NCERT Solutions For Class 10 Maths Chapter – 4 Exercise – 4.1
The exercise solutions provided here are created with a vision to assist the students in their first term exam preparation. Exercise solution cover all the questions given in Exercise 4.1 of the NCERT textbook. These solutions are researched and prepared by our subject experts. Studying this study material will aid you in solving different questions on distance from a point.
Exercise solutions are provided in PDF format for your easy access and download. By studying this solution you can clear your doubts on distance calculation. By studying this study material you can get well acquainted with all important formulas. Here, you can also get knowledge of alternative methods to solve distance from a point problems.
Q1. Check whether the following are quadratic equations:
- (x + 1)2= 2(x – 3)
- X2– 2x = (-2)(3 – x)
- (x – 2)(x+1) = (x – 1)(x +3)
- (x – 3)(2x + 1) = x(x+5)
- (2x – 1)(x – 3) = (x + 5)(x – 1)
- X2+ 3x + 1 = (x – 2)2
- X3– 4x2 – x + 1 = (x – 2)3
Solution:-
- (x +2)2= 2(x – 3)
= x2 + 2x + 1 = 2x – 6
= x2 + 7 = 0
It is of the form ax2 + bx + c = 0
Hence the given equation is quadratic equation.
- X2– 2x = (-2)(3-x)
= x2 – 2x = -6 + 2x
= x2 – 4x + 6 = 0
Quadratic equation
- (x-2)(x +1) = (x – 1)(x +3)
= x2 – x – 2 = x2 + 2x -3
= 3x – 1 = 0
It is not a quadratic equation.
- (x – 3)(2x +1) = x(x + 5)
= 2x2 – 5x – 3 = x2 + 5x
= x2 – 10x – 3 = 0
It is quadratic equation.
- (2x – 1)(x – 3) = (x+5)(x-1)
= 2x2 – 7x + 3 = x2 + 4x – 5
= x2 -11x + 8 = 0
It is quadratic equation.
- X2+ 3x + 1 = (x – 2)2
X2 + 3x + 1 = x2 + 4 – 4x
7x – 3 = 0 It is not quadratic equation.
- (x+2)3= 2x(x2-1)
= x3 + 8 + x+ 12x = 2x3 – 2x
= x3 + 14x – 6x2– 8 = 0
It is not a quadratic equation.
- X3– 4x2 – x + 1 = (x-2)3
X3 – 4x2 – x + 1 = x3 – 8 – 6x2 + 12x
= 2x2 – 13x + 9 = 0
It is the quadratic equation.
Q2. Represent the following situations in the form of quadratic equation.
- The area of a rectangular plot is 528m2. The length of the plot is one more than twice its breadth. We need to find the length and breadth of the plot.
Solution:-
Let the breadth of the rectangular plot = x m
Hence , the length of the plot is (2x +1)m.
Formula of area of rectangle = Length x Breadth = 528m2
Putting the value of length and width we get
(2x +1) x x = 528
2x2 + x = 528
2x2 + x – 528 = 0
- The product of two consecutive positive integer is 306. We need to find the integers.
Solution:-
X2 + x = 306
X2 + x – 306 = 0
- Rohan mother is 26 years older than him. The product of their ages (in years) 3 years from now will be be 360. We would like to find the Rohan preset age.
Solution:-
(x+3)(x+29) = 360
= x2 + 29x + 3x + 87 = 360
= X2 + 32x + 87 – 360 = 0
= x2 + 32x – 273 = 0
- A train travel a distance of 480 km at a uniform speed If the speed had been 8 km/h less then it would have taken 3 hour more to cover the same distance. We need to find the speed of the train.
Solution:-
(x-8)(480/x +3) = 480
= 480 + 3x – 3840/x – 24 = 480
3x – 3840/x = 24
3x2 – 8x – 1280 = 0