# MCQ | Straight Line

PRACTICE TEST – II

Question:21. If P = (1, 0), Q = (-1, 0), R = (2, 0) are 3 given points, then the locus of the point S satisfying the relation SQ2 + SR2 = 2SP2 is

(A) a straight line parallel to the x-axis

(B) circle through the origin

(C) circle with center at the origin

(D) a straight line parallel to the y-axis.

Ans: (D)

Question:22. If the quadratic equation ax2 + bx + c = 0 has –2 as one of its roots then ax + by + c = 0 represents

(A) A family of concurrent lines

(B) A family of parallel lines

(C) A single line

(D) A line perpendicular to x-axis

Ans: (A)

Question:23. The line 3x + 2y = 24 meets y-axis at A and x-axis at B. The perpendicular bisector of AB meets the x-axis at C, then area of ΔABC is

(A) 78

(B) 92

(C)

(D) none of these

Ans: (A)

Question:24. Two vertices of a triangle are (5, -1) and (-2, 3). If orthocenter of the triangle is origin, then the co-ordinates of third vertex is

(A) (4, 7)

(B) (3, 7)

(C) (-4, -7)

(D) None of these

Ans: (C)

Question:25. The number of integral values of m, for which the x-coordinate of the point of intersection of the lines 3x + 4y = 9 and y = mx + 1 is also an integer is

(A) 2

(B) 0

(C) 4

(D) 1

Ans: (A)

Question:26. If A(cosα, sinα), B(sinα, -cosα), C(2, 1) are the vertices of a ΔABC, then as a varies the locus of its centroid is

(A) x2 + y2 – 2x – 4y + 1 = 0

(B) 3(x2 + y2) – 2x – 4y + 1 = 0

(C) x2 + y2 – 2x – 4y + 3 = 0

(D) none of these

Ans: (D)

Question:27. The straight line y = x–2 rotates about a point where it cuts the x-axis and becomes perpendicular to the straight line ax + by + c = 0. Then its equation is

(A) ax + by + 2a = 0

(B) ax – by – 2a = 0

(C) bx + ay – 2b = 0

(D) ay – bx + 2b = 0

Ans: (D)

Question:28. It is desired to construct a right angled triangle ABC (∠C = π/2) in xy plane so that it’s sides are parallel to coordinates axes and the medians through A and B lie on the lines y = 3x + 1 and y = mx + 2 respectively. The values of ‘m’ for which such a triangle is possible is /are

(A) –12

(B)3/4

(C) 4/3

(D) 1/12

Ans: (B)

Question:29. If 3a + 2b + 6c = 0, the family of lines ax + by + c = 0 passes through a fixed point whose coordinates are given by

(A) (1/2 , 1/3)

(B) (2, 3)

(C) (3, 2)

(D) (1/3 , 1/2)

Ans: (A)

Question:30. Area of the parallelogram whose sides are x cosα + y sinα = p , x cosα + y sinα = q , xcosβ + y sinβ = r, x cosβ + y sinβ = s is

(A) pq + rs

(B) |pq tanα + rs tanβ|

(C) |(p – q)(r – s)cosec(α – β)|

(D) |(p – q)(r – s) tan(α + β)|

Ans: (C)

Question:31. Consider the equation y – y1 = m(x-x1). If m and x1 are fixed and different lines are drawn for different values of y1, then

(A) the line will pass through a fixed point

(B) there will be a set of parallel lines.

(C) all the lines will be parallel to the line y=y1.

(D) none of these

Ans: (B)

Question:32. The medians AD and BE of a triangle ABC with vertices A(0, b), B(0, 0) and C(a, 0) are perpendicular to each other if

(A) b = √2a

(B) a = √2b

(C) b = -√2a

(D) none of these

Ans: (B)

Question:33. If ΔOAB is an equilateral triangle (O is the origin and A is a point on the x-axis), then centroid of the triangle will be

(A) always rational

(B) rational if B is rational

(C) rational if A is rational

(D) never rational

(a point P(x, y) is said to be rational if both x and y are rational)

Ans: (D)

Question:34. Let 2x–3y =0 be a given line and P (sinθ, 0) and Q (0, cosθ) be the two points. Then P and Q lie on the same side of the given line, if q lies in the

(D) none of these

Ans: (B)

Question:35. Two sides of a rhombus ABCD are parallel to the lines y = x + 2 and y = 7x + 3. If the diagonals of the rhombus intersect at the point (1, 2) and the vertex A is on the y-axis, then possible co-ordinates of A is

(A) (0, 0)

(B) (0, 1)

(C) (0, 3)

(D) (0, -1)