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Two methods by which rusting of iron can be prevented are _ and _.

Answer: Two methods by which rusting of iron can be prevented are painting and galvanization. Rusting of iron refers to the formation of rust, a... View Article

Two mirrors A and B are placed at right angles to each other as shown in Fig.. A ray of light incident on mirror A at an angle of 250 falls on mirror B after reflection. The angle of reflection for the ray reflected from mirror B would be (a) 250 (b) 500 (c) 650 (d) 1150

Answer: (c) 650 In case of a plane mirror the ray of light after reflection follows the laws of reflection. The first law of reflection states... View Article

Two objects repel each other. This repulsion could be due to (a) frictional force only (b) electrostatic force only (c) magnetic force only (d) either a magnetic or an electrostatic force

Answer: (d) either a magnetic or an electrostatic force When there is a repulsive force between two objects, it could be due to an electrostatic... View Article

Two persons are applying forces on two opposite sides of a moving cart. The cart still moves with the same speed in the same direction. What do you infer about the magnitudes and direction of the forces applied?

Answer: The magnitude of the forces will be equal, and they will act in opposing directions, cancelling each other out. Force applied is of equal... View Article

Two rods of the same weight and equal length have different thickness. They are held vertically on the surface of sand as shown in Fig. Which one of them will sink move? Why?

Answer: The area where force is applied is inversely proportional to the pressure exerted by the body. As a result, the thinner rod, i.e. rod B... View Article

Two women are of the same weight. One wears sandals with pointed heels while the other wears sandals with flat soles. Which one would feel more comfortable while walking on a sandy beach? Give reasons for your answer.

Answer: Women are the same height and walk with the same weight. Women wearing flat-heeled sandals, will be more comfortable walking on a sandy... View Article

Ultrasound has a frequency of vibration (a) between 20 and 20,000 Hz (b) below 20 Hz (c) above 20,000 Hz (d) between 500 and 10,000 Hz

Answer: (c) above 20,000 Hz Sound waves with frequencies higher than the upper audible limit of human hearing are called ultrasound. The limit... View Article

Untreated human excreta is a health hazard. Explain

Answer: Excretion is the process through which metabolic wastes are ejected from an organism in biology. This process is typically carried out by... View Article

Use a suitable identity to get each of the following products. (i) (3a – 1/2)(3a – 1/2) (ii) (1.1m – 0.4) (1.1m + 0.4) (iii) (a²+ b²) (- a² + b²)

Answer: (3a - 1/2)(3a - 1/2) = (3a - 1/2)2 Using the identity (a - b)2= a2 + b2 - 2ab (3a - 1/2)2 = 9a2 + (1/4) - 3a Using the identity (a... View Article

Use a suitable identity to get each of the following products. (i) (6x – 7) (6x + 7) (ii) (- a + c) (- a + c) (iii) (1/2x + 3/4y) (1/2x + 3/4y) (iv) (7a – 9b) (7a – 9b)

Answer: (6x - 7)(6x + 7) Using the identity (a - b)(a + b) = a2 - b2 (6x - 7)(6x + 7) = 36x2 - 49 Using the identity (a - b)2 = a2 + b2 -... View Article

Use a suitable identity to get each of the following products. (i) (x + 3) (x + 3) (ii) (2y + 5) (2y + 5) (iii) (2a – 7) (2a – 7)

Answer: (x + 3)(x + 3) = (x + 3)2 Using Using the identity (a + b) 2 = a2 + b2 + 2ab (x + 3)2 = x2 + 6x + 9 (2y + 5) (2y + 5) = (2y + 5)2... View Article

Use suitable identities to find the following product: (x + 4)(x + 10)

Answer: To find the product of (x + 4)(x + 10) We know that (x + a)(x + b) = x2 + (a + b)x + ab In the expression (x + 4)(x + 10) a = 4 b = +10... View Article

Use suitable identities to find the following product: (y² + 3/2)(y² – 3/2)

Answer: Given (y2 + 3/2)(y2 - 3/2) Using the identity, (x+y)(x–y) = x2- y 2 Here x = y2 y = 3/2 We get, (y2 + 3/2)(y2 - 3/2) ⇒ (y2)2... View Article

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case: p(x) = 2x³ + x² – 2x – 1, g(x) = x + 1

Answer: A polynomial is an algebraic expression in which the exponent on any variable is a whole number. Polynomial’s degree is the highest... View Article

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case: p(x) = x³ – 4x² + x + 6, g(x) = x–3

Answer: A polynomial is an algebraic expression in which the exponent on any variable is a whole number. Polynomial’s degree is the highest or... View Article

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case: p(x) = x³ + 3x² + 3x + 1, g(x) = x + 2

Answer: A polynomial is an algebraic expression in which the exponent on any variable is a whole number. Polynomial’s degree is the highest... View Article

Use the identity (x + a) (x + b) = x² + (a + b) x + ab to find the following products. (i) (2a² + 9) (2a² + 5) (ii) (xyz – 4) (xyz – 2)

Answer: (2a2+ 9) × (2a2+ 5) = 2a2 × (2a2+ 5) + 9 × (2a2+ 5) = 4a4 + 10a2 + 18a2 + 45 = 4a4 + 28a2 + 45 (2a2+ 9)(2a2+ 5) = =... View Article

Use the identity (x + a) (x + b) = x² + (a + b) x + ab to find the following products. (i) (4x + 5) (4x – 1) (ii) (2x + 5y) (2x + 3y)

Answer: (4x + 5) × (4x - 1) = 4x × (4x - 1) + 5 × (4x - 1) = 16x2 - 4x + 20x - 5 = 16x2 + 16x - 5 (4x + 5)(4x - 1) = 16x2 +... View Article

Use the identity (x + a) (x + b) = x² + (a + b) x + ab to find the following products. (i) (x + 3) (x + 7) (ii) (4x + 5) (4x + 1) (iii) (4x – 5) (4x – 1)

Answer: (x + 3) × (x + 7) = x × (x + 7) + 3 × (x + 7) = x2 + 7x + 3x + 21 = x2 + (3 + 7)x + 21 = x2 + 10x + 21 (x + 3)(x +... View Article

Using (x + a) (x + b) = x² + (a + b) x + ab, find (103 x 104)

Answer: 10712 103 x 104 can be written as (100 + 3) × (100 + 4) 103 x 104 = (100 + 3) × (100 + 4) Using (x + a)(x + b) = x2 + (a +... View Article

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