RD Sharma XI (2020, 2021)_Volume 2 - GeniusJnr

Construct a histogram for the following data:
 

Find the median of the following data (1-8)
83, 37, 70, 29, 45, 63, 41, 70, 34, 54

Find the equation of a line making an angle of 150° with the x-axis and cutting off an intercept 2 from y-axis.

Find the mode and median of the data: 13, 16, 12, 14, 19, 12, 14, 13, 14
By using the empirical relation also find the mean.

Find the equation of the straight line passing through the point (6, 2) and having slope − 3.

Find the equation of the straight lines passing through the following pair of points:
(i) (0, 0) and (2, −2)
(ii) (a, b) and (a + c sin α, b + c cos α)
(iii) (0, −a) and (b, 0)
(iv) (a, b) and (a + b, a − b)
(v) (at₁, a/t₁) and (at₂, a/t₂)
(vi) (a cos α, a sin α) and (a cos β, a sin β)

Find the equation to the straight line
(i) Cutting off intercepts 3 and 2 from the axes.
(ii) Cutting off intercepts − 5 and 6 from the axes.

Find the equation of a line for which
(i) p = 5, α = 60°
(ii) p = 4, α = 150°
(iii) p = 8, α = 225°
(iv) p = 8, α = 300°

A line passes through a point A (1, 2) and makes an angle of 60° with the x-axis and intersects the line x + y = 6 at the point P. Find AP.

Reduce the equation $\sqrt{3}$ x + y + 2 = 0 to:
(i) slope-intercept form and find slope and y-intercept;
(ii) intercept form and find intercept on the axes;
(iii) the normal form and find p and α.

Find the point of intersection of the following pairs of lines:
(i) 2x − y + 3 = 0 and x + y − 5 = 0
(ii) bx + ay = ab and ax + by = ab.
(iii) $y=m_1 x+\frac{a}{m_1} and y=m_{2 }x+\frac{a}{m_2}.$

Prove that the following sets of three lines are concurrent:
(i) 15x − 18y + 1 = 0, 12x + 10y − 3 = 0 and 6x + 66y − 11 = 0

(ii) 3x − 5y − 11 = 0, 5x + 3y − 7 = 0 and x + 2y = 0

(iii) $\frac{x}{a}+\frac{y}{b}=1,\frac{x}{b}+\frac{y}{a}=1 \mathrm{and} y=x.$