List of top Questions asked in CBSE Class XI

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 \(b =3\), \(c =4\), 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)

How many terms of G.P. \(3,3^2,3^3\), … are needed to give the sum 120?

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola \(\dfrac{y^2}{9}-\dfrac{x^2}{27}=1\)

The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to n terms of the G.P.

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola \(9y^2-4x^2=37\)

Evaluate \([i^{18}+(\frac{1}{i})^{25}]^3.\)

For any two complex numbers z₁ and z₂, prove that Re (z₁z₂) = Re z₁ Re z₂-Im z₁ Im z₂.

Reduce \((\frac{1}{1-4i}-\frac{2}{1+i})(\frac{3-4i}{5+i})\) to the standard form .

\(if\, x-iy=√\frac{a-ib}{c-id}\) prove that \((x^2y^2)^2=\frac{a^2+b^2}{c^2+d^2}.\)

Find a G.P. for which sum of the first two terms is – 4 and the fifth term is 4 times the third term.

\(if\, x-iy=√\frac{a-ib}{c-id}\) prove that \((x^2y^2)^2=\frac{a^2+b^2}{c^2+d^2}.\)

\(If \,z_1=2-i,z_2=1+i, find \,|\frac{z_1+z_2+1}{z1-z2+1}|.\)