CBSE Class 10 Mathematics (Standard) — Long Answer Questions

Determine graphically, the coordinates of vertices of a triangle whose equations are $2x - 3y + 6 = 0$; $2x + 3y - 18 = 0$ and $x = 0$. Also, find the area of this triangle.

A faster train takes one hour less than a slower train for a journey of 200 km. If the speed of the slower train is 10 km/hr less than that of the faster train, find the speeds of the two trains.

OR The sum of the areas of two squares is $640 \text{ m}^2$. If the difference in their perimeters is 64 m, find the sides of the two squares.

State and prove Basic Proportionality Theorem.

OR In the given figure, CM and RN are respectively the medians of Δ ABC and Δ PQR. If Δ ABC ~ Δ PQR, then prove that : (i) Δ AMC ~ Δ PNR (ii) Δ CMB ~ Δ RNQ

The mean of the following frequency distribution is 35. Find the values of x and y, if the sum of frequencies is 25 : Class: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60, 60-70 Frequency: 1, x, 5, 7, y, 3, 1