solution: (i) $\mathrm{a}=7, \mathrm{~d}=10 \frac{1}{2}-7=3 \frac{1}{2}=\frac{7}{2}$ $\ell=t_{n}=84 \Rightarrow a+(n-1) d=84$ $\Rightarrow 7+(n-1) \times \frac{7}{2}=84$ $\Rightarrow(\mathrm{n}-1) \times \quad \frac{7}{2}=77$ $\Rightarrow \mathrm{n}-1=77 \times \frac{2}{7}=22$ $\Rightarrow \mathrm{n}=23$ The sum $=\frac...
Read More →Pick out the two scalar quantities in the following list:
[question] Question. Pick out the two scalar quantities in the following list: force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, relative velocity. [/question] [solution] solution: Work and current are scalar quantities. Work done is given by the dot product of force and displacement. Since the dot product of two quantities is always a scalar, work is a scalar physical quantity. Current is described only by its magnitude. Its direction is...
Read More →Convert the following into basic units
[question] Question. Convert the following into basic units (i)28.7 pm (ii)15.15 pm (iii)25365 mg [/question] [solution] Solution: (i) $28.7 \mathrm{pm}$ : $1 \mathrm{pm}=10^{-12} \mathrm{~m}$ $\therefore 28.7 \mathrm{pm}=28.7 \times 10^{-12} \mathrm{~m}$ $=2.87 \times 10^{-11} \mathrm{~m}$ (ii) $15.15 \mathrm{pm}$ : $1 \mathrm{pm}=10^{-12} \mathrm{~m}$ $\therefore 15.15 \mathrm{pm}=15.15 \times 10^{-12} \mathrm{~m}$ $=1.515 \times 10^{-12} \mathrm{~m}$ (iii) $25365 \mathrm{mg}$ : $1 \mathrm{mg}...
Read More →Pick out the two scalar quantities in the following list:
[question] Question. Pick out the two scalar quantities in the following list: force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, relative velocity. [/question] [solution] solution: calar: Volume, mass, speed, density, number of moles, angular frequency Vector: Acceleration, velocity, displacement, angular velocity A scalar quantity is specified by its magnitude only. It does not have any direction associated with it. Volume, mass, speed, ...
Read More →State, for each of the following physical quantities,
[question] Question. State, for each of the following physical quantities, if it is a scalar or a vector: volume, mass, speed, acceleration, density, number of moles, velocity, angular frequency, displacement, angular velocity. [/question] [solution] solution: Scalar: Volume, mass, speed, density, number of moles, angular frequency Vector: Acceleration, velocity, displacement, angular velocity A scalar quantity is specified by its magnitude only. It does not have any direction associated with it...
Read More →Find the sum of the following APs :
[question] Question. Find the sum of the following APs : (i) 2, 7, 12, .... to 10 terms. (ii) – 37, – 33, – 29, ... to 12 terms. (iii) 0.6, 1.7, 2.8, ... to 100 terms (iv) $\frac{1}{15}, \frac{1}{12}, \frac{1}{10}, \ldots$ to 11 terms [/question] [solution] Solution: (i) $a=2, d=5$ $S_{10}=\frac{10}{2}\{2 a+9 d\}$ $\left(\because \mathrm{S}_{\mathrm{n}}=\frac{\mathrm{n}}{2}\{2 \mathrm{a}+(\mathrm{n}-1) \mathrm{d}\}\right)$ $=5 \times\{2 \times 2+9 \times 5)=5 \times 49=245$ (ii) $\mathrm{a}=-37,...
Read More →If ten volumes of dihydrogen gas react with five volumes of dioxygen gas,
[question] Question. If ten volumes of dihydrogen gas react with five volumes of dioxygen gas, how many volumes of water vapour would be produced? [/question] [solution] Solution: Reaction of dihydrogen with dioxygen can be written as $2 \mathrm{H}_{2(x)}+\mathrm{O}_{2(x)} \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}_{(g)}$ Now, two volumes of dihydrogen react with one volume of dihydrogen to produce two volumes of water vapour. Hence, ten volumes of dihydrogen will react with five volumes of dio...
Read More →The velocity-time graph of a particle in one-dimensional
[question] Question. The velocity-time graph of a particle in one-dimensional motion is shown in Fig. 3.29: Which of the following formulae are correct for describing the motion of the particle over the time-interval $t_{2}$ to $t_{1}$ ? (a) $x\left(t_{2}\right)=x\left(t_{1}\right)+v\left(t_{1}\right)\left(t_{2}-t_{1}\right)+\left(\frac{1}{2}\right) a\left(t_{2}-t_{1}\right)^{2}$ (b) $v\left(t_{2}\right)=v\left(t_{1}\right)+a\left(t_{2}-t_{1}\right)$ (c) $v_{\text {Average }}=\left(x\left(t_{2}\...
Read More →Explain briefly the following terms with suitable examples:-
[question] Question. Explain briefly the following terms with suitable examples:- (i) protonema (ii) antheridium (iii) archegonium (iv) diplontic (v) sporophyll (vi) isogamy [/question] [solution] Solution: (i) Protonema – It is the first stage in the life cycle of a moss, developing directly from the spore. It consists of creeping, green, branched, and often filamentous structures. (ii) Antheridium – It is the male sex organ present in bryophytes and pteridophytes and is surrounded by a jacket ...
Read More →Ramkali saved Rs. 5 in the first week of a year and then increased her weekly savings by Rs. 1.75. If in the nth week,
[question] Question. Ramkali saved Rs. 5 in the first week of a year and then increased her weekly savings by Rs. 1.75. If in the nth week, her weekly savings become Rs. 20.75, find n. [/question] [solution] Solution: $\mathrm{t}_{1}=$ Rs. 5 (savings in the lst week) $t_{2}=R s .5+R s .1 .75=R s .6 .75$ (savings in the 2 nd week) $t_{3}=$ Rs. $6.75+$ Rs. $1.75=$ Rs. $8.50$ (savings in the $3 \mathrm{rd}$ week) ...................... $\mathrm{t}_{\mathrm{n}}=$ Rs. $20.75$ $\Rightarrow a+(n-1) d=2...
Read More →What is heterospory?
[question] Question. What is heterospory? Briefly comment on its significance. Give two examples. [/question] [solution] Solution: Heterospory is a phenomenon in which two kinds of spores are borne by the same plant. These spores differ in size. The smaller one is known as microspore and the larger one is known as megaspore. The microspore germinates to form the male gametophyte and the megaspore germinates to form the female gametophyte. The male gametophyte releases the male gametes and these ...
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