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Prove that √5 is irrational Sol. Let us assume to the contrary that √5 is an irrational number. So it can be written in the form of p/q where p and q are co-prime integers and q is not equal to zero. √5= p/q squaring both sides (√5)² = (p/q)² 5= p²/q² p²= 5 q² … Read more
Exercise 4.3 class 10 maths 1. Find the nature of the roots of the following quadratic equations. If the real roots exist ,find them. (i) 2x² – 3x + 5 =0 Here a = 2 , b = -3 , c = 5 D = b² – 4ac D = (-3)² – 4 … Read more
exercise 4.2 class 10 maths 1. Find the roots of the following quadratic equations by factorization. (i) x² – 3x – 10 = 0 (ii) 2x² + x – 6 = 0 (iii) √2 x² + 7x + 5√2 = 0 (iv) 2x² – x + 1/8 = 0 (v) 100x² – 20x + 1 … Read more
exercise 4.1 class 10 maths 1. Check whether the following are quadratic equations : 2. Represent the following situations in the form of quadratic equations: (i) The area of a rectangular plot is 528 m². The length of the plot ( in metres) is one more than twice its breadth. We need to find the … Read more
exercise 3.3 class 10 maths 1. Solve the following pair of linear equations by the elimination method and the substitution method. Put x= 2 in (ii) 3(2) – y = 9 6 – y = 9 – y = 9 – 6 y = -3 2. Form the pair of linear equations in the following … Read more
exercise 3.2 class 10 maths 1. Solve the following pair of linear equations by substitution method. 5 = -2 m + 3 2 = – 2m m = -1 Ans. 3. Form the pair of linear equations for the following problems and find their solution by substitution method. (i) The difference between … Read more
exercise 3.1 class 10 maths 1. Form the pair of linear equations in the following problems, and find their solutions graphically. (i) 10 students of Class X took part in a Mathematics quiz. If number of girls is 4 more than the number of boys,find the number of boys and girls who took part in … Read more
exercise 2.2 class 10 maths 1 Find the zeroes of the following Quadratic Polynomials and verify the relationship between the zeroes and the coefficients. (i) x²-2x-8 = x²-4x+2x-8 =x(x-4)+2(x-4) =(x+2)(x-4) for finding zeores x+2=0 , x=-2 x-4=0, x= 4 so zeroes are -2,4 Verifications : Sum of zeroes = -2+ 4 = 2= -(-2)/1 = … Read more
exercise 2.1 class 10 maths Solutions: For finding number of zeroses of polynomials from graph, we need to check that how many times the graph cuts the x-axis, that will be the number of zeroses of that polynomial (i) in this part the graph of the polynomial do not cut x-axis , so it has … Read more
exercise 1.2 Class 10 Maths 1. Prove that √5 is irrational. Sol. Let us assume to the contrary that √5 is an irrational number. So it can be written in the form of p/q where p and q are coprime integers and q is not equal to zero. √5= p/q squaring both sides (√5)² = … Read more
