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CBSE - Class 10 Mathematics Pair of linear equations in two variable Worksheet

1.
For what values of k,the following equations have infinite solution Kx + 3y - (K-3) = 0 & 12x + Ky - K = 0
2.
In a two digit number. The units digit is thrice the tens digit. If 36 is added to the number, the digits interchange their place. Find the number.
3.

if 2/x+3/y=10 and 3/x+2/y=5 ,then find 1/x + 1/y =........................

a.

3

b.

2

c.

4

d.

1/3

4.

If a pair of linear equations is consistent, then the lines will be

a.

always coincident

b.

parallel

c.

always intersecting

d.

intersecting or coincident

5.

If X+1⁄X=3 FIND THE VALUE OF X³+1/X³

a.

15

b.

16

c.

17

d.

18

6.
The sum of two numbers is 14 and their difference is 2. Find the numbers.
7.

Find the value of m, when (m+1)x=3ky+15=0 and 5x+ky+5=0 are coincident

a.

m=16

b.

m=-17

c.

m=-15

d.

m=-16

8.

If the sum of first 7 terms of an A.P. is 49 and that of first 17 terms is 289, find the sum of n terms.

a.

n^2

b.

n^3

c.

n/2

d.

2n

9.
Choose the correct option: Example of linear equation involving two variables is _________.
a. 7x + 3y + 4z = 20 b. 6x + 2y = 10 c. 8x = 2+10 d. 7a + 8b + 9c = 10 + 5
10.

The nth term of an AP is 3n + 5. what is the common difference

a.

5

b.

6

c.

3

d.

9

11.

If the lines given by 2x + ky = 1 and 3x – 5y = 7 are parallel, then the value of k is

a.

-10/3

b.

10/3

c.

-13

d.

-7

12.
Solve the following pair of linear equations by the substitution method. (vi) $\frac{3x}{2} - \frac{5y}{3} = -2$; $\frac{x}{3} + \frac{y}{2} = \frac{13}{6}$
13.

The graph of the equation 2x + 3y = 5 is a

a.

vertical line

b.

straight line

c.

horizontal line

d.

none of these

14.

Which term of the A.P.: 21, 18, 15, .... is zero  

a.

7

b.

6

c.

8

d.

9

15.
Which of the following pairs of linear equations are consistent/inconsistent? If consistent, obtain the solution graphically: (iv) 2x – 2y – 2 = 0, 4x – 4y – 5 = 0
16.

Your trading plan is something you should check

a.

Every month

b.

Every week

c.

Every day

d.

Every day before starting to trade

17.
Choose the correct option: In linear equation 'ax + by = c' a, b and c are considered as _______.
a. Variable b. Constants c. Zero d. Real numbers
18.

If a1x+b1y+c1=0 , a2x+b2y+c2=0 is a pair of linear eqns in two variables x and y such that if a1/a2=b1/b2=c1/c2 then pair of linear eqns is

a.

consistent with infinitely many solution

b.

inconsistent

c.

consistent with unique solution

d.

no solution

19.
Two pens and one eraser cost Rs. 35 and 3 pencil and four erasers cost Rs. 65. Find the cost of pencil and eraser separately.
20.
A mobile company charges a fixed amount as monthly rental which
includes 100 minutes free per month and charges a fixed amount there
after for every additional minute. Abhishek paid Rs. 433 for 370 minutes.
and Ashish paid Rs. 398 for 300 minutes. Find the bill amount under the
same plan, if Usha use for 400 minutes.

Worksheet Answers

1.
K=6
2.
26
3.
Option A

Solution:

add eqution 1 and equestion 2

so 2/x+3/y+3/x+2/y=10+5

5/x+5/y=15

5(1/x+1/y)=15

1/x+1/y = 15/5 =3

4.
Option D
5.
Option B

6.
x = 8, y = 6
7.
Option D

Solution:

(m+1)x=3ky+15=0 this equation can be written as (m+1)x-3ky-15=0 and other equation is 5x+ky+5=0 

the condition for coincident lines is the ratio of the coefficents of x, y and constants has to be equal.

=> (m+1)/5=-3k/k=-15/5

=> m+1=-15

=> m=-16

Hope it helps

thank you

8.
Option A
9.
Option B
10.
Option C
11.
Option A
13.
Option B
14.
Option C
16.
Option D

Solution:

Before the start of the trade, remind yourself the max. capital you will deply on each trade, max loss you are wiling to take, max. trades you will take and the conditions for stopping trades.

Preferably write it down and put it right in front of you.

17.
Option B
18.
Option A

19.
the cost of 1 pen is Rs. 15 and the cost of 1 eraser is Rs. 5.
20.
(Rs.298, Rs.1/2) Rs.448

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