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Identify the terms, their coefficients for each of the following expressions. (i) 5xyz² – 3zy (ii) 1 + x + x² (iii) 4x²y² – 4x²y²z² + z² (iv) 3 – pq + qr – p (v) (x/2) + (y/2) – xy (vi) 0.3a – 0.6ab + 0.5b

Answer: An algebraic expression is a mathematical phrase that contains integral or fractional constants (numbers), variables (alphabets) and... View Article

If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠ A = ∠ B.

Answer: Let us assume the triangle ABC in which CD⊥AB Give that the angles A and B are acute angles, such that Cos (A) = Cos (B) As per the... View Article

If 0.3 the multiplicative inverse of 3(1/3). Why or why not?

Answer: The multiplicative inverse of a number N is represented by 1/N or N-1. It is also called reciprocal, derived from the Latin word... View Article

If 3 cot A = 4, check whether (1-tan² A)/(1+tan² A) = cos²A – sin ² A or not.

Answer: Let △ABC in which ∠B=90° We know that the cot function is the reciprocal of the tan function and it is written as cot(A) = AB/BC... View Article

If A, B and C are interior angles of a triangle ABC, then show that sin (B+C/2) = cos A/2

Answer: We know that, for a given triangle, the sum of all the interior angles of a triangle is equal to 180° A + B + C = 180°... View Article

If air and cloud were good conductors of electricity, do you think lightning could occur? Explain.

Answer: No, there won't be any lightning since charge separation in conductors is impossible. As a result, all charges accumulated in the clouds... View Article

If cot θ = 7/8, evaluate : (i) (1 + sin θ)(1 – sin θ)/(1+cos θ)(1-cos θ) (ii) cot2 θ

Answer: Let us assume a △ABC in which ∠B = 90° and ∠C = θ Given cot θ = BC/AB = 7/8 Let us consider BC = 7k AB = 8k... View Article

If sec 4A = cosec (A – 20°), where 4A is an acute angle, find the value of A.

Answer: An angle that is measuring less than 90 degrees is called an acute angle. This angle is smaller than the right angle (which is equal to... View Article

If sin A = 3/4, Calculate cos A and tan A.

Answer: Let us assume a right-angled triangle ABC, right-angled at B. The sine function can be defined as the ratio of the length of the opposite... View Article

If tan (A + B) = √3 and tan (A – B) = 1/√3 ,0° < A + B ≤ 90°; A > B, find A and B.

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

If tan 2A = cot (A – 18°), where 2A is an acute angle, find the value of A.

Answer: An angle that is measuring less than 90 degrees is called an acute angle. This angle is smaller than the right angle (which is equal to... View Article

If tan A = cot B, prove that A + B = 90°.

Answer: tan A = cot B We know that cot B = tan (90° – B) To prove A + B = 90°, substitute the above equation in the given problem tan A = tan... View Article

If the materials used for constructing a building were good conductors, do you think lightning will strike the building? Will the lightning conductor be still required to be installed in the building?

Answer: Because charge separation cannot occur in conductors, lightning will not impact the building and any lightning that strikes it will fall... View Article

If the metal clip used in the electroscope is replaced by an ebonite rod and a charged body is brought in contact with it, will there be any effect on the aluminium strips? Explain.

Answer: There will be no repellent effect between the aluminium strips. Because the ebonite rod is an insulator, the charged body will not... View Article

If we apply oil on door hinges, the friction will (a) increases (b) decreases (c) disappear altogether (d) will remain unchanged

Answer: (b) decreases Friction will be reduced as oil acts as a lubricant, reducing friction. When the surface of one object comes into touch... View Article

If x + y + z = 0, show that x³ + y³ + z³ = 3xyz.

Answer: We know that x3 + y3 + z3 - 3xyz = (x + y + z)(x2 + y2 + z2 - xy - yz - xz) Now, according to the question, let (x + y + z) = 0, then,... View Article

If you pass current through copper sulphate solution, copper gets deposited on the plate connected to the ___________terminal of the battery.

Answer: If you pass current through copper sulphate solution, copper gets deposited on the plate connected to the negative Electroplating is a... View Article

Imagine that an object is falling through a long straight glass tube held vertical; the air has been removed completely from the tube. The object does not touch the walls of the tube. Will the object experience any force of friction?

Answer: No, the object will not be subjected to any frictional force since the force of friction requires two surfaces, and there is only one in... View Article

In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm. Determine: (i) sin A, cos A (ii) sin C, cos C

Answer: In a given triangle ABC, right-angled at B = ∠B = 90° Given AB = 24 cm BC = 7 cm According to the Pythagoras Theorem, in a... View Article

In ∆ PQR, right-angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P

Answer: In a given triangle PQR, right angled at Q, the following measures are PQ = 5 cm PR + QR = 25 cm Now let us assume, QR = x PR = 25 -... View Article

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