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🔰 Role of nutrients and their deficiency Symptoms 🔰 #Nitrogen ▪️Impart green colour to plant encourages vegetative growth ▪️ Nitrogen is essential constituent of protein ▪️ Constituent of Protoplasm of chlorophyll and coenzyme. ▪️ Play important role in synthesis of auxin #Deficiency ▪️ Lower leaves become yellow and dries. ▪️V shaped chlorosis on older leaves or yellowing at tip. #Disease ▪️Starvation disease due to nitrogen deficiency. ▪️Buttoning in cauliflower. #Phosphorous ▪️Increase the disease resistance. ▪️ Enhance new cell formation and necessary for root development. ▪️Required for grain formation and maturity of grains. ▪️Phosphorus is essential constituent for nucleic acid and phytin. ▪️Most essential functions are energy storage and transfer energy act as "energy currency". #Deficiency ▪️Due to deficiency of single element the life cycle of plant can't be completed hence (Agricultureexamslibrary) Phosphorus is called " key of life " ▪️Deficiency imparts dark green colour in leaves. ▪️Later develops red purple colourration. #Disease ▪️Sickle leaf diseases. #Potassium ▪️Most essential function of K+ is stomata regulation. ▪️Provides disease resistance in plants. ▪️Cofactor for enzymes. ▪️Formation and translocation of Sugars. ▪️Helps in chlorophyll formation. #Deficiency ▪️Spot of dead tissue at tips. ▪️Scorching and burning on margins of autumn leaves. #Disease ▪️Rottle/ dieback disease. #Calcium ▪️ It is constituent of cell wall ▪️ Calcium is a mobile in plants and deficiency symptoms appear on Meristem tip portion. # Deficiency ▪️ Terminal bud die #Disease ▪️Tip hooking. ▪️ Blossom end rot of tomato(BER). ▪️Popping in groundnut. #Magnesium ▪️ Essential constituent of chlorophyll. ▪️ Magnesium is a constituent of chlorophyll. ▪️Chlorosis between veins. #Disease ▪️Sand -drown disease of tobacco. #Sulphur ▪️ Sulphur oxidizing Bacteria is Thiobacillus. ▪️Sulphur is essential for oil seed and pulses because it improves oil content and protein content in oil seeds and pulses, respectively. #Disease ▪️Akiochi disease of rice due to Excess of hydrogen sulphide. ▪️Tea yellow disease of tea. #Iron ▪️Fe is the component of nitrate reductase. ▪️Required for nitrogen fixation. ▪️During respiration act as O2 carrier. #Deficiency ▪️Interveinal complete chlorosis. ▪️Scorching of leaf margin. ▪️Yellowing of iron chlorosis in groundnut. #Manganese ▪️Formation of chlorophyll. ▪️Co-factor of enzyme. ▪️Mn toxicity causes crinckle leaf of cotton. #Deficiency ▪️Dead spot on leaves. #Desease ▪️Marsh spot of pea. ▪️Pahala blight of sugarcane. #Copper @agricultureexams2020 ▪️Compound of plastocyanin. ▪Essential for photosynthesis/ respiration.Agriexams library ▪️Dieback and reclamation disease of cereals. #Boron ▪ Necessary for Pollen germination. ▪️Boron is the only non-metal element among the micronutrient. ▪️It is necessary for translocation of Sugars and is involved in reproduction and germination of pollen. #Disease : due to deficiency ▪️Browning of cauliflower is caused by Boron deficiency. ▪️Top sickness of tobacco. ▪️Fruit cracking of tomato. ▪️Hard fruit of citrus. ▪️Hen and chick disease of grape. #Zinc ▪️In plants it is required for biosynthesis of hormones. ▪️Zn deficiency causes- -White bud of maize. -Khaira disease of rice. -Little leaf of cotton. -Mottled leaf of citrus. -Rosette formation. #Cobalt ▪️It is component of Vitamin B ▪️It is essential for formation of type of hemoglobin in N-fixing nodule tissue known as leghaemogloin. ▪️Act as O2 carrier in roots. ▪️Also known as animal protein factor. #Molybdenum ▪️Mo: absorbed as molybdate MoO4-2 forms. ▪️Mo is important component of enzyme: Nitrate reductage. ▪️N-fixation in pulses. ▪️Whiptail of cauliflower is due to deficiency of Mo. ▪️Mo is required for carrot & raphanus for sweetness.

📚Notes on Trigonometric Equations and Identities📚 A function f(x) is said to be periodic if there exists some T > 0 such that f(x+T) = f(x) for all x in the domain of f(x). In case, the T in the definition of period of f(x) is the smallest positive real number then this ‘T’ is called the period of f(x). Periods of various trigonometric functions are listed below: 1) sin x has period 2π 2) cos x has period 2π 3) tan x has period π 4) sin(ax+b), cos (ax+b), sec(ax+b), cosec (ax+b) all are of period 2π/a 5) tan (ax+b) and cot (ax+b) have π/a as their period 6) |sin (ax+b)|, |cos (ax+b)|, |sec(ax+b)|, |cosec (ax+b)| all are of period π/a 7) |tan (ax+b)| and |cot (ax+b)| have π/2a as their period ➖Sum and Difference Formulae of Trigonometric Ratios 1) sin(a + ß) = sin(a)cos(ß) + cos(a)sin(ß) 2) sin(a – ß) = sin(a)cos(ß) – cos(a)sin(ß) 3) cos(a + ß) = cos(a)cos(ß) – sin(a)sin(ß) 4) cos(a – ß) = cos(a)cos(ß) + sin(a)sin(ß) 5) tan(a + ß) = [tan(a) + tan (ß)]/ [1 - tan(a)tan (ß)] 6)tan(a - ß) = [tan(a) - tan (ß)]/ [1 + tan (a) tan (ß)] 7) tan (π/4 + θ) = (1 + tan θ)/(1 - tan θ) 8) tan (π/4 - θ) = (1 - tan θ)/(1 + tan θ) 9) cot (a + ß) = [cot(a) . cot (ß) - 1]/ [cot (a) +cot (ß)] 10) cot (a - ß) = [cot(a) . cot (ß) + 1]/ [cot (ß) - cot (a)] ➖Double or Triple -Angle Identities 1) sin 2x = 2sin x cos x 2) cos2x = cos2x – sin2x = 1 – 2sin2x = 2cos2x – 1 3) tan 2x = 2 tan x / (1-tan 2x) 4) sin 3x = 3 sin x – 4 sin3x 5) cos3x = 4 cos3x – 3 cosx 6) tan 3x = (3 tan x - tan3x) / (1- 3tan 2x) ➖For angles A, B and C, we have 1) sin (A + B +C) = sinAcosBcosC + cosAsinBcosC + cosAcosBsinC - sinAsinBsinC 2) cos (A + B +C) = cosAcosBcosC- cosAsinBsinC - sinAcosBsinC - sinAsinBcosC 3) tan (A + B +C) = [tan A + tan B + tan C –tan A tan B tan C]/ [1- tan Atan B - tan B tan C –tan A tan C 4) cot (A + B +C) = [cot A cot B cot C – cotA - cot B - cot C]/ [cot A cot B + cot Bcot C + cot A cotC–1] ➖List of some other trigonometric formulas: 1) 2sinAcosB = sin(A + B) + sin (A - B) 2) 2cosAsinB = sin(A + B) - sin (A - B) 3) 2cosAcosB = cos(A + B) + cos(A - B) 4) 2sinAsinB = cos(A - B) - cos (A + B) 5) sin A + sin B = 2 sin [(A+B)/2] cos [(A-B)/2] 6) sin A - sin B = 2 sin [(A-B)/2] cos [(A+B)/2] 7) cosA + cos B = 2 cos [(A+B)/2] cos [(A-B)/2] 8) cosA - cos B = 2 sin [(A+B)/2] sin [(B-A)/2] 9) tanA ± tanB = sin (A ± B)/ cos A cos B 10)cot A ± cot B = sin (B ± A)/ sin A sin B ➖Method of solving a trigonometric equation: 1) If possible, reduce the equation in terms of any one variable, preferably x. Then solve the equation as you used to in case of a single variable. 2) Try to derive the linear/algebraic simultaneous equations from the given trigonometric equations and solve them as algebraic simultaneous equations. 3) At times, you might be required to make certain substitutions. It would be beneficial when the system has only two trigonometric functions. ➖Some results which are useful for solving trigonometric equations: 1) sin θ = sina and cosθ = cosa ⇒ θ = 2nπ + a 2) sin θ = 0 ⇒ θ = nπ 3) cosθ = 0 ⇒ θ = (2n + 1)π/2 4) tan θ = 0 ⇒ θ = nπ 5) sinθ = sina⇒ θ = nπ + (-1)na where a ∈ [–π/2, π/2] 6) cosθ= cos a ⇒ θ = 2nπ ± a, where a ∈[0,π] 7) tanθ = tana⇒ θ = nπ+ a, where a ∈[–π/2, π/2] 8) sinθ = 1 ⇒ θ= (4n + 1)π/2 9) sin θ = -1 ⇒ θ = (4n - 1) π /2 10) sin θ = -1 ⇒ θ = (2n +1) π /2 11) |sinθ| = 1⇒ θ =2nπ 12) cosθ = 1 ⇒ θ =(2n + 1) 13) |cosθ| = 1⇒ θ =nπ Credit - @DCPANDEYBOOKFREE @IRODOV_dc_pandey