 # Quant Quiz on “COORDINATE GEOMETRY” for SSC CGL 2016

For the first time SSC 2016 examination will be held in Computer Based pattern and managing time will be one of the important factor while solving the questions. So in order to make students familiar with such a situations we are providing questions in a time based manner , which will help students to manage the time properly. 1. What is the distance of point of intersection of straight lines 2x+3y=6 and y=x+7 from origin ?

7
3
4
5

2. The length intercepted by the straight line 12x-9y=108 between the coordinate axes is

12 unit
18 unit
15 unit
9 unit

3. Area of triangle formed by straight lines 4x-3y+4=0,4x+3y-20=0 and x- axis is

3 sq. unit
6 sq. unit
12 sq. unit
24 sq. unit
Solution:

Area =1/2*(difference between x-intercept)*(y-coordinate of point of intersection)
Required Area =1/2 |5-(-1) |×4=12 square unit

4. Area of triangle formed by straight lines 4x-y=4,3x+2y=14 and y-axis is

11/2 sq. unit
11/4 sq. unit
22 sq. unit
11 sq. unit
Solution:

Required Area =1/2 |-4-7|×2=11 square unit

5. Ratio of area of triangle formed by straight lines 2x+3y=4 and 3x-y+5=0 with x-axis and y-axis is

1 : 2
2 : 1
4 : 1
None of these

6. Area of quadrilateral formed by straight lines 2x=-5,2y=3,x+1=0 and y+2=0 is

21/2 sq. unit
21/4 sq. unit
21/8 sq. unit
21/16 sq. unit

7. Area enclosed by equation |x|+|y|=4 is

16
32
24
48

8. For what value of k system of equations 3x+4y=19, y-x=3 and 2x+3y=k has a solution ?

11
-11
14
-14
Solution:

Solving 3x+4y=19 and y-x=3
We get x=1,y=4
Putting (x,y)=(1,4) in 2x+3y=k
We have 2×1+3×4=k
⇒k=14

9. Which of the following pair represent equation of parallel straight lines.

2x+3y=4,4x+6y=9
x+2y=4,2x+y=4
y=3x+5,x=3y+5
None of these
Solution:

In option (a) a1/a2 =b1/b2 ≠c1/c2 . Hence lines given in alternative (a) shows parallel lines.

10. For what value of Ksystem of equation x+3y=K and 2x+6y=2K has infinitely many solution ?

K=1
K=2
for all real values of K
for no real value of K
Solution:

Here a1/a2 =b1/b2 =c1/c2 is always true. It has infinitely many solution for all real values of K.

11. Values of a andb so that system of equations 2x+3y=7 and 2ax+(a+b)y=28 has infinitely many solutions are

a=4,b=8
a=8,b=4
a=-4,b=-8
a=-8,b=-4
Solution:

Required condition is 2a/2=(a+b)/3=28/7
or, a=(a+b)/3=4
∴a=4,a+b=12
or,a=4,b=8

12. Value of k for which system of equations kx+2y=5, 3x+y=1 has unique solution is

k=1
k=2
k=3
All are true
Solution:

System has unique solution if a1/a2 ≠b1/b2
⇒k/3≠2/1
⇒k≠6
so options (a), (b), (c) are correct

13.

a
b
c
d

14. Area of triangle formed by the straight line 8x-3y+24=0 and coordinate axes is

24 sq. unit
12 sq. unit
6 sq. unit
18 sq. unit

15. Area of triangle formed by straight line y=mx+c with coordinate axes is

a
b
c
d

×

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