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Factorize the following using appropriate identities: 4y² −4y + 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

Factorize the following using appropriate identities: 9x² + 6xy + y²

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

Factorize the following using appropriate identities: x² – y²/100

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

Factorize the following: 27y³ + 125z³

Answer: 27y3 + 125z3 = (3y + 5z)(9y2 - 15yz + 25z2) The expression, 27y3 + 125z3 can be written as (3y)3 + (5z)3 27y3 + 125z3 = (3y)3 + (5z)3 We... View Article

Factorize the following: 64m³ – 343n³

Answer: (4m)3 - (7n)3 = (4m - 7n)(16m2 + 28mn + 49n2) The expression, 64m3 - 343n3 can be written as (4m)3 - (7n)3 64m3 - 343n3 = (4m)3 - (7n)3... View Article

Factorize: 2x² + y² + 8z² – 2√2xy + 4√2yz – 8xz

Answer: Given 2x2 + y2 + 8z2 - 2√2xy + 4√2yz - 8xz Using identity, (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx We can say that, x2... View Article

Factorize: 3x² – x – 4

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

Factorize: 4x² + 9y² + 16z² + 12xy – 24yz – 16xz

Answer: Given 4x2 + 9y2 + 16z2 + 12xy - 24yz - 16xz Using identity, (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx We can say that, x2 + y2 + z2 +... View Article

Factorize: 6x² – 5x – 6

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

Factorize: x³ + 13x² + 32x + 20

Answer: Let p(x) = x3+13x2+32x+20 Factors of 20 are ±1, ±2, ±4, ±5, ±10 and ±20 By trial method, we... View Article

Fig. shows a car sticking to an electromagnet. Name the forces acting on the car? Which one of them is larger?

Answer: The forces working on the car are Force of gravity which is the downward force The magnetic force which is the upward force Because the... View Article

Fig. shows a container filled with water. Which of the following statements is correct about the pressure of water?

Answer: (d) The pressure at A < Pressure at B Water pressure increases with an increase in depth. The pressure is defined as the force... View Article

Fig. shows a man with a parachute. Name the force which is responsible for his downward motion. Will he come down with the same speed without the parachute?

Answer: His downward motion is due to the force of gravity. His speed will be faster if he lands without a parachute. Without a parachute, he... View Article

Fig. shows comets without their tail. Show the tails of the comets at position A, B, and C. In which position will the tail be longest?

Answer: The comet's tail is always pointed away from the Sun. Because the tail is visible only when the comet travels through the inner solar... View Article

Fig. shows the word REST written in two ways in front of a mirror. Show how the word would appear in the mirror.

Answer: Answer: The left of the object appears on the right and the right appears on the left in an image formed by a plane mirror, i.e. the... View Article

Fig. shows two boys applying force on a box. If the magnitude of the force applied by each is equal, will the box experience any force of friction?

Answer: Frictional force refers to the force generated by two surfaces that contact and slide against each other. Friction is caused due to the... View Article

Fill in the blanks with appropriate words. (a) Synthetic fibres are also called or fibres. (b) Synthetic fibres are synthesised from raw material called . (c) Like synthetic fibres, plastic is also a

Answer: Synthetic fibres are manmade fibres that have been prepared with chemicals. They're made up of small units that link to form long... View Article

Fill in the blanks. (a) Phosphorus is a very _____non-metal. (b) Metals are _ conductors of heat and . (c) Iron is reactive than copper. (d) Metals react with acids to produce ____ gas.

Answer: (a) Phosphorus is a very reactive non-metal. Non-metals are the elements that form negative ions by accepting or gaining electrons.... View Article

Find and correct the errors in the following mathematical statements. (1) (2x) 2+ 4(2x) + 7 = 2x² + 8x + 7 (2) (2x)² + 5x = 4x + 5x = 9x (3) (3x + 2)² = 3x² + 6x + 4

Answer: Find and correct the errors in the following mathematical statements. LHS = (2x)2 + 4(2x) + 7 = 4x2 + 8x + 7 RHS = 2x2 + 8x + 7... View Article

Find and correct the errors in the following mathematical statements. (1) 4(x – 5) = 4x – 5 (2) x(3x + 2) = 3×2 + 2 (3) 2x + 3y = 5xy

Answer: In the given statement LHS = 4(x - 5) RHS = 4x - 5 ∴ LHS ≠ RHS 4x - 20 ≠ 4x - 5 The correct statement is 4(x - 5) = 4x -... View Article

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