List of top Questions asked in CBSE Class XI

Find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity, and the length of the latus rectum of the ellipse \(\dfrac{x^2}{100}+\dfrac{y^2}{400}=1\)

Find \(sin \frac{x}{2},\,cos \frac{x}{2} \,and \,tan\frac{ x}{2}\, for \,cos x=-\frac{1}{2} \,for\,cosx=-\frac{1}{3},\) in quadrant III.

Find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity, and the length of the latus rectum of the ellipse \(\dfrac{x^2}{49}+\dfrac{y^2}{36}=1\)

Find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity, and the length of the latus rectum of the ellipse \(\dfrac{x^2}{16}+\dfrac{y^2}{9}=1\).
Find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity, and the length of the latus rectum of the ellipse \(\dfrac{x^2}{4}+\dfrac{y^2}{25}=1\)
Find the coordinates of the foci, the vertices, the length of the major axis, the minor axis, the eccentricity, and the length of the latus rectum of the ellipse\( \dfrac{x^2}{36} + \dfrac{y^2}{16} = 1\)
Find \(sin \frac{x}{2},\,cos \frac{x}{2} \,and \,tan\frac{ x}{2}\, for \,cos x=-\frac{1}{2} \,for\,cosx=-\frac{1}{3},\) in quadrant III.

Find the equation of the parabola that satisfies the following conditions: Vertex \((0, 0)\), passing through \((5, 2) \)and symmetric with respect to the y-axis

\(\text{tan x}=-\frac{4}{3},\text{x\, in\, quadrant \,II.}\)
Prove that  \(\frac{(sin 7x+sin 5x)+(sin 9x+sin3x)}{cos 7x+cos5x)+(cos9x+cos3x)}=tan\,6x.\)
Find the equation of the parabola that satisfies the following conditions: Vertex \((0, 0)\) focus \((-2, 0)\)
Find the sum to indicated number of terms in each of the geometric progressions in Exercises 7 to 10: 0.15, 0.015, 0.0015, ... 20 terms.

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0); focus (3, 0)

Find the equation of the parabola that satisfies the following conditions: Focus\( (0, -3);\) directrix \(y = 3\)

Find the equation of the parabola that satisfies the following conditions: Focus \((6, 0)\); directrix \(x = -6\).
For what values of x, the numbers \(\frac{-2}{7}\), x , \(\frac{-7}{2}\) are in G.P.?
Find the coordinates of the focus, the axis of the parabola, the equation of directrix, and the length of the latus rectum for \(x^2 = -9y\)

Prove that (sin 3x+sin x) sinx+(cos 3x–cos x) cos x=0

Find the coordinates of the focus, the axis of the parabola, the equation of directrix, and the length of the latus rectum for \(y^2 = 10x\)

Which term of the following sequences: 

(a) 2 ,\(2\sqrt{2}\) , 4 ,.... is 128 ?

 (b) \(\sqrt{3}\), 3, \(3\sqrt{3}\),... is 729 ? 

(c) \(\frac{1}{3},\frac{1}{9},\frac{1}{27}\) ,.... is \(\frac{1}{19683}\) ?

Prove that \(tan\,4x=\frac{4\,tanx(1-tan^2x)}{1-6\,tan^2x+tan^4x}\).

Find the coordinates of the focus, the axis of the parabola, the equation of directrix, and the length of the latus rectum for \(y^2 = 12x\).

Prove that cotx cot2x-cot2x cot3x-cot3x cotx=1.

Find the coordinates of the focus, the axis of the parabola, the equation of directrix, and the length of the latus rectum for \(x^2 = - 16y\)

Find the coordinates of the focus, the axis of the parabola, the equation of directrix, and the length of the latus rectum for \(x^2 = 6y\)