List of top Questions asked in CBSE Class XI

Prove that \((cos\,x-cos\, y)^2 + (sin\,x – sin\,y)^2 = 4sin^2 \frac{x-y}{2}\)
For what values of x, the numbers \(\frac{-2}{7}\), x , \(\frac{-7}{2}\) are in G.P.?
Find the equation of the parabola that satisfies the following conditions: Focus \((6, 0)\); directrix \(x = -6\).

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

Prove that sin x+sin 3x+sin 5x+sin 7x=4 cos x cos 2x sin 4x.

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

Reduce the following equations into intercept form and find their intercepts on the axes.
(i)  \(3x+2y-12=0\)
(ii)  \(4x-3y=6\)
(iii)  \(3y+2=0. \)
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 \((-2, 0)\)

Find the equation of the parabola that satisfies the following conditions: Vertex \((0, 0) \)passing through \((2, 3) \)and the axis is along the x-axis

Find the distance of the point (–1, 1) from the line \(12(x + 6) = 5(y – 2)\)
Find the points on the x-axis, whose distances from the line \(\frac{ x}{3}+\frac{y}{4}=1\) are 4 units.
Prove that  \(\frac{(sin 7x+sin 5x)+(sin 9x+sin3x)}{cos 7x+cos5x)+(cos9x+cos3x)}=tan\,6x.\)
Prove that  \(sin 3x + sin 2x – sin x = 4sin \,x cos\, \frac{x}{2} cos \frac{3x}{2}\)
Find the distance between parallel lines
(i) \(15x + 8y – 34 = 0\) and \(15x + 8y + 31 = 0\)
(ii) \(l (x + y) + p = 0\) and \(l (x + y) – r = 0.\)
Find equation of the line parallel to the line \(3x - 4y + 2 = 0\) and passing through the point (-2, 3).
\(\text{tan x}=-\frac{4}{3},\text{x\, in\, quadrant \,II.}\)
Find equation of the line perpendicular to the line \(x – 7y + 5 = 0\) and having x intercept 3.

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

Find angles between the lines \(\sqrt3x+y=1\) and \(x+\sqrt3y=1.\)
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\( \dfrac{x^2}{36} + \dfrac{y^2}{16} = 1\)
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 \(\dfrac{x^2}{16}+\dfrac{y^2}{9}=1\).
The line through the points (h, 3) and (4, 1) intersects the line \(7x - 9y - 19 = 0\). at right angle. Find the value of h.