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The equations of the lines through (1, 1) and making angles of 45⁰ with the line x + y = 0 are

1) x - 1= 0, x - y = 0 2) x - y = 0, y - l = 0 3) x + y - 2 = 0, y - 1 = 0 4) x - 1 = 0, y - 1 = 0 Solution: Given line x + y = 0 => y =... View Article

The equation of a straight line, which passes through the point (a cos³ θ, a sin³θ) and perpendicular to the line x sec θ + y cosec θ = a, is

1) x cos θ - y sin θ = a cos 2 θ 2) x cos θ + y sin θ = a cos 2 θ 3) x cos θ + y sin θ - a cos 2 θ = 1 4) x cos θ -y sin θ + a cos 2 θ = -1... View Article

The equations y = ±√3x, y = 1 are the sides of

1) an equilateral triangle 2) a right-angled triangle 3) an isosceles triangle 4) a scalene triangle Solution: Given y = √3x ..(i) y = -√3x... View Article

The straight line 3x + y = 9 divides the line segment joining the points (1, 3) and (2, 7) in the ratio

1) 3 : 4 externally 2) 3 : 4 internally 3) 4 : 5 internally 4) 5 : 6 externally Solution: By section formula if a point (x,y) divides the... View Article

The equations to a pair of opposite sides of parallelogram are x² – 5x + 6 = 0 and y² – 6y + 5 = 0, the equations to its diagonals are

1) x + 4y = 13, y = 4x – 7 2) 4x + y = 13, 4y = x – 7 3) 4x + y = 13, y = 4x – 7 4) y – 4x = 13, y + 4x = 7 Solution: x2 - 5x + 6 = 0 …(i)... View Article

The point of intersection of lines represented by the equation 3x² + 8xy – 3y² + 29x – 3y + 18 = 0 is

(1) (-3/2, -5/2) (2) (2/3, 5/2) (3) (3, -5) (4) none of these Solution: Given 3x2 + 8xy - 3y2 + 29x - 3y + 18 = 0 Comparing above equation... View Article

If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is

1) square 2) circle 3) straight line 4) two intersecting lines Solution: Consider that the perpendicular lines are chosen along the x-axis... View Article

Let A (2, – 3) and B (- 2, 1) be vertices of a ∆ABC. If the centroid of this triangle moves on the line 2x + 3y = 1, then the locus of the vertex C is the line

1) 3x - 2y = 3 2) 2x + 3y = 9 3) 2x - 3y = 7 4) 3x + 2y = 5 Solution: The equation of centroid of a triangle = [(x1+x2+x3)/3, (y1+y2+y3)/3]... View Article

Line L has intercepts a and b on the coordinate axes. When the axes are rotated through a given angle, keeping the origin fixed, the same line L has intercepts p and q, then

(1) a2 + b2 = p2 + q2 (2) a2 + p2 = b2 + q2 (3) 1/a2 + 1/b2 = 1/p2 + 1/q2 (4) none of these Solution: Consider the axes are rotated in the... View Article

The straight lines x + y = 0, 5x + y = 4 and x + 5y = 4 form

1) an isosceles triangle 2) an equilateral triangle 3) a scalene triangle 4) a right angled triangle Solution: Given x + y = 0 ..(i) 5x + y... View Article

A straight line perpendicular to the line 2x + y = 3 is passing through (1, 1). Its y-intercept is

1) 1 2) 2 3) 3 4) 1/2 Solution: Equation of given line is 2x + y = 3 => y = -2x + 3 Here slope is m1 = -2 The perpendicular line will... View Article

The points (2, 5) and (5, 1) are two opposite vertices of a rectangle. If the other two vertices are points on the straight line y = 2x + k, then the value of k is

1) 4 2) 3 3) -4 4) -3 Solution: The given points (2,5) and (5,1) will form a diagonal of the rectangle. so, the midpoint of these points... View Article

The straight lines x + y = 0, 3x + y – 4 = 0, x + 3y – 4 = 0 form a triangle which is

1) isosceles 2) equilateral 3) right angled 4) none of these Solution: Given x + y = 0 …(i) 3x + y - 4 = 0 …(ii) x + 3y - 4 = 0 …(iii) From... View Article

A wholesale merchant wants to start the business of cereal with Rs 24000. Wheat is Rs 400 per quintal and rice is Rs 600 per quintal. He has the capacity to store 200 quintal cereal. He earns the profit of Rs 25 per quintal on wheat and Rs 40 per quintal on rice. If he stores x quintal rice and y quintal wheat, then maximum profit of the objective function is

1) 25x + 40y 2) 40x + 25y 3) 400x + 600y 4) (400 / 40) x + (600 / 25) y Solution: (2) 40x + 25y Let rice be represented by ‘x’ quintals and... View Article

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