English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

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) = ______.

Statement A (Assertion): If product of two numbers is 5780 and their HCF is 17, then their LCM is 340.

Statement R (Reason): HCF is always a factor of LCM.

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.

Write the next two terms of the A.P.: `sqrt(27), sqrt(48), sqrt(75)`......

The number of quadratic polynomials having zeroes –5 and –3 is ______.

If α and β are the zeroes of the polynomial x² – 1, then the value of (α + β) is ______.

Show the 6ⁿ cannot end with digit 0 for any natural number 'n'.

Find the HCF and LCM of 72 and 120.