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The equation √((x – 2)² + y²) + √((x + 2)² + y²) = 4 represents a/an

1) circle 2) straight lines 3) parabola 4) ellipse Solution: Given √((x – 2)2 + y2) + √((x + 2)2... View Article

If C is the reflection of A(2, 4) in the x-axis and B is the reflection of C in the y-axis, then |AB| is

1) 20 2) 2√5 3) 4√5 4) 4 Solution: Given A = (2,4) So C = (2, -4) B =... View Article

Two vertices of a triangle are (5, -1) and (-2, 3). If orthocentre is the origin then coordinates of the third vertex are

1) (7, 4) 2) (-4, 7) 3) (4, -7) 4) (-4, -7) Solution: Let A(h, k), B(5, -1) and C(-2,... View Article

The intercept of a line between the coordinates axes is divided by point (-5, 4) in the ratio 1 : 2. The equation of the line will be

1) 5x – 8y + 60 = 0 2) 8x – 5y + 60 = 0 3) 2x – 5y... View Article

The lines ax + by + c = 0, where 3a + 2b + 4c = 0 are concurrent at the point

1) (1/2, 3/4) 2) (1, 3) 3) (3, 1) 4) (3/4, 1/2) Solution: Given ax + by + c =... View Article

All points lying inside the triangle formed by the points (1,3), (5,0) and (-1,2) satisfy

1) 3x + 2y ≥ 0 2) 2x + y – 13 ≥ 0 3) 2x – 3y – 12... View Article

The locus of point P which divides the line joining (1, 0) and (2 cos ?, 2 sin ?) internally in the ratio 2 : 3 for all ?, is a

1) Straight line 2) Circle 3) Pair of straight lines 4) Parabola Solution: Let the point P(h, k) divides the... View Article

The area enclosed within the curve |x| + |y| = 1 is

1) √2 2) 1 3) √3 4) 2 Solution: Given equation is |x| + |y| = 1 The diagram of... View Article

The diagonals of a parallelogram PQRS are along the lines x + 3y = 4 and 6x – 2y = 7.Then PQRS must be a

1) Rectangle 2) Square 3) Cyclic quadrilateral 4) Rhombus Solution: Given diagonals are x + 3y = 4 …(i) 6x... View Article

A variable line passes through a fixed point P. The algebraic sum of the perpendicular drawn from (2, 0), (0, 2), and (1, 1) on the line is zero, then the coordinates of the P are

1) (1, –1) 2) (1, 1) 3) (2, 1) 4) (2, 2) Solution: Let the variable line be ax +... View Article

The equation of the line joining the point (3,5) to the point of intersection of the lines 4x + y – 1 = 0 and 7x – 3y – 35 = 0 is equidistant from the points (0,0) and (8,34)

1) True 2) False 3) Nothing can be said 4) None of these Solution: Given lines 4x + y –... View Article

The sides AB, BC, CD and DA of a quadrilateral are x + 2y = 3, x = 1, x – 3y = 4, 5x + y + 12 = 0 respectively.The angle between diagonals AC and BD is

1) 450 2) 600 3) 900 4) 300 Solution: Given equation of the sides are x + 2y = 3... View Article

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

1) 2 2) 0 3) 4 4) 1 Solution: Given 3x + 4y = 9 …(i) y = mx +... View Article

If p and p’ be the distances of origin from the lines x sec α + y cosec α = k and x cos α – y sin α = k cos 2α, then 4p² + p’²

1) k 2) 2k 3) k2 4) 2k2 Solution: Given x sec α + y cosec α = k…(i) The... View Article

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