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.
Click to See Answer :
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
Click to See Answer :
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
Click to See Answer :
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
Click to See Answer :
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
Click to See Answer :
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
Click to See Answer :
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
Click to See Answer :
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
Click to See Answer :
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)
Click to See Answer :
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)|
Click to See Answer :
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
Click to See Answer :
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
Click to See Answer :
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)
Click to See Answer :
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
(A) 1st quadrant
(B) 2nd quadrant
(C) 3rd quadrant
(D) none of these
Click to See Answer :
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)
Click to See Answer :
Click to See All Answers :