Binayak Bhaiya

Quadratic Equations Question 1.Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:(i) 2×2 – 3x + 5 = 0(ii) 3×2 – 4√3x + 4 = 0(iii) 2×2 – 6x + 3 = 0 Solution:(i) The given equation is 2×2 – 3x + 5 = 0.Here, a = 2, b = […]

Quadratic Equations Question 1.Find the roots of the following quadratic equations, if they exist by, the method of completing the square:(i) 2×2 – 7x + 3 = 0(ii) 2×2 + x – 4 = 0(iii) 4×2 + 4√3x + 3 = 0(iv) 2×2 + x + 4 = 0 Solution:(i) The equation 2×2 – 7x + 3 is the same

Quadratic Equations Question 1.Find the roots of the following quadratic equations by factorisation:(i) x3 – 3x – 10 = 0(ii) 2×2 + x – 6 = 0(iii) √2×2 + 7x + 5√2 = 0(iv) 2×2 – x + 1/8 = 0(v) 100×2 – 20x + 1 = 0 Solution:(i) We have:x2 – 3x – 10 = 0or x2 – 5x + 2x – 10 = 0or

Quadratic Equations Question 1.Check whether the following are quadratic equations:(i) (x + 1)2 = 2(x – 3)(ii) x2 – 2x = (- 2)(3 – x)(iii) (x – 2)(x + 1) = (x – 1)(x + 3)(iv) (x – 3)(2x + 1) = x(x + 5)(v) (2x – 1)(x -3) = (x + 5)(x – 1)(vi) x2 + 3x

Pair of Linear Equations in Two Variables Question 1.The ages of two friends Ani and Biju differ by 3 years. Ani’s father Dharam is twice as old as Ani and Biju is twice as old as his sister Cathy.The ages of Cathy and Dharam differ by 30 years. Find the ages of Ani and Biju?

Question 1.Solve the following pairs of equations by reducing them to a pair of linear equations:1. 1/2x + 1/3y = 21/3x + 1/2y = 13/6 2. 2/√x + 3/√y = 24/√x – 9/√y = – 1 3. 4/x + 3y = 143/x – 4y = 23 4. 5/(x−1) + 1/(y−2) = 26/(x−1) – 3/(y−2) = 1 5. (7x−2y)/xy = 5(8x+7y)/xy = 15 6. 6x + 3y = 6xy2x + 4y = 5xy 7. 10/(x+y) + 2/(x−y) = 415/(x+y) – 5/(x−y) = – 2 8. 1/(3x+y) + 1/(3x−y) = 3/41/2(3x+y) – 1/2(3x−y) = −1/8 Solution:1. Taking 1/x = u and 1/y = v, the

Pair of Linear Equations in Two Variables Question 1.Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions? In case there is a unique solution, find it by using cross multiplication method.1.  x – 3y – 3 = 03x – 9y – 2 = 0 2. 2x +

Pair of Linear Equations in Two Variables Question 1.Solve the following pair of linear equations by the elimination method and the substitution method: Solution:1. By elimination method:The given system of equations isx +y = 5 ……………….. (1) and2x – 3y = 4 ………………….. (2)Multiplying (1) by 3, we get3x + 3y = 15 ……………….. (3)Adding

Pair of Linear Equations in Two Variables Question 1.Solve the following pair of linear equations by the substitution method:1. x + y = 14x – y = 4 2. s – t = 3s/3 + t/2 = 6 3. 3x – y = 39x – 3y = 9 4. 0.2x + 0.3y = 1.30.4x + 0.5y = 2.3

Question 1.Form the pair of linear equations in the following problems, and find their solution graphically. 1. 10 students of Class X took part in a Mathematics quiz. If the number of girls is 4 more than the number of boys, If the number of girls is 4 more than the number of boys, find