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Simplify: (ab + bc)²– 2ab²c

Answer: a2b2 + b2c2 Using the identities (a + b) 2 = a2 + b2 + 2ab (a - b) 2 = a2 + b2 - 2ab Consider (ab + bc)2 Using identity (a + b) 2 = a2... View Article

Simplify: (m² – n²m)² + 2m³n²

Answer: m4 + n4m2 Using the identities (a + b) 2 = a2 + b2 + 2ab (a - b) 2 = a2 + b2 - 2ab Consider (m2 - n2m)2 Using identity (a - b) 2 = a2 +... View Article

Simplify: (t + s²)(t² – s)

Answer: t3 - s3 - st + s2t2 (t + s2) × (t2 - s) =t × (t2 – s)+s2 × (t2 - s) = (t × t2) - (t × s) + (s2... View Article

Simplify: (x + y)(2x + y) + (x + 2y)(x – y)

Answer: 3x2 - y2 + 4xy (x + y) × (2x + y) + (x + 2y) × (x - y) Consider (x + y) × (2x + y) (x + y) × (2x + y) = x... View Article

Simplify: (x + y)(x² – xy + y²)

Answer: x3 + y3 (x + y) × (x2- xy + y2) = x × (x2- xy + y2) + y × (x2- xy + y2) = (x × x2) - (x × xy) + (x... View Article

Simplify: (x² – 5) (x + 5) + 25

Answer: x3 + 5x2 - 5x (x2 - 5) × (x + 5) + 25 = [x2 × (x + 5) - 5(x + 5)] + 25 = [(x2 × x) + (x2 × 5) - (5× x) -... View Article

Small amount of a mineral salt present naturally in water makes it a______________ of electricity.

Answer: A small amount of a mineral salt present naturally in water makes it a conductor of electricity. Electrical conductor is defined as... View Article

Sometimes, a crackling sound is heard while taking off a sweater during winters. Explain.

Answer: Wool, which is a poor conductor of electricity, is used to make sweaters. When we wear the sweater, the wool comes into contact with our... View Article

Soni says that the acceleration in an object could be zero even when several forces are acting on it. Do you agree with her? Why?

Answer: Acceleration is defined as the rate of change of velocity with respect to time. Acceleration is a vector quantity as it has both... View Article

State two experiences that made you think that air exerts pressure

Answer: The molecules of several gases make up air. The molecules are constantly interacting with each other and with the container's walls.... View Article

State whether the following are true or false. Justify your answer. (i) sin (A + B) = sin A + sin B. (ii) The value of sin θ increases as θ increases.

Answer: Answer: False Sin Values sin 0° = √(0/4) = 0 sin 30° = √(1/4) = 1/2 sin 45° = √(2/4) = 1/√2 sin... View Article

State whether the following are true or false. Justify your answer. (i) The value of cos θ increases as θ increases. (ii) sin θ = cos θ for all values of θ. (ii) cot A is not defined for A = 0°.

Answer: Answer: False According to the values obtained as per the unit circle, the values of cos are: Cos value cos 0° = 1 cos 30°... View Article

State whether the following are true or false. Justify your answer. (i) The value of tan A is always less than 1. (ii) sec A = 12/5 for some value of angle A. (iii) cos A is the abbreviation used for the cosecant of angle A. (iv) cot A is the product of cot and A. (v) sin θ = 4/3 for some angle θ.

Answer: Answer: False Proof: In ΔMNC in which ∠N = 90∘ MN = 3 NC = 4 MC = 5 Value of tan M = 4/3 which is greater than 1. The... View Article

State whether the following statement is true or false. Justify your answer. sec A = 12/5 for some value of angle A.

Answer: True Proof: Let a ΔMNC in which ∠N = 90º MC=12k MB=5k Where k is a positive real number. By Pythagoras theorem we get,... View Article

State whether the following statement is true or false. Justify your answer. The value of tan A is always less than 1.

Answer: False Proof: In ΔMNC in which ∠N = 90∘ MN = 3 NC = 4 MC = 5 Value of tan M = 4/3 which is greater than 1. The triangle can be... View Article

State whether the following statements are true or false. In case a statement is false, write the corrected statement in your notebook. (a) Cutting a log of wood into pieces is a chemical change. (True/False) (b) Formation of manure from leaves is a physical change. (True/False) (c) Iron pipes coated with zinc do not get rusted easily. (True/False) (d) Iron and rust are the same substances. (True/False) (e) Condensation of steam is not a chemical change. (True/False)

Answer: Physical change - A substance is said to undergo a physical change when only the physical properties such as the shape, size, color,... View Article

State whether the following statements are true or false. Justify your answer. (i) cos A is the abbreviation used for the cosecant of angle A. (ii) cot A is the product of cot and A. (iii) sin θ = 4/3 for some angle θ.

Answer: Answer: False Justification: Abbreviation used for cosecant of angle M is cosec M. cos M is the abbreviation used for cosine of angle... View Article

Study the following statements about ozone: (a) It is essential for breathing of living organisms. (b) It is used to disinfect water. (c) It absorbs ultraviolet rays. (d) Its proportion in air is about 3%. Which of these statements are correct? (i) (a), (b) and (c) (ii) (b) and (c) (iii) (a) and (d) (iv) All four

Answer: (ii) (b) and (c) Ozone (O3) an unstable, blue, diamagnetic gas with a characteristic pungent odor, protects the earth and its inhabitants... View Article

Substituting x = – 3 in (1) x² + 5x + 4 gives (– 3)² + 5(-3) + 4 = 9 + 2 + 4 = 15 (2) x ² – 5x + 4 gives (-3) ² – 5(-3) + 4 = 9 – 15 + 4 = -2 (3)x² + 5x gives (-3) ² + 5(-3) = -9 -15 = -24

Answer: Put x = -3 x2 + 5x + 4 ⇒ (-3) 2 + 5(-3) + 4 ⇒ 9 - 15 + 4 ⇒ -2 x2 + 5x + 4 = -2 This is the correct answer Substituting... View Article

Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz

Answer: 2xy - 7yz + 5zx + 10xyz (5xy - 2yz - 2zx + 10xyz) - (3xy + 5yz - 7zx) (5xy - 2yz - 2zx + 10xyz) - (3xy + 5yz - 7zx) = 5xy - 2yz - 2zx +... View Article

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