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NCERT 10th Maths

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 $\frac{1}{4}$ m and a tread of $\frac{1}{2}$ m. (see in below Fig). Calculate the total volume of concrete required to build the terrace.

A ladder has rungs 25 cm apart. (see in below Fig). 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 are $2\frac{1}{2}$ m apart, what is the length of the wood required for the rungs?

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 preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x. [Hint: $S_{x-1} = S_{49} -S_x$ ]

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.

Which term of the AP: 121, 117, 113, …, is its first negative term? [Hint: Find n for $a_n$ <0]

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.). In how many rows are the 200 logs placed and how many logs are in the top row?

A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, . . . as shown in Fig. What is the total length of such a spiral made up of thirteen consecutive semicircles?

A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.

Find the sum of the odd numbers between 0 and 50.

Find the sum of the first 15 multiples of 8.

Find the sum of the first 40 positive integers divisible by 6.

If the sum of the first n terms of an AP is $4n - n^2$ , what is the first term (that is S1)? What is the sum of first two terms? What is the second term? Similarly, find the 3rd, the 10th and the nth terms.

Show that $a_1, a_2, ..., a_n, ...$ form an AP where $a_n$ is defined as $a_n =9-5n$ . Also find the sum of the first 15 terms.

Show that $a_1, a_2, ..., a_n, ...$ form an AP where $a_n$ is defined as $a_n =3+4n$ . Also find the sum of the first 15 terms.

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.

The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?

The first term of an AP is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

How many terms of the AP: 9, 17, 25, … must be taken to give a sum of 636 ?

In an Ap: given l = 28, S = 144, and there are total 9 terms. Find a.

In an Ap: given a = 3, n = 8, S = 192, find d.

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