Find the greatest number of 6 digits exactly divisible by 24,
Question: Find the greatest number of 6 digits exactly divisible by 24, 15 and 36. Solution: TO FIND: Greatest number of 6 digits exactly divisible by 24, 15 and 36 The greatest 6 digit number be 999999 24, 15 and 36 $24=2^{3} \times 3$ $15=3 \times 5$ $36=2^{2} \times 3^{2}$ L.C.M of 24,15 and $36=360$ Since $\frac{999999}{360}=2777 \times 360+279$ Therefore, the remainder is 279. Hence the desired number is equal to $=999999-279$ $=999720$ Hence $=999720$ is the greatest number of 6 digits exa...
Read More →Differentiate the following w.r.t. x:
Question: Differentiate the following w.r.t.x: $\frac{e^{x}}{\sin x}$ Solution: Let $y=\frac{e^{x}}{\sin x}$ By using the quotient rule, we obtain $\frac{d y}{d x}=\frac{\sin x \frac{d}{d x}\left(e^{x}\right)-e^{x} \frac{d}{d x}(\sin x)}{\sin ^{2} x}$ $=\frac{\sin x \cdot\left(e^{x}\right)-e^{x} \cdot(\cos x)}{\sin ^{2} x}$ $=\frac{e^{x}(\sin x-\cos x)}{\sin ^{2} x}, x \neq n \pi, n \in \mathbf{Z}$...
Read More →Name any five hybrid varieties of crop plants which have been developed in India.
Question: Name any five hybrid varieties of crop plants which have been developed in India. Solution: The five hybrid varieties of crop plants which have been developed in India are:...
Read More →Find the LCM and HCF of the following integers by applying the prime factorisation method:
Question: Find the LCM and HCF of the following integers by applying the prime factorisation method: (i) 12, 15 and 21 (ii) 17, 23 and 29 (iii) 8, 9 and 25 (iv) 40, 36 and 126 (v) 84, 90 and 120 (vi) 24, 15 and 36 Solution: TO FIND: LCM and HCF of following pairs of integers (i) 15, 12 and 21 Let us first find the factors of 15, 12 and 21 $12=2^{2} \times 3$ $15=3 \times 5$ $21=3 \times 7$ L.C.M of 12,15 and $21=2^{2} \times 3 \times 5 \times 7$ L.C.M of 12,15 and $21=420$ H.C.F of 12,15 and $21...
Read More →Find out what the various components of the medium used for propagation of explants in vitro are?
Question: Find out what the various components of the medium used for propagation of explantsin vitroare? Solution: The major components of medium used for propagation of explantsin vitroare carbon sources such as sucrose, inorganic salts, vitamins, amino acids, water,agar-agar, and certain growth hormones such as auxins and gibberellins....
Read More →Find the LCM and HCF of the following integers by applying the prime factorisation method:
Question: Find the LCM and HCF of the following integers by applying the prime factorisation method: (i) 12, 15 and 21 (ii) 17, 23 and 29 (iii) 8, 9 and 25 (iv) 40, 36 and 126 (v) 84, 90 and 120 (vi) 24, 15 and 36 Solution: TO FIND: LCM and HCF of following pairs of integers (i) 15, 12 and 21 Let us first find the factors of 15, 12 and 21 $12=2^{2} \times 3$ $15=3 \times 5$ $21=3 \times 7$ L.C.M of 12,15 and $21=2^{2} \times 3 \times 5 \times 7$ L.C.M of 12,15 and $21=420$ H.C.F of 12,15 and $21...
Read More →Find
Question: Find $\frac{d y}{d x}$ $y=\sec ^{-1}\left(\frac{1}{2 x^{2}-1}\right), 0x\frac{1}{\sqrt{2}}$ Solution: The given relationship is $y=\sec ^{-1}\left(\frac{1}{2 x^{2}-1}\right)$ $y=\sec ^{-1}\left(\frac{1}{2 x^{2}-1}\right)$ $\Rightarrow \sec y=\frac{1}{2 x^{2}-1}$ $\Rightarrow \cos y=2 x^{2}-1$ $\Rightarrow 2 x^{2}=1+\cos y$ $\Rightarrow 2 x^{2}=2 \cos ^{2} \frac{y}{2}$ $\Rightarrow x=\cos \frac{y}{2}$ Differentiating this relationship with respect tox, we obtain $\frac{d}{d x}(x)=\frac{...
Read More →Which part of the plant is best suited for making virus-free plants and why?
Question: Which part of the plant is best suited for making virus-free plants and why? Solution: Apical and axillary meristems of plants is used for making virus-free plants. In a diseased plant, only this region is not infected by the virus as compared to the rest of the plant region. Hence, the scientists remove axillary and apical meristems of the diseased plant and grow itin vitroto obtain a disease-free and healthy plant. Virus-free plants of banana, sugarcane, and potato have been obtained...
Read More →Find the distance of the line 4x + 7y + 5 = 0 from
Question: Find the distance of the line 4x+ 7y+ 5 = 0 from the point (1, 2) along the line 2xy= 0. Solution: The given lines are 2xy= 0 (1) 4x+ 7y+ 5 = 0 (2) A (1, 2) is a point on line (1). Let B be the point of intersection of lines (1) and (2). On solving equations (1) and (2), we obtain $x=\frac{-5}{18}$ and $y=\frac{-5}{9}$. $\therefore$ Coordinates of point B are $\left(\frac{-5}{18}, \frac{-5}{9}\right)$. By using distance formula, the distance between points A and B can be obtained as $\...
Read More →Explain what is meant by biofortification.
Question: Explain what is meant by biofortification. Solution: Biofortification is a process of breeding crops with higher levels of vitamins, minerals, proteins, and fat content. This method is employed to improve public health. Breeding of crops with improved nutritional quality is undertaken to improve the content of proteins, oil, vitamins, minerals, and micro-nutrients in crops. It is also undertaken to upgrade the quality of oil and proteins. An example of this is a wheat variety known as ...
Read More →Briefly describe various steps involved in plant breeding.
Question: Briefly describe various steps involved in plant breeding. Solution: Plant breeding is the process in which two genetically dissimilar varieties are purposely crossed to produce a new hybrid variety. As a result, characteristics from both parents can be obtained in the hybrid plant variety. Thus, it involves the production of a new variety with the desired characteristics such as resistance to diseases, climatic adaptability, and better productivity. The various steps involved in plant...
Read More →Discuss the role of fishery in enhancement of food production.
Question: Discuss the role of fishery in enhancement of food production. Solution: Fishery is an industry which deals with catching, processing, and marketing of fishes and other aquatic animals that have a high economic value. Some commercially important aquatic animals are prawns crabs, oysters, lobsters, and octopus. Fisheries play an important role in the Indian economy. This is because a large part of the Indian population is dependent on fishes as a source of food, which is both cheap and ...
Read More →Find :
Question: Find $\frac{d y}{d x}$ $y=\sin ^{-1}\left(2 x \sqrt{1-x^{2}}\right),-\frac{1}{\sqrt{2}}x\frac{1}{\sqrt{2}}$ Solution: The given relationship is $y=\sin ^{-1}\left(2 x \sqrt{1-x^{2}}\right)$ $y=\sin ^{-1}\left(2 x \sqrt{1-x^{2}}\right)$ $\Rightarrow \sin y=2 x \sqrt{1-x^{2}}$ Differentiating this relationship with respect tox, we obtain $\cos y \frac{d y}{d x}=2\left[x \frac{d}{d x}\left(\sqrt{1-x^{2}}\right)+\sqrt{1-x^{2}} \frac{d x}{d x}\right]$ $\Rightarrow \sqrt{1-\sin ^{2} y} \frac...
Read More →Find the LCM and HCF of the following pairs of integers and verify that
Question: Find the LCM and HCF of the following pairs of integers and verify that LCM HCF = Product of the integers: (i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54 Solution: TO FIND: LCM and HCF of following pairs of integers TO VERIFY: L.C.M $\times$ H.C.F $=$ product of the numbers (i) 26 and 91 Let us first find the factors of 26 and 91 $26=2 \times 13$ $91=7 \times 13$ L.C.M of 26 , and $91=2 \times 7 \times 13$ L.C.M of 26, and $91=182$ H.C.F of 26, and $91=13$ We know that, L. C. $M \times...
Read More →In what ratio, the line joining (–1, 1) and (5, 7)
Question: In what ratio, the line joining (1, 1) and (5, 7) is divided by the line x+y= 4? Solution: The equation of the line joining the points (1, 1) and (5, 7) is given by $y-1=\frac{7-1}{5+1}(x+1)$ $y-1=\frac{6}{6}(x+1)$ $x-y+2=0$ $\ldots(1)$ The equation of the given line is x+y 4 = 0 (2) The point of intersection of lines (1) and (2) is given by x= 1 andy= 3 Let point (1, 3) divide the line segment joining (1, 1) and (5, 7) in the ratio 1:k. Accordingly, by section formula, $(1,3)=\left(\f...
Read More →Find the LCM and HCF of the following pairs of integers and verify that
Question: Find the LCM and HCF of the following pairs of integers and verify that LCM HCF = Product of the integers: (i) 26 and 91 (ii) 510 and 92 (iii) 336 and 54 Solution: TO FIND: LCM and HCF of following pairs of integers TO VERIFY: L.C.M $\times$ H.C.F $=$ product of the numbers (i) 26 and 91 Let us first find the factors of 26 and 91 $26=2 \times 13$ $91=7 \times 13$ L.C.M of 26 , and $91=2 \times 7 \times 13$ L.C.M of 26, and $91=182$ H.C.F of 26, and $91=13$ We know that, L. C. $M \times...
Read More →What is apiculture? How is it important in our lives?
Question: What is apiculture? How is it important in our lives? Solution: Apiculture is the practice of bee-keeping for the production of various products such as honey, bees wax, etc. Honey is a highly nutritious food source and is used as an indigenous system of medicines. It is useful in the treatment of many disorders such as cold, flu, and dysentery. Other commercial products obtained from honey bees include bees wax and bee pollen. Bees wax is used for making cosmetics, polishes, and is ev...
Read More →Name the methods employed in animal breeding
Question: Name the methods employed in animal breeding. According to you which one of the methods is best? Why? Solution: Animal breeding is the method of mating closely related individuals. There are several methods employed in animals breeding, which can be classified into the following categories: (A)Natural methods of breeding include inbreeding and out-breeding. Breeding between animals of the same breed is known as inbreeding, while breeding between animals of different breeds is known as ...
Read More →What is meant by the term ‘breed’?
Question: What is meant by the term breed? What are the objectives of animal breeding? Solution: A breed is a special variety of animals within a species. It is similar in most characters such as general appearance, size, configuration, and features with other members of the same species. Jersey and Brown Swiss are examples of foreign breeds of cattle. These two varieties of cattle have the ability to produce abundant quantities of milk. This milk is very nutritious with high protein content. Ob...
Read More →If your family owned a dairy farm, what measures would you undertake to improve the quality and quantity of milk production?
Question: If your family owned a dairy farm, what measures would you undertake to improve the quality and quantity of milk production? Solution: Dairy farm management deals with processes which aim at improving the quality and quantity of milk production. Milk production is primarily dependent on choosing improved cattle breeds, provision of proper feed for cattle, maintaining proper shelter facilities, and regular cleaning of cattle. Choosing improved cattle breeds is an important factor of cat...
Read More →Show that the equation of the line passing through the origin and making
Question: Show that the equation of the line passing through the origin and makingan angle $\theta w i t h$ the line $y=m x+c$ is $\frac{y}{x}=\frac{m \pm \tan \theta}{1 \mp m \tan \theta}$. Solution: Let the equation of the line passing through the origin be $y=m_{1} x$. If this line makes an angle of $\theta$ with line $y=m x+c$, then angle $\theta$ is given by $\therefore \tan \theta=\left|\frac{\mathrm{m}_{1}-\mathrm{m}}{1+\mathrm{m}_{1} \mathrm{~m}}\right|$ $\Rightarrow \tan \theta=\left|\f...
Read More →Check whether
Question: Check whether 6ncan end with the digit 0 for any natural numbern. Solution: TO CHECK: Whether $6^{n}$ can end with the digit 0 for any natural number $\mathrm{n}$. We know that $6^{n}=(2 \times 3)^{n}$ $6^{n}=2^{n} \times 3^{n}$ Therefore, prime factorization of $6^{n}$ does not contain 5 and 2 as a factor together. Hence $6^{n}$ can never end with the digit 0 for any natural number $n$...
Read More →Explain in brief the role of animal husbandry in human welfare.
Question: Explain in brief the role of animal husbandry in human welfare. Solution: Animal husbandry deals with the scientific management of livestock. It includes various aspects such as feeding, breeding, and control diseases to raise the population of animal livestock. Animal husbandry usually includes animals such as cattle, pig, sheep, poultry, and fish which are useful for humans in various ways. These animals are managed for the production of commercially important products such as milk, ...
Read More →Find
Question: Find $\frac{d y}{d x}$ : $y=\cos ^{-1}\left(\frac{2 x}{1+x^{2}}\right),-1x1$ Solution: The given relationship is $y=\cos ^{-1}\left(\frac{2 x}{1+x^{2}}\right)$ $y=\cos ^{-1}\left(\frac{2 x}{1+x^{2}}\right)$ $\Rightarrow \cos y=\frac{2 x}{1+x^{2}}$ Differentiating this relationship with respect tox, we obtain $\frac{d}{d x}(\cos y)=\frac{d}{d x} \cdot\left(\frac{2 x}{1+x^{2}}\right)$' $\Rightarrow-\sin y \cdot \frac{d y}{d x}=\frac{\left(1+x^{2}\right) \cdot \frac{d}{d x}(2 x)-2 x \cdot...
Read More →Explain why
Question: Explain why 7 11 13 + 13 and 7 6 5 4 3 2 1 + 5 are composite numbers. Solution: EXPLAIN: Why $7 \times 11 \times 13+13$ and $7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1+5$ are composite numbers We can see that both the numbers have common factor 7 and 1. $7 \times 11 \times 13+13=(77+1) \times 13$ $=78 \times 13$ $7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1+5=(7 \times 6 \times 4 \times 3 \times 2+1) \times 5$ $=1008 \times 5$ And we know that composite numbers ...
Read More →