Class 11 maths jee Brilliant Pala class notes - straight lines Question paper

Class(XI)[JW-2023 Module-I]




CHAPTER - 09
STRAIGHT LINE



QUESTIONS
1. If the lines  k,3 ,  2, k  ,  k,3 are collinear, then the values of k are

1
A) 2,3 B) 1,0 C) 1,2 D) 1,  E) 0,3
2
2. If A(3,5), B(–5,–4), C(7,10) are the vertices of a parallelogram, taken in order then the co-ordinates of
the fourth vertex are
A) (10,19) B) (15,10) C) (19,10) D) (19,15) E) (15,19)
3. The centroid of a triangle is (2,7) and two of its vertices are (4,8) and (–2,6). The third vertex is
A) (0,0) B) (4,7) C) (7,4) D) (7,7) E) (4,4)
4. If the lines x  y  1,4x  3y  k and 2x  3y  1  0 are concurrent, then k is
A) 1 B) –1 C) 25 D) 5 E) –20

5. ABC is a triangle with vertices A  1, 4  ,B  6, 2  and C  2, 4  . D, E and F are the points which divide
each AB, BC and CA respectively in the ratio 3:1 internally. Then the centroid of the triangle DEF is
A) (3,6) B) (1,2) C) (4,8) D) (–3,6) E) (–1,2)
6. The ratio in which the line x  y  4 divides the line joining the points (–1,1) and (5,7) is
A) 1:2 B) 2:1 C) 1:3 D) 3:1 E) 3:2

7. If the equation of the base of an eqiolateral triangle is 2x  y  1 and the vertex is  1, 2  , then the length
of the side of the triangle is

20 2 8 15
A) B) C) D) E) 5
3 15 15 2
8. The vertices A,B,C of a triangle are (2,1),(5,2) and (3,4) respecitvely. Then the circumcentre is

 13 9   13 9   13 9   13 9   13 9 
A)  ,  B)  ,  C)  ,  D)  ,  E)  , 
4 4   4 4  4 4   4 4  2 4
9. The X axis, y axis and a line passing throught he point A(6,0) form a triangle ABC. If A  30 , then the
area of the triangle, in sq units is
A) 6 3 B) 12 3 C) 4 3 D) 8 3 E) 2 3

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10. The mid point of the line joining the points (–10,8) and (–6,12) divides the line joining the points (4,–2)
and (–2,4) in the ratio
A) 1:2 internally B) 1:2 internally C) 2:1 internally D) 2:1 externally E) 2:3 externally
11. If A(0,0), B(12,0) C(12,2), D(6,7) and E (0,5) are vertices of a pentagon ABCDE, then its area in square
units is
A) 58 B) 60 C) 61 D) 62 E) 63
12. The circumcentre of the triangle with vertices (0,30) (4,0) and (30,0) is
A) (10,10) B) (10, 12) C) (12,12) D) (15,15) E) (17,17)
13. Triangle ABC has vertices (0,0), (11,60) and (91,0). If the line y = kx cuts the triangle into two triangles
of equal area, then k is equal to

30 4 7 30 25
A) B) C) D) E)
31 7 4 91 37
14. If the distance between (2,3) and (–5,2) is equal to the distance between (x,2) and (1,3), then the
values of x are
A) –6,8 B) 6,8 C) –8,6 D) –7,7 E) –8,–6
15. If the three points (0,1) (0,–1) and (x,0) are vertices of an equilateral triangle, then the values of x are
A) 3, 2 B) 3,  3 C)  5, 3 D) 2,  2 E) 5,  5

16. The distance between the points  a cos ,a sin   and  a cos ,a sin   is

          
A) 2 sin   B) 2 a sin   C) 2 a cos  
 2   2   2 

   
D) a cos   E) 2 a 1  cos      
 2 
17. The vertices of a rectangle ABCD are A (–1,0) B (2,0) C (a,b) and D(–1,4). Then the length of the
diagonal AC is
A) 2 B) 3 C) 4 D) 5 E) 6
18. The vertices of a triangle PQR are P(0,b), Q (0,0) and R (a,0). If the medians PM and QN of PQR are
perpendicular, then
A) b2  2a 2 B) b  a 2 C) a 2  2b 2 D) a  b E) a   b
19. The slope of the straight line which does not intersect X axis is equal to

1 1
A) B) C) 3 D) 1 E) 0
2 2
20. If the distance between the two points (–1,a) and (–1,–4a) is 10 units, then the values of a are
A) 1 B) 2 C) 3 D) 4 E) 5

1  1
21. If the area of the triangle formed by (0,0), (a,0) and  ,a  is equal to units2, then the values of a are
2  2
A) 2 B) 3 C) 1 D) 4 E) 5

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22. The orthocentre of the triangle formed by the lines x  2y  1, x  0 and 2x  y  2 is

A) (0,1) B) 1,0  C)  1, 2  D) 1,2  E)  0,0 
23. The locus of the point which is equidistant from the points (1,1) and (3,3) is
A) y  x  4 B) x  y  4 C) x  2 D) y  2 E) y  x  0
24. The orthocentre of the triangle whose vertices are (5,–2), (–1,2) and (1,4) is

 1 14   14 1  1 1  14 14  5 5
A)  ,  B)  ,  C)  ,  D)  ,  E)  , 
5 5   5 5 5 5 5 5  14 14 
25. The x-coordinate of the incentre of the triangle where the mid points of the sides are (0,1), (1,1) and
(1,0) is
A) 2  2 B) 2  2 C) 3  2 D) 1  2 E) 1  2

26. Let O(0,0), P(3,4), Q(6,0) be the vertices of OPQ . The point R lie inside the OPQ such that the
triangles OPR, OQR and PQR are of equal Area. Then the co-ordinates of R is

4   2  4  4 2
A)  ,3  B)  3,  C)  3,  D)  , 
3   3  3  3 3

27. A straight line L through the pint (3, –2) is inclined at an angle 60° with the line 3x  y  1 . If L also
intersects the X-axis them equation of L is

A) y  3x  2  3 3  0 B) y  3x  2  3 3  0

C) 3y  x  3  2 3  0 D) 3y  x  3  2 3  0

28. If a line L is perpendicular to the line 5x–y=1 and the area of  formed by the line L and the co-ordinate
axis is 5 sq. units, then the distance of the line L from the line x+5y = 0 is

7 5 7 5
A) B) C) D)
5 13 13 7
29. A square of side a units lies above the x axis and has one vertex at the origin. The side passing through

the origin makes an angle (0  ) with the positive direction of x axis. The equation of its diagonal
4
not passing through the origin is

A) y(cos   sin )  x  sin   cos    a

B) y(cos   sin )  x  sin   cos    a

C) y(cos   sin )  x  sin   cos    a

D) y(cos   sin )  x  cos   sin    a


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