List of top Mathematics Questions asked in CBSE Class XI

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.

Two lines passing through the point (2, 3) intersects each other at an angle of \(60º .\) If slope of one line is 2, find equation of the other line.

Find \(sin \frac{x}{2},\,cos \frac{x}{2} \,and \,tan\,\frac{ x}{2}\, for \,sin\,\,x=\frac{1}{4}\) in quadrant II.

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 the equation of the right bisector of the line segment joining the points (3,4) and (–1,2).

Find the mean deviation about the mean for the data

\(x_i\)	10	30	50	70	90
\(f_i\)	4	24	28	16	8

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 \(36x^2+4y^2=144\)

Find the mean deviation about the median for the data.

\(x_i\)	5	7	9	10	12	15
\(f_i\)	8	6	2	2	2	6

Find the coordinates of the foot of perpendicular from the point \( (–1, 3) \) to the line \(3x – 4y – 16 = 0.\)

The perpendicular from the origin to the line \(y = mx + c\) meets it at the point \((-1, 2)\). Find the values of m and c.

If p and q are the lengths of perpendiculars from the origin to the lines \(x \space cos θ − y \space sin θ = k\space cos 2θ\) and \(x \space sec θ + y\space cosec θ = k\), respectively, prove that \(p^2 + 4q^2 = k^2\)

Find the mean deviation about the median for the data

x_i	15	21	27	30	35
f_i	3	5	6	7	8

Find the mean deviation about the mean for the data.

Income per day	0-100	100-200	200-300	300-400	400-500	500-600	600-700	700-800
Number of persons	4	8	9	10	7	5	4	3

Find the mean deviation about the mean for the data

Height in cms	95-105	105-115	115-125	125-135	135-145	145-155
Number of boys	9	13	26	30	12	10

Find the mean deviation about median for the following data

Marks	0-10	10-20	20-30	30-40	40-50	50-60
Number of Girls	6	8	14	16	4	2

Calculate the mean deviation about median age for the age distribution of 100 persons given below

Age (in years)	16-20	21-25	26-30	31-35	36-40	41-45	46-50	51-55
Number	5	6	12	14	26	12	16	9

Find the mean and variance for the data 6, 7, 10, 12, 13, 4, 8, 12.

Find the mean and variance for the first n natural numbers.

Find the sum to indicated number of terms in each of the geometric progressions in \(\sqrt{7},\sqrt{21},3\sqrt{7},\) ... n terms.

Find the mean and variance for the first 10 multiples of 3.

In the triangle ABC with vertices A (2, 3), B (4, –1) and C (1, 2), find the equation and length of altitude from the vertex A.

Find the sum to indicated number of terms in each of the geometric progressions in 1, – a, \(a^2\), –\(a^3\), ... n terms (if a ≠ – 1).

Find the mean and variance for the data

\(x_i\)	6	10	14	18	24	28	30
\(f_i\)	2	4	7	12	8	4	3

Find the mean and variance for the data

\(x_i\)	62	93	97	98	102	104	106
\(f_i\)	3	2	3	2	6	3	3

If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a and b, then show that \(\frac{1}{p^2}=\frac{1}{a^2}+\frac{1}{b^2}.\)