PRACTICE TEST – I
Question:1. Let P and Q be the points on the line joining A(–2 , 5) and B(3 , 1) such that AP = PQ = QB , then the mid point of PQ is
(A) (1/2 , 3)
(B) (-1/4 ,4)
(C) (2, 3)
(D) (– 1, 4)
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Question:2. P is a point lying on line y = x then maximum value of |PA – PB| , ( where A ≡ (1 , 3) , B ≡(5 , 2)) is
(A) √5
(B) 2√2
(C) √17
(D) 3/ √2
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Question:3. Locus of point of intersection of the perpendicular lines one belonging to (x + y – 2) + λ(2x + 3y – 5) = 0 and other to (2x + y – 11) + λ(x + 2y – 13) = 0 is a
(A) circle
(B) straight line
(C) pair of lines
(D) None of these
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Question:4. A(-3, 4), B(5, 4), C and D form a rectangle. If x – 4y + 7 = 0 is a diameter of the circumcircle of the rectangle ABCD then area of rectangle ABCD is
(A) 8
(B) 16
(C) 32
(D) 64
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Question:5. The triangle ABC has medians AD, BE, CF. AD lies along the line y = x + 3 , BE lies along the line y = 2x + 4, AB has length 60 and angle C = 90°, then the area of ΔABC is
(A) 400
(B) 200
(C) 100
(D) none of these
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Question:6. A line passes through (1, 0). The slope of the line, for which its intercept between y = x – 2 and y = -x + 2 subtends a right angle at the origin, is
(A) ± 2/3,
(B) ± 3/2
(C) ± 1
(D) none of these
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Question:7. The locus of the image of origin in line rotating about the point (1 , 1) is
(A) x2 + y2 = 2(x + y)
(B) x2 + y2 = (x + y)
(C) x2 + y2 = 2(x – y)
(D) x2 + y2 = (x – y)
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Question:8. A line through the point (–a, 0) cuts from the second quadrant a triangular region with area T. The equation for the line is
(A) 2Tx + a2 y + 2aT = 0
(B) 2Tx – a2y + 2aT = 0
(C) 2Tx + a2y – 2aT = 0
(D) 2Tx – a2y – 2aT = 0
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Question:9. If A1 , A2 , A3 , … , An are n points in a plane whose coordinates are (xi , yi), i = 1 , 2 , … , n respectively. A1A2 is bisected by the point G1 ; G1A3 is divided by G2 in ratio 1 : 2 and G2A4 is divided by G3 in the ratio 1 : 3 , G3A5 at G4 in the ratio 1 : 4 and so on until all the points are exhausted, then the coordinates of fixed point Gn – 1 so obtained will be
(A) $ \displaystyle ( \sum_{i=1}^{i=n}\frac{i x_i}{n} , \sum_{i=1}^{i=n}\frac{i y_i}{n} ) $
(B) $ \displaystyle ( \sum_{i=1}^{i=n}\frac{ x_i}{n} , \sum_{i=1}^{i=n}\frac{ y_i}{n} ) $
(C) $ \displaystyle ( \sum_{i=1}^{i=n}\frac{(i-1) x_i}{(n-1)} , \sum_{i=1}^{i=n}\frac{(i-1) y_i}{(n-1)} ) $
(D) $ \displaystyle ( n\sum_{i=1}^{i=n}x_i , n\sum_{i=1}^{i=n}y_i ) $
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Question:10. The vertex A of a triangle ABC is the point (-2, 3) whereas the line perpendicular to the sides AB and AC are x – y – 4 = 0 and 2x – y – 5 = 0 respectively. The right bisectors of sides meet at P(3/2 , 5/2) . Then the equation of the median of side BC is
(A) 5x + 2y = 10
(B) 5x – 2y = 16
(C) 2x – 5y = 10
(D) none of these
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Question:11. The orthocentre of a triangle whose vertices are (0, 0), (√3 , 0) and (0, √6) is
(A) (2, 1)
(B) (3, 2)
(C) (4, 1)
(D) none of these
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Question:12. The locus of a point P which divides the line joining (1, 0) and (2 cosθ, 2 sinθ) internally in the ratio 2 : 3 for all θ ∈ R is
(A) a straight line
(B) a circle
(C) a pair of straight line
(D) a parabola
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Question:13. Let ax + by + c = 0 be a variable straight line, where a, b and c are 1st, 3rd and 7th terms of some increasing A.P. Then the variable straight line always passes through a fixed point which lies on
(A) x2 + y2 = 13
B) x2 + y2 = 5
(C) y2 = 9x
(D) 3x + 4y = 9
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Question:14. The image of the point (3, 8) with respect to the line x + 3y = 7 is
(A) (–1, –4)
(B) (–1, 4)
(C) (1, 4)
(D) none of these
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Question:15. Number of points lying on the line 7x + 4y + 2 = 0 which is equidistant from the lines 15x2 + 56xy + 48y2 = 0 is
(A) 0
(B) 1
(C) 2
(D) 4
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Question:16. The point (4, 1) undergoes the following three transformations successively
(a) Reflection about the line y = x
(b) Transformation through a distance 2 units along the positive direction of the x-axis.
(c) Rotation through an angle p/4 about the origin in the anti clockwise direction.
The final position of the point is given by the co-ordinates
(A) (-4/√2 , 1/√2)
(B) (-1/√2 , 7/√2)
(C) (-1/√2 , 4/√2)
(D) (-3/√2 , 4/√2 )
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Question:17. The three lines 4x – 7y + 10 = 0, x + y = 5 and 7x + 4y = 15 form the sides of a triangle. Then the point (1, 2) is its
(A) centroid
(B) incentre
(C) orthocentre
(D) none of these
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Question:18. If (-6, -4) and (3, 5) are the extremities of the diagonal of a parallelogram and (-2, 1) is its third vertex, then its fourth vertex is
(A) (-1, 0)
(B) (0, -1)
(C) (-1, 1)
(D) none of these
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Question:19. Area of the triangle formed by the line x + y = 3 and angle bisector of the pair of straight lines x2 – y2 + 2y – 1 = 0 is
(A) 2 sq. units
(B) 4 sq. units
(C) 6 sq. units
(D) 8 sq. uints
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Question:20. If P1, P2, P3 be the perpendicular from the points (m2, 2m), (mm’, m + m’) and (m’2, 2m’) respectively on the line x cosα + y sinα + sin2α/cos2α = 0, then P1, P2, P3 are in
(A) A.P.
(B) G.P.
(C) H.P.
(D) none of these
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