**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) x^{2} + y^{2} = 2(x + y)

(B) x^{2} + y^{2} = (x + y)

(C) x^{2} + y^{2} = 2(x – y)

(D) x^{2} + y^{2} = (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 + a^{2} y + 2aT = 0

(B) 2Tx – a^{2}y + 2aT = 0

(C) 2Tx + a^{2}y – 2aT = 0

(D) 2Tx – a^{2}y – 2aT = 0

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Question:9. If A_{1} , A_{2} , A_{3} , … , A_{n} are n points in a plane whose coordinates are (x_{i} , y_{i}), i = 1 , 2 , … , n respectively. A_{1}A_{2} is bisected by the point G_{1} ; G_{1}A_{3} is divided by G_{2} in ratio 1 : 2 and G_{2}A_{4} is divided by G_{3} in the ratio 1 : 3 , G_{3}A_{5} at G_{4} in the ratio 1 : 4 and so on until all the points are exhausted, then the coordinates of fixed point G_{n} – 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) x^{2} + y^{2} = 13

B) x^{2} + y^{2} = 5

(C) y^{2} = 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 15x^{2} + 56xy + 48y^{2} = 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 x^{2} – y^{2} + 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 (m^{2}, 2m), (mm’, m + m’) and (m’^{2}, 2m’) respectively on the line x cosα + y sinα + sin^{2}α/cos^{2}α = 0, then P1, P2, P3 are in

(A) A.P.

(B) G.P.

(C) H.P.

(D) none of these

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