List of top Mathematics Questions

Evaluate \(\displaystyle\sum_{k=1}^{11}\) (2 + 3k).
Find the equation of the line parallel to y-axis and drawn through the point of intersection of the lines  \(x - 7y+ 5 = 0\) and \(3x + y = 0.\)
Find the equation of a line drawn perpendicular to the line \(\frac{x}{4} +\frac{ y}{6} = 1 \) through the point where it meets the y-axis
Find the area of the triangle formed by the lines  \(y -x = 0, x + y = 0\) and \(x - k = 0.\)

Find the equation for the ellipse that satisfies the given conditions: Vertices \((0, ±13),\) foci \((0, ±5)\)

Find the equation for the ellipse that satisfies the given conditions:Vertices (±6,0),foci (±4,0)
Find the value of p so that the three lines  \( 3x + y - 2 = 0, px + 2y - 3 = 0\) and  \(2x - y - 3 = 0\) may intersect at one point

Find the equation for the ellipse that satisfies the given conditions: Ends of major axis \((±3,0)\) ends of the minor axis \((0,±2)\)

Find the equation for the ellipse that satisfies the given conditions: Ends of major axis(0,±√5) ends of minor axis ( ±1,0)
If three lines whose equations are y = m1x + c1, y = m2x + c2 and y = m3x + c3 are concurrent, then show that m1 (c2 – c3) + m2 (c3 – c1) + m3 (c1 – c2) = 0.
Find the equation of the lines through the point (3, 2) which make an angle of 45° with the line  \(x -2y = 3.\)
Find the equation of the line passing through the point of intersection of the lines \(4x + 7y - 3 = 0\) and \(2x - 3y+ 1 = 0\)  that has equal intercepts on the axes.
Find the equation for the ellipse that satisfies the given conditions: Length of major axis 26, foci (±5,0) 
Find the equation for the ellipse that satisfies the given conditions: Length of minor axis 16, foci (0,±6) 
Find the equation for the ellipse that satisfies the given conditions: Foci \((±3,0),\) \(a=5\)

Find the equation for the ellipse that satisfies the given conditions \(b =3\), \(c =4\), center at the origin; foci on the \(x-axis.\) 

Find the equation for the ellipse that satisfies the given conditions:Centre at (0,0), major axis on the y-axis and passes through the points(3,2) and (1,6). 

Show that the equation of the line passing through the origin and making an angle θ with the line \(y=mx+c\) is \(\frac{y}{x}=\frac{m±tanθ}{1-+mtanθ}\)
A point is on the x-axis. What are its y-coordinates and z-coordinates?

Find the equation for the ellipse that satisfies the given conditions:Major axis on the x-axis and passes through the points (4,3) and (6,2).

A point is in the XZ plane. What can you say about its y-coordinate?
The sum of first three terms of a G.P. is \(\frac{39}{10}\) and their product is 1. Find the common ratio and the terms.
Name the octants in which the following points lie:
(1, 2, 3), (4, -2, 3), (4, -2, -5), (4, 2, -5), (-4, 2, -5), (-4, 2, 5), (-3, -1, 6), (2, -4, -7).
Fill in the blanks:
(i) The x-axis and y-axis taken together determine a plane known as_______.
(ii) The coordinates of points in the XY-plane are of the form _______.
(iii) Coordinate planes divide the space into ______ octants.
Find the distance between the following pairs of points:
(i) (2, 3, 5) and (4, 3, 1) (ii) (–3, 7, 2) and (2, 4, –1)
(iii) (–1, 3, – 4) and (1, –3, 4) (iv) (2, –1, 3) and (–2, 1, 3)