English Medium इयत्ता १० - CBSE Question Bank Solutions for Mathematics

The point A(2, 7) lies on the perpendicular bisector of line segment joining the points P(6, 5) and Q(0, – 4).

Name the type of triangle formed by the points A(–5, 6), B(–4, –2) and C(7, 5).

Find the points on the x-axis which are at a distance of `2sqrt(5)` from the point (7, – 4). How many such points are there?

What type of a quadrilateral do the points A(2, –2), B(7, 3), C(11, –1) and D(6, –6) taken in that order, form?

Find the value of a, if the distance between the points A(–3, –14) and B(a, –5) is 9 units.

Find a point which is equidistant from the points A(–5, 4) and B(–1, 6)? How many such points are there?

If (– 4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the interior of the triangle.

Ayush starts walking from his house to office. Instead of going to the office directly, he goes to a bank first, from there to his daughter’s school and then reaches the office. What is the extra distance travelled by Ayush in reaching his office? (Assume that all distances covered are in straight lines). If the house is situated at (2, 4), bank at (5, 8), school at (13, 14) and office at (13, 26) and coordinates are in km.

The zeroes of the quadratic polynomial x² + kx + k, k ≠ 0 ______.

If the zeroes of the quadratic polynomial ax² + bx + c, c ≠ 0 are equal, then ______.

Which of the following is not the graph of a quadratic polynomial?

The point P(–2, 4) lies on a circle of radius 6 and centre C(3, 5).

The points A(–1, –2), B(4, 3), C(2, 5) and D(–3, 0) in that order form a rectangle.

If the point A(2, – 4) is equidistant from P(3, 8) and Q(–10, y), find the values of y. Also find distance PQ.

If (a, b) is the mid-point of the line segment joining the points A(10, –6) and B(k, 4) and a – 2b = 18, find the value of k and the distance AB.

The centre of a circle is (2a, a – 7). Find the values of a if the circle passes through the point (11, –9) and has diameter `10sqrt(2)` units.

1. Make a labelled figure on the basis of the given information and calculate the distance of the boat from the foot of the observation tower.
2. After 10 minutes, the guard observed that the boat was approaching the tower and its distance from tower is reduced by 240(`sqrt(3)` - 1) m. He immediately raised the alarm. What was the new angle of depression of the boat from the top of the observation tower?

Based on the above information answer the following questions using the coordinate geometry.

1. Find the distance between Lucknow (L) to Bhuj (B).
2. If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
3. Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P)
   [OR]
   Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).

Find a and b so that the numbers a, 7, b, 23 are in A.P.

In an A.P. if the sum of third and seventh term is zero. Find its 5^th term.