English Medium कक्षा १० - CBSE Question Bank Solutions

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.

If two positive integers a and b are written as a = x³ y² and b = xy³; x, y are prime numbers, then HCF (a, b) is ______.

If two positive integers p and q can be expressed as p = ab² and q = a³b; a, b being prime numbers, then LCM (p, q) is ______.

The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is ______.

Can two numbers have 18 as their HCF and 380 as their LCM? Give reasons.

Show that 12ⁿ cannot end with the digit 0 or 5 for any natural number n.

On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?

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).

Let a and b be two positive integers such that a = p³q⁴ and b = p²q³, where p and q are prime numbers. If HCF (a, b) = p^mqⁿ and LCM (a, b) = p^rq^s, then (m + n)(r + s) = ______.