The speed-time graph of a particle moving along a fixed direction is
[question] Question. The speed-time graph of a particle moving along a fixed direction is shown in Fig. 3.28. Obtain the distance traversed by the particle between (a) $t=0$ s to $10 \mathrm{~s}$, (b) $t=2 \mathrm{~s}$ to 6 [/question] [solution] solution: (a) Distance travelled by the particle = Area under the given graph $=\frac{1}{2} \times(10-0) \times(12-0)=60 \mathrm{~m}$ Average speed $=\frac{\text { Distance }}{\text { Time }}=\frac{60}{10}=6 \mathrm{~m} / \mathrm{s}$ (b) Let $s_{1}$ and...
Read More →Subba Rao started work in 1995 at an annual salary of Rs. 5000 and received an increment of Rs. 200 each year.
[question] Question. Subba Rao started work in 1995 at an annual salary of Rs. 5000 and received an increment of Rs. 200 each year. In which year did his income reach Rs. 7000 ? [/question] [solution] Solution: It can be observed that the incomes that Subba Rao obtained in various years are in A.P. as every year, his salary is increased by Rs. 200. Therefore, the salaries of each year after 1995 are 5000, 5200, 5400, ..... Here, a = 5000 d = 200 Let after $\mathrm{n}^{\text {th }}$ year, his sal...
Read More →Both gymnosperms and angiosperms bear seeds,
[question] Question. Both gymnosperms and angiosperms bear seeds, then why are they classified separately? [/question] [solution] Solution: Gymnosperms and angiosperms are seed-producing plants with diplontic life cycles. In gymnosperms, the sporophylls are aggregated to form compact cones. The microsporophylls are broad and are not distinguished into filaments and anthers. The megasporophylls are woody and lack the ovary, style, and stigma, because of which the ovules lie exposed. The female ga...
Read More →How are $0.50 \mathrm{~mol} \mathrm{Na}_{2} \mathrm{CO}_{3}$ and $0.50 \mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3}$ different?
[question] Question. How are $0.50 \mathrm{~mol} \mathrm{Na}_{2} \mathrm{CO}_{3}$ and $0.50 \mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3}$ different? [/question] [solution] Solution: Molar mass of $\mathrm{Na}_{2} \mathrm{CO}_{3}=(2 \times 23)+12.00+(3 \times 16)=106 \mathrm{~g} \mathrm{~mol}^{-1}$ Now, 1 mole of $\mathrm{Na}_{2} \mathrm{CO}_{3}$ means $106 \mathrm{~g}$ of $\mathrm{Na}_{2} \mathrm{CO}_{3}$. $\therefore 0.5 \mathrm{~mol}$ of $\mathrm{Na}_{2} \mathrm{CO}_{3} \quad=\frac{106 \mathrm{~...
Read More →The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44.
[question] Question. The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP. [/question] [solution] Solution: $\mathrm{t}_{4}+\mathrm{t}_{8}=24 ; \mathrm{t}_{6}+\mathrm{t}_{10}=44$ $\Rightarrow(a+3 d)+(a+7 d)=24$ $(a+5 d)+(a+9 d)=44$ $\Rightarrow 2 \mathrm{a}+10 \mathrm{~d}=24 ; 2 \mathrm{a}+14 \mathrm{~d}=44$ We have $a+5 d=12$ ...(1) and $\mathrm{a}+7 \mathrm{~d}=22$ ...(2) Subtracting (1) from (2), we get $2 d=10 \Righ...
Read More →Write a note on economic importance of algae and gymnosperms.
[question] Question. Write a note on economic importance of algae and gymnosperms. [/question] [solution] Solution: Economic importance of algae Algae have diverse economic uses. They perform half of the total carbon dioxide-fixation on earth by photosynthesis, acting as the primary producers in aquatic habitats. (a) Food source: Many species of marine algae such as Porphyra, Sargassum, and Laminaria are edible. Chlorella and Spirulina are rich in proteins. Thus, they are used as food supplement...
Read More →Find the 20th term from the last term of the AP
[question] Question. Find the 20th term from the last term of the AP 3, 8, 13, ....., 253. [/question] [solution] Solution: The AP is 3, 8, 13, ..., 253 Its first term = 3 and the common difference = 5. Now, the AP in the reverse order will have the first term = 253 and the common difference = – 5. The 20th term from the end of the AP (1) = The 20 term of the AP in the reverse order $=a+19 d$ $=253+19 \times(-5)=253-95=158$ [/solution]...
Read More →Determine the AP whose third term is 16
[question] Question. Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12. [/question] [solution] Solution: $a_{3}=16$ $a+(3-1) d=16$ $a+2 d=16$ ...(1) $a_{7}-a_{5}=12$ $[a+(7-1) d]-[a+(5-1) d]=12$ $(a+6 d)-(a+4 d)=12$ $2 d=12$ d = 6 From equation (1), we obtain a + 2 (6) = 16 a + 12 = 16 a = 4 Therefore, A.P. will be $4,10,16,22, \ldots$ [/solution]...
Read More →Dinitrogen and dihydrogen react with each other
[question] Question. Dinitrogen and dihydrogen react with each other to produce ammonia according to the following chemical equation $\mathrm{N}_{2}(g)+\mathrm{H}_{2}(g) \rightarrow 2 \mathrm{NH}_{3}(g)$ (i) Calculate the mass of ammonia produced if $2.00 \times 10^{3} \mathrm{~g}$ dinitrogen reacts with $1.00$ $\times 10^{3} \mathrm{~g}$ of dihydrogen. (ii) Will any of the two reactants remain unreacted? (iii) If yes, which one and what would be its mass? [/question] [solution] Solution: (i)Bal...
Read More →Mention the ploidy of the following: protonemal cell of a moss; primary endosperm nucleus in dicot
[question] Question. Mention the ploidy of the following: protonemal cell of a moss; primary endosperm nucleus in dicot, leaf cell of a moss; prothallus cell of a fern; gemma cell in Marchantia; meristem cell of monocot, ovum of a liverwort, and zygote of a fern. [/question] [solution] Solution: (a) Protonemal cell of a moss – Haploid (b) Primary endosperm nucleus in a dicot – Triploid (c) Leaf cell of a moss – Haploid (d) Prothallus of a fern – Haploid (e) Gemma cell in Marchantia – Haploid (f)...
Read More →For what value of n, are the nth terms of two APs 63, 65, 67, ...
[question] Question. For what value of n, are the nth terms of two APs 63, 65, 67, ... and 3, 10, 17, .... equal? [/question] [solution] Solution: l. Two APs are 63, 65, 67, ..., 3, 10, 17, ... From (1), First term = 63 and common difference = 2 Its $n$th term $=63+(n-1) \times 2=2 n+61$ From $(2)$, First term $=3$ and common difference $=7$ Its nth term $=3+(n-1) \times 7=7 n-4$ Putting $7 \mathrm{n}-4=2 \mathrm{n}+61$ $\Rightarrow 7 n-2 n=61+4 \Rightarrow 5 n=65 \Rightarrow n=13$ [/solution]...
Read More →How many multiples of 4 lie between 10 and 250?
[question] Question. How many multiples of 4 lie between 10 and 250? [/question] [solution] Solution: The multiples of 4 between 10 and 250 are 12, 16, 20, 24...., 248. Let these numbers be n. $a=12, d=4$ $\mathrm{t}_{\mathrm{n}}=248$ $\Rightarrow a+(n-1) d=248$ $\Rightarrow 12+(n-1) \times 4=248$ $\Rightarrow 4 n+8=248 \Rightarrow n=60$ [/solution]...
Read More →Name three groups of plants that bear archegonia.
[question] Question. Name three groups of plants that bear archegonia. Briefly describe the life cycle of any one of them. [/question] [solution] Solution: Archegonium is the female sex organ that produces the female gamete or egg. It is present in the life cycles of bryophytes, pteridophytes, and gymnosperms. Life cycle of a fern (Dryopteris) Dryopteris is a common fern with pinnately-compound leaves. The main plant-body is sporophytic. Many sporangia are borne on the lower surfaces of its matu...
Read More →How many three-digit numbers are divisible by 7?
[question] Question. How many three-digit numbers are divisible by 7? [/question] [solution] Solution: First three-digit number that is divisible by 7 = 105 Next number = 105 + 7 = 112 Therefore, 105, 112, 119,\ldots All are three digit numbers which are divisible by 7 and thus, all these are terms of an A.P. having first term as 105 and common difference as 7. The maximum possible three-digit number is 999. When we divide it by 7, the remainder will be 5. Clearly, 999 - 5 = 994 is the maximum p...
Read More →When and where does reduction division take place in the life cycle of a liverwort
[question] Question. When and where does reduction division take place in the life cycle of a liverwort, a moss, a fern, a gymnosperm and an angiosperm? [/question] [solution] Solution: liverwort – In liverworts, the main plant-body is haploid (gametophytic). It bears the male and female sex organs which produce gametes. These gametes fuse to form a zygote. The zygote develops on the gametophytic plant-body to form a sporophyte. The sporophyte is differentiated into the foot, seta, and capsule. ...
Read More →In a reaction
[question] Question. In a reaction $A+B_{2} \rightarrow A B_{2}$ Identify the limiting reagent, if any, in the following reaction mixtures (i) 300 atoms of $A+200$ molecules of $B$ (ii) $2 \mathrm{~mol} A+3 \mathrm{~mol} B$ (iii) 100 atoms of $A+100$ molecules of $B$ (iv) $5 \mathrm{~mol} \mathrm{~A}+2.5 \mathrm{~mol} \mathrm{~B}$ (v) $2.5 \mathrm{~mol} \mathrm{~A}+5 \mathrm{~mol} \mathrm{~B}$ [/question] [solution] Solution: A limiting reagent determines the extent of a reaction. It is the reac...
Read More →Two APs have the same common difference.
[question] Question. Two APs have the same common difference. The difference between their 100 th terms is 100, what is the difference between their 1000th terms? [/question] [solution] Solution: Let the two APs with same common difference d be $a, a+d, a+2 d, \ldots$ $b, b+d, b+2 d, \ldots .(ab)$ we are given that $\{100$ th term of the first $A P\}$ $-\{100$ th term of the second $A P\}=100$ $\Rightarrow\{a+99 d\}-\{b+99 d\}=100$ $\Rightarrow a-b=100$ ...(1) Now, $\{1000$ th term of the first ...
Read More →What is the basis of classification of algae?
[question] Question. What is the basis of classification of algae? [/question] [solution] Solution: Algae are classified into three main classes – Chlorophyceae, Phaeophyceae, and Rhodophyceae. These divisions are based on the following factors: (a) Major photosynthetic pigments present (b) Form of stored food (c) Cell wall composition (d) Number of flagella and position of insertion Class I – Chlorophyceae Common name – Green algae Major pigments – Chlorophylls a and b Stored food – Starch Cell...
Read More →Which term of the AP :
[question] Question. Which term of the AP : 3, 15, 27, 39, .... will be 132 more than its 54th term? [/question] [solution] Solution: $a=3, d=12$ Let us suppose $t_{n}=t_{54}+132$ $\Rightarrow a+(n-1) d=a+53 d+132$ $\Rightarrow(\mathrm{n}-1) \mathrm{d}-53 \mathrm{~d}=132$ $\Rightarrow\{n-1-53) d=132$ $\Rightarrow(n-54) \times 12=132$ $\Rightarrow \mathrm{n}-54=11$ $\Rightarrow \mathrm{n}=65$ Hence, $\mathrm{t}_{65}$ is 132 more than $\mathrm{t}_{54}$. [/solution]...
Read More →Organise a discussion in your class on the topic- Are viruses living or non-living?
[question] Question. Organise a discussion in your class on the topic- Are viruses living or non-living? [/question] [solution] Solution: Viruses are microscopic organisms that have characteristics of both living and non-living. A virus consists of a strand of DNA or RNA covered by a protein coat. This presence of nucleic acid (DNA or RNA) suggests that viruses are alive. In addition, they can also respond to their environment (inside the host cell) in a limited manner. However, some other chara...
Read More →If the speed of light is $3.0 \times 10^{8} \mathrm{~m} \mathrm{~s}^{-1}$,
[question] Question. If the speed of light is $3.0 \times 10^{8} \mathrm{~m} \mathrm{~s}^{-1}$, calculate the distance covered by light in $2.00 \mathrm{~ns}$. [/question] [solution] Solution: According to the question: Time taken to cover the distance $=2.00 \mathrm{~ns}$ $=2.00 \times 10^{-9} \mathrm{~s}$ Speed of light $=3.0 \times 10^{8} \mathrm{~ms}^{-1}$ Distance travelled by light in $2.00 \mathrm{~ns}$ $=$ Speed of light $\times$ Time taken $=\left(3.0 \times 10^{8} \mathrm{~ms}^{-1}\rig...
Read More →The 17th term of an AP exceeds its 10th term by 7.
[question] Question. The 17th term of an AP exceeds its 10th term by 7. Find the common difference [/question] [solution] Solution: $a_{17}-a_{10}=7$ $(a+16 d)-(a+9 d)=7$ $7 d=7$ $d=1$ Therefore, the common difference is 1 . [/solution]...
Read More →Give a brief account of viruses with respect to their structure and nature of genetic material.
[question] Question. Give a brief account of viruses with respect to their structure and nature of genetic material. Also name four common viral diseases. [/question] [solution] Solution: Viruses are sub-microscopic infectious agents that can infect all living organisms. A virus consists of genetic material surrounded by a protein coat. The genetic material may be present in the form of DNA or RNA. Most of the viruses, infecting plants, have single stranded RNA as genetic material. On the other ...
Read More →If the 3rd and 9th terms of an AP are 4 and – 8 respectively,
[question] Question. If the 3rd and 9th terms of an AP are 4 and – 8 respectively, which term of this AP is zero? [/question] [solution] Solution: Given that, $a_{2}=4$ $a_{9}=-8$ We know that, $a_{n}=a+(n-1) d$ $a_{2}=a+(3-1) d$ $4=a+2 d$ ...(i) $a_{9}=a+(9-1) d$ $-8=a+8 d$ ...(ii) On subtracting equation (I) from (II), we obtain $-12=6 d$ $d=-2$ From equation (I), we obtain $4=a+2(-2)$ $4=a+2(-2)$ $4=a-4$ $a=8$ Let $\mathrm{n}^{\text {th }}$ term of this A.P. be zero. $a_{n}=a+(n-1) d$ 0 = 8 +...
Read More →What are the characteristic features of Euglenoids?
[question] Question. What are the characteristic features of Euglenoids? [/question] [solution] Solution: Some characteristic features of Euglenoids are as follows. Euglenoids (such as Euglena) are unicellular protists commonly found in fresh water. Instead of cell wall, a protein-rich cell membrane known as pellicle is present. They bear two flagella on the anterior end of the body. A small light sensitive eye spot is present. They contain photosynthetic pigments such as chlorophyll and can thu...
Read More →