The coordinates of the point on the ellipse
Question: The coordinates of the point on the ellipse $16 x^{2}+9 y^{2}=400$ where the ordinate decreases at the same rate at which the abscissa increases, are (a) (3, 16/3)(b) (3, 16/3)(c) (3, 16/3)(d) (3, 3) Solution: (a) (3, 16/3) According to the question, $\frac{d y}{d t}=\frac{-d x}{d t}$ $16 x^{2}+9 y^{2}=400$ $\Rightarrow 32 x \frac{d x}{d t}+18 y \frac{d y}{d t}=0$ $\Rightarrow 32 x \frac{d x}{d t}=-18 y \frac{d y}{d t}$ $\Rightarrow 32 x=18 y$ $\Rightarrow x=\frac{9 y}{16}$ .....(1) No...
Read More →Which activity of the farmer can promote
Question: Which activity of the farmer can promote growth of earthworms and microbes in the field? Solution: Ploughing of the soil during soil preparation creates spaces in the soil thus, leading to aeration and the soil also loosens which promotes the growth and survival of earthworms and microbes and release of nutrients in the soil...
Read More →During which months do farmers
Question: During which months do farmers grow mustard in India? Solution: Farmers grow mustard during the months from October-March. Mustard is a rabi crop that is sown in beginning of winters (October-November) as they need low temperature and harvested at the end of winter (April-May)....
Read More →The coordinates of the point on the ellipse
Question: The coordinates of the point on the ellipse $16 x^{2}+9 y^{2}=400$ where the ordinate decreases at the same rate at which the abscissa increases, are (a) (3, 16/3)(b) (3, 16/3)(c) (3, 16/3)(d) (3, 3) Solution: (a) (3, 16/3) According to the question, $\frac{d y}{d t}=\frac{-d x}{d t}$ $16 x^{2}+9 y^{2}=400$ $\Rightarrow 32 x \frac{d x}{d t}+18 y \frac{d y}{d t}=0$ $\Rightarrow 32 x \frac{d x}{d t}=-18 y \frac{d y}{d t}$ $\Rightarrow 32 x=18 y$ $\Rightarrow x=\frac{9 y}{16}$ .....(1) No...
Read More →State whether the following statements are True/False
Question: State whether the following statements are True/False Using good quality seed is the only criterion to get high yield. Growing different crops in different seasons in the same field will deplete the soil of nutrients. Ail crop plants are sown as seeds in the field. Cells of root nodules of leguminous plants fix nitrogen. Freshly harvested grains must be dried before shoring. Solution: False, apart from good quality seeds, using appropriate agricultural practices are important for getti...
Read More →If you are given a dry piece of land for cultivation,
Question: If you are given a dry piece of land for cultivation, what will you do before sowing the seeds? Solution: If the field is dry for cultivation of crops, the soil preparation is done accordingly before sowing of crops. Preparation of dry soil includes adequate watering to restore the moisture content and then tilled and ploughed to allow growth of microbes and aeration, Finally, the soil is turned and its crumbs are levelled and manures are mixed. The soil is ready for sowing of crops in...
Read More →Pick out the odd one from the following words
Question: Pick out the odd one from the following words given in the box and give reason for it.Plough, Seed drill, Hoe, Chain pump. Sickle Solution: Seed drill is the odd one in the above given set of tools as it is a modern agricultural tool used to sow seeds at uniform distances and to properly cover them with soil. Rest of the tools, i.e. plough (used for tilling), hoe (for removal of weeds and loosening of soil), chain pump (irrigation method) and sickle (tool for removing weeds) are all tr...
Read More →The system of irrigation where water is supplied
Question: The system of irrigation where water is supplied drop by drop near the roots of plants, is called (a) pulley system (b) drip system (c) sprinkler system (d) lever system Solution: (b) Drip system is the method of irrigation which conserves water and avoids wastage as water is made to fall drop by drop at the position of roots. It is best technique for watering fruit plants, trees and gardens. Sprinkler system is also a modern method of irrigation that efficiently uses water in the form...
Read More →The monsoon season in our country
Question: The monsoon season in our country is during the months (a) April-December (b) June-September (c) November-March (d) January-May Solution: (b) The monsoon season in India is during the months June to September, The crops grown in this season are called kharif crop, e.g. paddy, maize, cotton, etc. The kharif crops sown in June are harvested towards the end of rainy season (October-November)....
Read More →For what values of x is the rate of increase
Question: For what values of $x$ is the rate of increase of $x^{3}-5 x^{2}+5 x+8$ is twice the rate of increase of $x ?$ (a) $-3,-\frac{1}{3}$ (b) $-3, \frac{1}{3}$ (c) $3,-\frac{1}{3}$ (d) $3, \frac{1}{3}$ Solution: (d) $3, \frac{1}{3}$ Let $y=x^{3}-5 x^{2}+5 x+8$ $\Rightarrow \frac{d y}{d t}=\left(3 x^{2}-10 x+5\right) \frac{d x}{d t}$ According to the question, $\Rightarrow 2 \frac{d x}{d t}=\left(3 x^{2}-10 x+5\right) \frac{d x}{d t}$ $\Rightarrow 3 x^{2}-10 x+5=2$ $\Rightarrow 3 x^{2}-10 x+...
Read More →The process of loosening and turning of soil is called
Question: The process of loosening and turning of soil is called (a) irrigation and manuring (b) digging and winnowing (c) tilling and ploughing (d) harvesting and storage Solution: (c) The process of loosening and turning of soil is called tilling and ploughing . It is the first step in preparation of soil for cultivation of crop. Ploughing is done using a plough, made of wood or iron....
Read More →If the (p + q)th and (p – q)th terms of a GP are m and n respectively,
Question: If the (p + q)th and (p q)th terms of a GP are m and n respectively, find its pth term. Solution: Let, $t_{p+q}=m=A r^{p+q-1}=A r^{p-1} r^{q}$ And $t_{p-q}=n=A r^{p-q-1}=A r^{p-1} r^{-q}$ We know that $\mathrm{p}^{\text {th }}$ term $=\mathrm{Ar}^{\mathrm{p}-1}$ $\therefore m \times n=A^{2} r^{2 p-2}$ $\Rightarrow \mathrm{Ar}^{\mathrm{p}-1}=(\mathrm{mn})^{1 / 2}$ $\Rightarrow \mathrm{p}^{\text {th }}$ term $=(\mathrm{mn})^{1 / 2}$ Ans: $p^{\text {th }}$ term $=(m n)^{1 / 2}$...
Read More →Given below are statements about the harmful effects
Question: Given below are statements about the harmful effects of weeds on crop plants. They interfere in harvesting. They help crop plants to grow healthily. They compete with crop plants for water, nutrients, space and light. They affect the plant growth. (a) (1), (3) and (4) (b) Only (3) (c) (3) and (4) (d) (1), (2), (3) and (4) Solution: (a) Statements (1), (3) and (4) are correctly suggesting the harmful effects of weeds. Weeds are the undesirable plants that grow along the main crops. Remo...
Read More →Which of the following is not true for fertilisers?
Question: Which of the following is not true for fertilisers? (a) They increase the yield (b) Their excessive use disturbs the balance of nutrients in soil (c) They are generally used in small quantity (d) They are environment friendly Solution: (d) Fertilisers are not environment friendly as they are chemical substances rich in particular nutrient, Though, they increase the crop yield, the repeated and excessive use of fertilisers in the same field reduces the soil fertility, It also pollutes w...
Read More →The altitude of a cone is 20 cm
Question: The altitude of a cone is 20 cm and its semi-vertical angle is 30. If the semi-vertical angle is increasing at the rate of 2 per second, then the radius of the base is increasing at the rate of (a) $30 \mathrm{~cm} / \mathrm{sec}$ (b) $\frac{160}{3} \mathrm{~cm} / \mathrm{sec}$ (c) $10 \mathrm{~cm} / \mathrm{sec}$ (d) $160 \mathrm{~cm} / \mathrm{sec}$ Solution: (b) $\frac{160}{3} \mathrm{~cm} / \mathrm{sec}$ Let $r$ be the radius, $h$ be the height and $\alpha$ be the semi $-$ vertical...
Read More →Which of the following tools would
Question: Which of the following tools would a farmer use to remove weeds from the field? (a) Hoe (b) Plough (c) Axe (d) Cultivator Solution: (a) Hoe is a simple tool used for removing weeds from the field and loosening of soil, it works like a blade, pulled by the animals In the field. Plough is used for tilling of soil, axe is used for cutting trees and cultivator is another tool implemented for ploughing,...
Read More →The altitude of a cone is 20 cm
Question: The altitude of a cone is 20 cm and its semi-vertical angle is 30. If the semi-vertical angle is increasing at the rate of 2 per second, then the radius of the base is increasing at the rate of (a) $30 \mathrm{~cm} / \mathrm{sec}$ (b) $\frac{160}{3} \mathrm{~cm} / \mathrm{sec}$ (c) $10 \mathrm{~cm} / \mathrm{sec}$ (d) $160 \mathrm{~cm} / \mathrm{sec}$ Solution: (b) $\frac{160}{3} \mathrm{~cm} / \mathrm{sec}$ Let $r$ be the radius, $h$ be the height and $\alpha$ be the semi $-$ vertical...
Read More →Read the statements given below.
Question: Read the statements given below. Seeds require moisture for germination. Plants can absorb nutrients mostly in dissolved form. Irrigation protects crops from both frost and hot air currents. Irrigation improves soil texture. Choose combination of statements which indicate need to irrigate crops. (a) (1) and (2) (b) (1), (2) and (3) (c) (1), (2), (3) and(4)-, (d) (1) and (3) Solution: (a) The combination of statements (1) and (2) indicate need for irrigation. Irrigation is the supply of...
Read More →The term used for the process of separation
Question: The term used for the process of separation of grains from chaff is (a) sieving (b) winnowing (c) threshing (d) hand picking Solution: (c) The process of separating the edible part of the harvested grains (crop) by loosening and removing the scaly, inedible chaff surrounding the grain. The process utilises a machine called combine which is a combination of harvester and a thresher....
Read More →Which of the following statements
Question: Which of the following statements is not true for organic manure? (a) It enhances water holding capacity of soil (b) It has a balance of all plant nutrients (c) It provides humus to soil (d) It improves texture of soil Solution: (b) Organic manures are obtained from decomposition of plant and animal wastes that are rich in nutrients and humus. But all nutrients might not be present in a proportionate amount in it, thus will not solve : the problem if soil is particularly deficient in o...
Read More →Propagation of ginger is generally
Question: Propagation of ginger is generally done using (a) seed (b) stem (rhizome) (c) root (d) leaf Solution: (b) The ginger is a modified underground stem, which is propagated vegetatively by stem (rhizome) cultivation. It does not propagate by roots, leaves or seeds....
Read More →Which one of the following conditions
Question: Which one of the following conditions is not essential to grow maize? (a) High temperature (b) Humidity (c) Low temperature (d) Rainfall Solution: (c) Maize is a kharif crop, which requires high temperature, rainfall and humidity to grow, while rabi crops require low temperature for their growth,...
Read More →If the 5th term of a GP is 2, find the product of its first nine terms.
Question: If the $\mathbf{5}^{\text {th }}$ term of a GP is 2, find the product of its first nine terms. Solution: Given: $5^{\text {th }}$ term of a GP is $2 .$ To find: the product of its first nine terms. First term is denoted by a, the common ratio is denote by r. $\therefore a r^{4}=2$ We have to find the value of: $a \times a r^{1} \times a r^{2} \times a r^{3} \times \ldots \times a r^{8}$ $=a^{9} r^{1+2+3+4+\ldots+8}$ $=a^{9} r^{36}$ $=\left(a r^{4}\right)^{9}$ $=(2)^{9}$ $=512$ Ans: 512...
Read More →The distance moved by the particle in time
Question: The distance moved by the particle in time $t$ is given by $x=t^{3}-12 t^{2}+6 t+8$. At the instant when its acceleration is zero, the velocity is (a) 42 (b) $-42$ (c) 48 (d) $-48$ Solution: (b) $-42$ $x=t^{3}-12 t^{2}+6 t+8$ $\Rightarrow \frac{d x}{d t}=3 t^{2}-24 t+6$ $\Rightarrow \frac{d^{2} x}{d t^{2}}=6 t-24$ $\Rightarrow 6 t-24=0 \quad[\because$ acceleration is zero $]$ $\Rightarrow t=4$ $\mathrm{So}$, Velocity at $t=4$ $\Rightarrow \frac{d x}{d t}=3(4)^{2}-24 \times 4+6$ $\Right...
Read More →The sum of an infinite GP is 57, and the sum of their cubes is 9747.
Question: The sum of an infinite GP is 57, and the sum of their cubes is 9747. Find the GP. Solution: Let the first term Of G.P. be a, and common ratio be r. $\frac{\mathrm{a}}{\therefore 1-\mathrm{r}}=57 \ldots$ (1) On cubing each term will become, $a^{3,} a^{3} r^{3}, \ldots$ $\therefore$ This sum $=\frac{\mathrm{a}^{3}}{1-\mathrm{r}^{3}}=9747 \ldots$ (2) a=57(1-r) put this in equation 2 we get $\frac{(57 \times(1-r))^{3}}{1-r^{3}}=9747$ $\Rightarrow \frac{57^{3} \times(1-r)^{3}}{1-r^{3}}=9747...
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