NCERT full solutions here you can find full detailed solutions for all the questions with proper format. class 10 maths ncert solutions chapter 3 exercise 3.2.
You can see the solution for complete chapter here –
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Complete 10th Class Maths Solution
- NCERT Solutions For Class 10 Maths – Chapter 1 Exercise 1.2 Real Number
- NCERT Solutions For Class 10 Maths – Chapter 1 Exercise 1.3 Real Number
- NCERT Solutions For Class 10 Maths – Chapter 1 Exercise 1.4 Real Number
- NCERT Solutions For Class 10 Maths – Chapter 2 Exercise 2.1 Polynomials Real Number
- NCERT Class 10th – Chapter 2 Polynomial Solutions – Exercise 2.2
- NCERT Class 10th – Chapter 2 Polynomial Solutions – Exercise 2.3
EXERCISE -3.2
QUE:- 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 the number of girls is 4
more than the number of boys, find the number of boys and girls who took part in
the quiz.
(ii) 5 pencils and 7 pens together cost ` 50, whereas 7 pencils and 5 pens together
cost ` 46. Find the cost of one pencil and that of one pen.
SOL:-
(i) let the number of girls = x
and let the numbers of boys =y
total number of students =10
therefore , x +y = 10……………(1)
according to quetion , number of girl 4is more than number of boys so
x=y+4 …………………….(2)
to represent graphically ,three solution of each equation is needed.
to represent graphicaly , three solution of each equation is needed.
from the equation (1) we get
x= 10-y
| x | 5 | 4 | 6 |
| y | 5 | 6 | 4 |
from the equation (2) , we get
x= y +4
| x | 5 | 4 | 3 |
| y | 1 | 0 | -1 |
(ii)
let the cost of one pencil =x rs and let the cost of one pen = y rs
according to first condition
5x+7y =50……………..(1)
according to second condition
7x +5y =46……………….(2)
to represent graphically three solutions of each equation is given below ,
from the equation (1) , we get
x= (50-7y)/5
| x | 3 | 10 | -4 |
| y | 5 | 0 | 10 |
from the equation (2) , we get
x=(46 -5y)/7
| x | 8 | 3 | -2 |
| y | -2 | 5 | 12 |
QUE :-2 On compairing the ratio a1/a2,b1/b2, and c1/c2 find out whether the lines representing the following pairs of linear equations intersect at a point , are parallel or cioncident:
(i) 5x 4y +8 =0
7x + 6y -9 =0
(ii) 9x +3y +12 =0
18 x +6y +24 = 0
(iii) 6x -3y =10=0
2x -y = 9 =0
SOL:-
(i) 5x 4y +8 =0
7x + 6y -9 =0
here, a1/a2 =5/7,b1/b2 =-4/6=-2/3
⇒ a1/a2 ≠ b1/b2 ,so , the following pairs of linear equations intersect at a point.
(ii) 9x +3y +12 =0
18 x +6y +24 = 0
here , a1/a2 =9/18=1/2,b1/b2=3/6=1/2,c1/c2 =12/24=1/2
⇒ a1/a2 =b1/b2 =c1/c2 , so the following pairs of linear equation are coincident.
(iii) 6x -3y =10=0
2x -y = 9 =0
here , a1/a2 =6/2=3/1,b1/b2=-3/-1=3/1,c1/c2 =10/9
⇒ a1/a2 =b1/b2 ≠ c1/c2 , so the following pairs of linear equation are parallel.
QUE :-3 On compairing the ratio a1/a2,b1/b2, and c1/c2 find out whether the following pairs of linear equations are consistence , or inconsistent :
(i) 3x +2y =5 ; 2x -3y =7 (ii) 2x -3y =8 ; 4x+6y =9
(iii) (3/2)x +(5/3)y =7 ;9x -10y =14 (iv) 5x -3y =11; -10x+6y =-22
(v) 4/3x+2y =8 ; 2x +3y = 12
SOL:-
(i) 3x +2y =5
2x -3y =7
here , a1/a2 =3/2,b1/b2=2/-3=1/2,c1/c2 =12/24=1/2
⇒ a1/a2 ≠b1/b2 , so the following pairs of linear equation are coinsistent.
(ii) 2x -3y =8
4x -6y =9
here , a1/a2 =2/4=1/2 ,b1/b2=-3/-6=1/2,c1/c2 =8/9
⇒ a1/a2 =b1/b2 ≠c1/c2 , so the following pairs of linear equation are incoinsistent.
(iii) 3/2x +5/3y =7
9x -10y =14
here , a1/a2 =(3/2)/9=1/6,b1/b2=(5/3)/-10=-1/6
⇒ a1/a2 ≠b1/b2 , so the following pairs of linear equation are coinsistent.
(iv) 5x -3y =11
-10x +6y =-22
here , a1/a2 =5/-10=-1/2,b1/b2=-3/6=-1/2,c1/c2 =11/22=-1/2
⇒ a1/a2 =b1/b2 =c1/c2 , so the following pairs of linear equation are coinsistent.
(v) 4/3x +2y =8
2x +3y =12
here , a1/a2 =(4/3)/2=2/3,b1/b2=2/3,c1/c2 =8/12=2/3
⇒ a1/a2 =b1/b2 =c1/c2 , so the following pairs of linear equation are coinsistent.
QUE:-4 Which of the following pairs of linear equations are consistent/inconsistent? If
consistent, obtain the solution graphically:
(i) x + y = 5, 2x + 2y = 10
(ii) x – y = 8, 3x – 3y = 16
(iii) 2x + y – 6 = 0, 4x – 2y – 4 = 0
(iv) 2x – 2y – 2 = 0, 4x – 4y – 5 = 0
SOL :-
(i) x + y = 5,
2x + 2y = 10
a1/a2 =1/2,b1/b2=1/2,c1/c2 =5/10=1/2
⇒ a1/a2 =b1/b2 =c1/c2 , so the following pairs of linear equation are coinsistent.
for three solutions of each equation,
from equation (1)
x=5-y
| x | 4 | 3 | 2 |
| y | 1 | 2 | 3 |
from equation (2)
x= (10-2y)/2
| x | 4 | 3 | 2 |
| y | 1 | 2 | 3 |
que 4 (i)
(ii) x – y = 8,
3x – 3y = 16
a1/a2 =1/3,b1/b2=1/3,c1/c2 =8/16=1/2
⇒ a1/a2 =b1/b2 ≠c1/c2 , so the following pairs of linear equation are incoinsistent.
(iii) 2x + y – 6 = 0,
4x – 2y – 4 = 0
a1/a2 =2/4=1/2,b1/b2=1/-2,
⇒ a1/a2 ≠b1/b2 , so the following pairs of linear equation are coinsistent/inconsistent.
from equation (1) we get
x= 6-y/2
| x | 0 | 1 | 2 |
| y | 6 | 4 | 2 |
from equation (2) we get
x= 4+2y/4
| x | 1 | 2 | 3 |
| y | 0 | 2 | 4 |
que.4 (iii)
(iv) 2x – 2y – 2 = 0,
4x – 4y – 5 = 0
a1/a2 =2/4=1/2,b1/b2=-2/-4=1/2,c1/c2 =-2/-5=2/5
⇒ a1/a2 =b1/b2 ≠c1/c2 , so the following pairs of linear equation are incoinsistent.
QUE:-5. Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is
36 m. Find the dimensions of the garden.
SOL:-
let breadth(B) of garden= x meter
let length(L) of gaeden = y meter
half of perimeter =36 meter
so 1/2[2(x+y)]=36
x +y =36 ……………….(1)
according to the question L is 4 meter more than B so,
y = x + 4
to get 3 solution of each equation
from equqtion (1)
x =36 – y
| x | 0 | 36 | 16 |
| y | 36 | 0 | 20 |
from equqtion (2)
y = x + 4
| x | 0 | 8 | 12 |
| y | 4 | 8 | 16 |
graph of que.5
both the lines intersect at (16,20 ).
so the B of garden is 16 meter and L of garden is 20 meter .
QUE:-6 Given the linear equation 2x + 3y – 8 = 0, write another linear equation in two variables
such that the geometrical representation of the pair so formed is:
(i) intersecting lines (ii) parallel lines (iii) coincident lines
SOL:-
(i) given line 2x + 3y-8 =0 is intersect the line x + y -10=0
a1/a2 ≠b1/b2
(ii) given line 2x + 3y-8 =0 is parallel to 4x +6y – 9 =0
a1/a2 =b1/b2 ≠c1/c2
(iii) given line 2x + 3y-8 =0 is coincident to 4x + 6y -16 =0
a1/a2 =b1/b2 =c1/c2
QUE7. Draw the graphs of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Determine the
coordinates of the vertices of the triangle formed by these lines and the x-axis, and
shade the triangular region.
SOL:-
x – y + 1 = 0 ……………………(1)
3x + 2y – 12 = 0 ………………..(2)
equation (1) we get x = y -1
| x | 0 | 1 | 2 |
| y | 1 | 2 | 3 |
equation (2) we get x=(12-2y)/3
| x | 4 | 2 | 0 |
| y | 0 | 3 | 6 |
graph of que.7
the cordinates of the verticle of the triangle formed by tjese lines and the x- axis are
(-1 ,0 ) , (4 , 0) and ( 2,3)
You can see the solution for complete chapter here –
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