Angle between x = 2 and x – 3y = 6 is
1) ∞ 2) tan-1(3) 3) tan-1(1/3) 4) None of these Solution: Given x = 2 …(i) This line is parallel... View Article
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To which of the following types the straight lines represented by 2x + 3y – 7 = 0 and 2x + 3y – 5 = 0 belong?
1) Parallel to each other 2) Perpendicular to each other 3) Inclined at 450 to each other 4) Coincident pair... View Article
Angle between the lines x/a + y/b = 1 and x/a – y/b = 1 is
1) 2 tan-1 (b/a) 2) tan-1 (2ab/(a2 – b2)) 3) tan-1(a2 – b2)/(a2 + b2) 4) none of these Solution:... View Article
The angle between the lines whose intercepts on the axes are a, -b and b, -a respectively, is
1) tan-1(a2 – b2)/ab 2) tan-1(a2 – b2)/2ab 3) tan-1(a2 – b2)/2 4) none of these Solution: Given the intercepts... View Article
The acute angle between the lines y = 3 and y = ?3x + 9 is
1) 300 2) 600 3) 450 4) 900 Solution: Given y = 3 ..(i) y = √3x + 9 ..(ii)... View Article
If a, b, c form a G.P. with common ratio r, the sum of the ordinates of the points of intersection of the line ax + by + c = 0 and the curve x + 2y2 = 0 is
1) -r2/2 2) -r/2 3) r/2 4) r2/2 Solution: Given a, b, c form a G.P. with a common ratio... View Article
The centroid of a triangle lies at the origin and the coordinates of its two vertices are (- 8, 7) are (9, 4). The area of the triangle is
1) 95/6 2) 285/2 3) 190/3 4) 285 Solution: We know the centroid of a triangle is {(x1+x2+x3)/3, (y1+y2+y3)/3} Here... View Article
If the midpoint of join of (x, y+1) and (x + 1, y + 2) is (3/2, 5/2) then the midpoint of join of (x – 1, y + 1) and (x + 1, y – 1) is
1) (-1, -1) 2) (1, 1) 3) (1, -1) 4) (-1, 1) Solution: We know that midpoint of line joining... View Article
The points P(a, b+c), Q (b, c+ a) and R (c, a + b) are such that PQ = QR if
1) a, b, c are in A.P 2) a, b, c are in G.P 3) a, b, c are in... View Article
The slope of the straight line which does not intersect the x-axis is equal to
1) 1/2 2) 1 3) √3 4) 0 Solution: The line which does not intersect the x-axis will be a... View Article
The points (1, 3) and (5, 1) are the opposite vertices of a rectangle. The other two vertices lie on the line y = 2x + c, then the value of c will be
1) 4 2) -4 3) 2 4) –2 Solution: We know that the diagonals of a rectangle bisect each other.... View Article
If a + b + c = 0 and p ? 0 the lines ax + (b + c)y = p, bx + (c + a)y = p and cx + (a + b)y = p
1) Do not intersect 2) Intersect 3) Are concurrent 4) None of these Solution: Given a + b + c... View Article
If a and b are two arbitrary constants, then the straight line (a – 2b) x + (a + 3b)y + 3a + 4b = 0 will pass through
1) (–1, –2) 2) (1, 2) 3) (–2, –3) 4) (2, 3) Solution: Given equation of straight line is (a... View Article
If the straight line ax + by + c = 0 always passes through (1, -2), then a, b, c are
1) In A.P 2) In H.P 3) In G.P 4) None of these Solution: Given line ax + by +... View Article
A straight line moves so that the sum of the reciprocals of its intercepts on two perpendicular lines is constant, then the line passes through
1) A fixed point 2) A variable point 3) Origin 4) None of these Solution: The equation of a straight... View Article
A vertex of square is (3, 4) and diagonal x + 2y = 1, then the second diagonal which passes through given vertex will be
1) 2x – y + 2 = 0 2) x + 2y = 11 3) 2x – y = 2... View Article
The diagonal passing through origin of a quadrilateral formed by x = 0, y = 0, x + y = 1 and 6x + y = 3, is
1) 3x – 2y = 0 2) 2x – 3y = 0 3) 3x + 2y = 0 4) None... View Article
The ends of the base of an isosceles triangle are at (2a, 0) and (0, a). The equation of one sides is x = 2a.The equation of the other side is
1) x + 2y – a = 0 2) x + 2y = 2a 3) 3x + 4y – 4a... View Article
The opposite vertices of a square are (1, 2) and (3, 8), then the equation of a diagonal of the square passing through the point (1, 2), is
1) 3x – y – 1 = 0 2) 3y – x – 1 = 0 3) 3x + y... View Article
For the lines 2x + 5y = 7 and 2x + 5y = 9, which of the following statements is true ?
1) Lines are parallel 2) Lines are coincident 3) Lines are intersecting 4) Lines are perpendicular Solution: Given 2x +... View Article
