Simplify: (ab + bc)2– 2ab2c
Answer: a2b2 + b2c2 Using the identities (a + b) 2 = a2 + b2 + 2ab (a – b)... View Article
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Simplify: (m2 – n2m)2 + 2m3n2
Answer: m4 + n4m2 Using the identities (a + b) 2 = a2 + b2 + 2ab (a – b)... View Article
Simplify: (t + s2)(t2 – s)
Answer: t3 – s3 – st + s2t2 (t + s2)(t2 – s) (t + s2) × (t2 – s)... View Article
Simplify: (x + y)(2x + y) + (x + 2y)(x – y)
Answer: 3x2 – y2 + 4xy (x + y)(2x + y) + (x + 2y)(x – y) (x + y)... View Article
Simplify: (x + y)(x2 – xy + y2)
Answer: x3 + y3 (x + y)(x2– xy + y2) (x + y) × (x2– xy + y2) = x... View Article
Simplify: (x2 – 5) (x + 5) + 25
Answer: x3 + 5x2 – 5x (x2 – 5)(x + 5) + 25 (x2 – 5) × (x + 5)... 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... 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... 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... 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... 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: (i) sin (A + B) = sin A + sin B Answer: False Sin Values sin 0° = √(0/4)... 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: (i) The value of cos θ increases as θ increases. Answer: False According to the values obtained as per... 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: (i) The value of tan A is always less than 1. Answer: False Proof: In ΔMNC in which ∠N... 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.... 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... 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... 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: (i) cos A is the abbreviation used for the cosecant of angle A. Answer: False Justification: Abbreviation used for... 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... 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: (1) x2 + 5x + 4 Put x = -3 x2 + 5x + 4 ⇒ (-3) 2 +... View Article
Subtract 3xy + 5yz – 7zx from 5xy – 2yz – 2zx + 10xyz
Answer: 2xy – 7yz + 5zx + 10xyz 3xy + 5yz – 7zx from 5xy – 2yz – 2zx +... View Article
