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Carry out the following division: 66pq²r³ ÷ 11qr²

Answer: 6pqr The four important terms used in the division operation are dividend, divisor, quotient and remainder. The formula to calculate the... View Article

Carry out the multiplication of the expressions in each of the following pairs. (i) 4p, q + r (ii) ab, a – b (iii) a + b, 7a²b² (iv) a² – 9, 4a (v) pq + qr + rp, 0

Answer: 4p × (q + r) ⇒ 4p × q + 4p × r ⇒ 4pq + 4pr ab × (a - b) ⇒ (ab × a) - (ab × b)... View Article

Cartilage is present in the joints of our body, which helps in their smooth movement. With advancing age, this cartilage wears off. How would this affect the movement of joints?

Answer: Cartilage is found in our body's joints and helps to minimise friction during joint movement. However, as this cartilage wears away, the... View Article

Categorise the materials of the following products into ‘can be recycled’ and ‘cannot be recycled’. Telephone instruments, plastic toys, cooker handles, carry bags, ball point pens, plastic bowls, plastic covering on electrical wires, plastic chairs, electrical switches.

Answer: Recycling waste product is very important as it helps in processing waste or used products into useful or new products. Recycling also... View Article

Changes in which new substances are formed are called _________ changes.

Answer: Changes in which new substances are formed are called chemical changes. A substance is said to undergo a chemical change when the... View Article

Changes in which only _________ properties of a substance change are called physical changes.

Answer: Changes in which only physical properties of a substance change are called physical changes. A substance is said to undergo a physical... View Article

Check whether 7 + 3x is a factor of 3x³ + 7x.

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

Choose the correct option and justify your choice : 1 tan²45°/1+tan²45° = ? (A) tan 90° (B) 1 (C) sin 45° (D) 0

Answer: (D) 0 Trigonometry values for angles 0°, 30°, 45°, 60°and 90°, with respect to sin, cos, tan, cot, sec, cosec... View Article

Choose the correct option and justify your choice : 2tan 30°/1+tan²30° = ? (A) sin 60° (B) cos 60° (C) tan 60° (D) sin 30°

Answer: (A) sin 60° Trigonometry values for angles 0°, 30°, 45°, 60°and 90°, with respect to sin, cos, tan, cot, sec,... View Article

Choose the correct option and justify your choice : sin 2A = 2 sin A is true when A = ? (A) 0° (B) 30° (C) 45° (D) 60°

Answer: (A) 0° sin 2A = 2 sin A is true when A = 0° To find the value of A, substitute the degree given in the options one by one As sin... View Article

Choose the correct option and justify your choice: 2tan30°/1-tan²30° = ? (A) cos 60° (B) sin 60° (C) tan 60° (D) sin 30°

Answer: (C) tan 60° Substitute the of tan 30° in the given equation 2 tan30°/1-tan230° Trigonometry values for angles... View Article

Choose the correct option. Justify your choice. (1 + tan θ + sec θ) (1 + cot θ – cosec θ) =?. (A) 0 (B) 1 (C) 2 (D) – 1

Answer: (C) 2 (1 + tan θ + sec θ) (1 + cot θ – cosec θ) We know that, tan θ = sin θ/cos θ sec... View Article

Choose the correct option. Justify your choice. (sec A + tan A) (1 – sin A) =? (A) sec A (B) sin A (C) cosec A (D) cos A

Answer: (D) cos A We know that, sec A= 1/cos A tan A = sin A / cos A Now, substitute the above values in the given problem, we get (secA +... View Article

Choose the correct option. Justify your choice. 1 + tan²A/1 + cot²A =? (A) sec2 A (B) -1 (C) cot2A (D) tan2A

Answer: (D) tan2A We know that, tan2A =1/cot2A Now, substitute this in the given equation, we get 1 + tan2A/1 + cot2A = (1 + 1/cot2A)/1 + cot2A =... View Article

Choose the correct option. Justify your choice. 9 sec²A – 9 tan²A =? (A) 1 (B) 9 (C) 8 (D) 0

Answer: (B) 9 9 sec2A – 9 tan2A Take 9 outside, and it becomes = 9 (sec2A – tan2A) ∵ sec2 A – tan2 A = 1 = 9×1 = 9... View Article

Classify the changes involved in the following processes as physical or chemical changes: (a) Photosynthesis (b) Dissolving sugar in water (c) Burning of coal (d) Melting of wax (e) Beating aluminium to make aluminium foil (f ) Digestion of food

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

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