Practice Question on Straight Lines For IITJEE , NDA and Airforce

Straight Lines

---

Question no. 1

If (a,0), (0, b) and (1, 1) are collinear, what is ( a + b - ab ) equal to ?

looks_one 2

looks_two 1

looks_3 0

looks_4 -1

Option looks_3 0

Solution :
Points (a,0), (0, b) and (1, 1) are collinear
it means area will be zero

a(b-1) + 1(-b) = 0
a + b -ab = 0

Question no. 2

Let p, q, r, s be the distances from origin of the points (2, 6), (3, 4), (4,5) and ( -2, 5) respectively. Which one of the following is a whole number?

looks_one p

looks_two q

looks_3 r

looks_4 s

Option looks_two q

Solution :
Distance Formula

Question no. 3

The line y =0 divides the line joining the points (3,-5) and (-4,7) in the ratio

looks_one 3: 4

looks_two 4: 5

looks_3 5: 7

looks_4 7: 9

Option looks_3 5: 7

Solution :
(x₁ , y₁) = (3 , -5)
(x₂ , y₂) = (-4,7)
(x,y) = (x,0)
Using section Formula
y = (m y₂ + n y₁)/( m + n)
0 = ( m(7) + n(-5) ) /(m+n)
0 = 7m - 5n
m/n = 5/7

Question no. 4

The equation of a straight line which makes an angle 45^o with the x-axis with y-intercept 101 units is

looks_one 10x+ 101y=1

looks_two 101x + y =1

looks_3 x+ y -101=0

looks_4 x-y+101=0

Option looks_4 x-y+101=0

Solution :
y = mx+ c where m = tanθ (Slope of line) and c = y intercept
Given : θ = 45^o
m = tan45^o = 1
c = 101
y = mx + c
y = x + 101

Question no. 5

If the points (2, 4),(2, 6) and (2+√3, k) are the vertices of an equilateral triangle, then what is the value of k?

looks_one 6

looks_two 5

looks_3 -3

looks_4 1

Option looks_two 5

Solution :
Given : ABC is an equilateral triangle
AB = BC = AC
AB = [(2-2)² + (4-6)² ]^1/2 = 2
AC = [(2+√3 -2)² + (k-4)² ]^1/2 = 2
3 + (k-4)² = 4
(k-4)² = 1
k-4 = ± 1
k = 5 , 3

Question no. 6

What is the area of the triangle whose vertices are (3,0), (0,4) and (3,4) ?

looks_one 6 sq. unit

looks_two 7.5 sq. unit

looks_3 9 sq. unit

looks_4 12 sq. unit

Option looks_one 6 sq. unit

Solution :

ABC is right angled triangle at A
Area = (1/2)* Base * height = (1/2) * 3 * 4 = 6

Question no. 7

A straight line passes through the point (5,0) and (0, 3). The length of the perpendicular from the point (4, 4) on the line is

looks_one

looks_two

looks_3

looks_4

Option looks_two

Solution :

Equation of line

Question no. 8

Two straight line paths are represented by the equation 2x-y=2 and -4x+ 2y= 6. Then the paths will

looks_one cross each other at one point

looks_two not cross each other

looks_3 cross each other at two points

looks_4 cross each other at infinitely many points

Option looks_two not cross each other

Solution :
2x-y=2
-4x+ 2y= 6

Question no. 9

For what value of k, the equations 3x -y= 8 and 9x -ky = 24 will have infinitely many solutions ?

looks_one 6

looks_two 5

looks_3 3

looks_4 1

Option looks_3 3

Solution :
3x -y= 8
9x -ky = 24

Question no. 10

What is the area of the triangle bounded by the side x= 0, y = 0, and x+ y= 2?

looks_one 1 sq. unit

looks_two 2 sq. unit

looks_3 4 sq. unit

looks_4 8 sq. unit

Option looks_two 2 sq. unit

Solution :

Area of triangle = (1/2)*B*H
= (1/2)*2 *2 = 2

Question no. 11

If the sum of the squares of the distances of the point (x, y) from the points (a, 0) and (- a, 0) is 2b² then which one of the following is correct ?

looks_one x² + a² = b² + y²

looks_two x² + a²= 2b² - y²

looks_3 x² - a²= b² + y²

looks_4 x² + a² = b² - y²

Option looks_4 x² + a² = b² - y²

Solution :
squares of the distances of the point (x, y) from the points (a, 0) = (x-a)² + y²
squares of the distances of the point (x, y) from the points (-a, 0) = (x + a)² + y²
(x-a)² + y² + (x + a)² + y² = 2b²
x² + a² - 2ax + y² + x² + a² + 2ax + y² = 2b²
2 (x² + a² + y² ) = 2b²
x² + a² = b² - y²

Question no. 12

The line mx + ny - 1=0 passes through the points (1, 2) and (2, 1). What is the value of m?

looks_one 1

looks_two 3

looks_3 1/2

looks_4 1/3

Option looks_4 1/3

Solution :
mx + ny - 1=0
(1,2) and (2,1) satisfy given equation
m(1) + n(2) - 1 = 0
m+2n - 1 = 0 ........[1]
m(2) + n(1) - 1 = 0
2m + n - 1 = 0 ........[2]
Solve both the equation
m = 1/3

Question no. 13

What is the equation of the line passing through (2,-3) and parallel to Y-axis?

looks_one Y=-3

looks_two Y=2

looks_3 X=2

looks_4 X=-3

Option looks_3 X=2

Solution :
Equation of the line passing through (2,-3) and parallel to Y-axis

y + 3 = (1/0)(x -2)
0 = x-2
x = 2

Question no. 14

What is the locus of the point which is at a distance 8 units to the left of Y-axis?

looks_one X=8

looks_two X=-8

looks_3 Y=-8

looks_4 Y=8

Option looks_3 Y=-8

Solution :

X = -8

Question no. 15

Two straight lines x - 3y -2= 0 and 2x-6y-6 =0

looks_one never intersect

looks_two intersect at a single point

looks_3 intersect at infinite number of points

looks_4 intersect at more than one point

Option looks_one never intersect

Solution :
x - 3y -2= 0
2x-6y-6 =0

Previous Next