problem archive
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200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on (see Fig. 5.5). In how... -
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a strai... -
Which term of the AP: 121, 117, 113, ... is its first negative term? -
The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP. -
A ladder has rungs 25 cm apart. The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and the bottom rungs a... -
The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of \(x\) such that the sum of the numbers of the houses preced... -
A small terrace at a football ground comprises of 15 steps each of which is 50 m long and built of solid concrete. Each step has a rise of \(\frac{1}{... -
The general form of an AP is a, a + d, a + 2d, a + 3d, ... -
A given list of numbers a1, a2, a3, ... is an AP, if the differences a2 - a1, a3 - a2, a4 - a3, ..., give the same value, i.e., if ak+1 - ak is the sa... -
In an AP with first term a and common difference d, the nth term (or the general term) is given by an = a + (n - 1)d. -
The sum of the first n terms of an AP is given by: S = n/2 [2a + (n - 1)d] -
If l is the last term of the finite AP, say the nth term, then the sum of all terms of the AP is given by: S = n/2 (a + l) -
Find a relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5). -
Find a point on the y-axis which is equidistant from the points A(6, 5) and B(-4, 3). -
Find the distance between the following pairs of points: (i) (2, 3), (4, 1) (ii) (-5, 7), (-1, 3) (iii) (a, b), (-a, -b) -
Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2. -
Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear. -
Check whether (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle. -
In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. 7.8. Champa and Chameli walk into the class and after observing for ... -
Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer: (i) (-1, -2), (1, 0), (-1, 2), (-3, 0) (ii) ...