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Question 1. Solution: Question 2.Solution: Question 3. Solution: Question 4.Solve the following equations. Solution:This equation is true for x = 0∴ x = 0 is one of the solutions.If x ≠ 0, then x2 ≠ 0∴ 8x + 12 = 12x – 20∴ 12 + 20 = 12x – 8x∴ 32 = 4x∴ x = 8∴ … Read more

Question 1. Solution: Question 2.Find the following ratios.i. The ratio of radius to circumference of the circle.ii. The ratio of circumference of circle with radius r to its area.iii. The ratio of diagonal of a square to its side, if the length of side is 7 cm.iv. The lengths of sides of a rectangle are … Read more

Question 1.From the following pairs of numbers, find the reduced form of ratio of first number to second number.i. 72,60ii. 38,57iii. 52,78Solution:i. 72, 60 Question 2.Find the reduced form of the ratio of the first quantity to second quantity.i. ₹ 700, ₹ 308ii. ₹ 14, ₹ 12 and 40 paiseiii. 5 litres, 2500 mliv. 3 … Read more

Question 1.Write the correct alternative answer for each of the following questions. i. Which of the following is a polynomial? Answer: ii. What is the degree of the polynomial √7 ?(A) 1/2(B) 5(C) 2(D) 0Answer:(D) 0 iii. What is the degree of the polynomial ?(A) 0(B) 1(C) undefined(D) any real numberAnswer:(C) undefined iv. What is … Read more

Question 1.Find the factors of the polynomials given below: Solution:i. 2×2 + x – 1= 2×2 + 2x – x – 1= 2x(x + 1)- 1(x + 1)= (x + 1)(2x – 1) ii. 2m2 + 5m – 3= 2m2 + 6m – m – 3= 2m(m + 3) – 1(m + 3)= (m + 3)(2m – 1) iii. … Read more

Question 1.Find the value of the polynomial 2x – 2×3 + 7 using given values for x.i. x = 3ii. x = -1iii. x = 0Solution:i. p(x) = 2x – 2×3 + 7Put x = 3 in the given polynomial.∴ p(3) = 2(3) – 2(3)3 + 7= 6 – 2 x 27 + 7= 6 – 54 + … Read more

Question 1.For x = 0, find the value of the polynomial x2 – 5x + 5.Solution:p(x) = x2 – 5x + 5Put x = 0 in the given polynomial.∴ P(0) = (0)2 – 5(0) + 5= 0 – 0 + 5∴ p(0) = 5 Question 2.If p(y) = y2 – 3√2 + 1, then find p( 3√2 ).Solution:p(y) = … Read more

Question 1.Divide each of the following polynomials by synthetic division method and also by linear division method. Write the quotient and the remainder.i. (2m2 – 3m + 10) ÷ (m – 5)ii. (x4 + 2×3 + 3×2 + 4x + 5) ÷ (x + 2)iii. (y3 – 216) ÷ (y – 6)iv. (2×4 + 3×3 + 4x – 2×2) ÷ (x + … Read more

Question 1.Use the given letters to write the answer.i. There are ‘a’ trees in the village Lat. If the number of trees increases every year by ’b‘. then how many trees will there be after ‘x’ years?ii. For the parade there are y students in each row and x such row are formed. Then, how … Read more

Question 1.State whether the given algebraic expressions are polynomials? Justify. ii. 2 – 5√xiii. x2 + 7x + 9iv. 2m-2 + 7m – 5v. 10Answer:i. No, because power of v in the term 5√x is -1 (negative number).ii. No, because the power of x in the term 5√x isi. e. 0.5 (decimal number).iii. Yes. All the coefficients … Read more