(English Medium) ICSE Class 10 - CISCE Question Bank Solutions for Mathematics

How many terms of the A.P. 25, 22, 19, … are needed to give the sum 116 ? Also find the last term.

How many terms of the A.P. 24, 21, 18, … must be taken so that the sum is 78? Explain the double answer.

If the third term of an A.P. is 1 and 6th term is – 11, find the sum of its first 32 terms.

Show that a₁, a₂, a₃, … form an A.P. where a_n is defined as a_n = 3 + 4n. Also find the sum of first 15 terms.

If a_n = 3 – 4n, show that a₁, a₂, a₃,... form an AP. Also find S₂₀.

 Find the common difference of an A.P. whose first term is 5 and the sum of first four terms is half the sum of next four terms.

The sum of first n terms of an A.P. whose first term is 8 and the common difference is 20 equal to the sum of first 2n terms of another A.P. whose first term is – 30 and the common difference is 8. Find n.

The sum of first six terms of an arithmetic progression is 42. The ratio of the 10th term to the 30th term is `(1)/(3)`. Calculate the first and the thirteenth term.

In an A.P., the sum of its first n terms is 6n – n². Find is 25th term.

If x – 2 is a factor of x³ – kx – 12, then the value of k is ______.

The coordinates of the vertices of ΔABC are respectively (–4, –2), (6, 2), and (4, 6). The centroid G of ΔABC is ______.

Find the value of 'a' if x – a is a factor of the polynomial 3x³ + x² – ax – 81.

The 5^th term and the 9^th term of an Arithmetic Progression are 4 and – 12 respectively.

Find:

1. the first term
2. common difference
3. sum of 16 terms of the AP.

Which term of the Arithmetic Progression (A.P.) 15, 30, 45, 60...... is 300?

Hence find the sum of all the terms of the Arithmetic Progression (A.P.)

In the given diagram, ABC is a triangle, where B(4, – 4) and C(– 4, –2). D is a point on AC.

1. Write down the coordinates of A and D.
2. Find the coordinates of the centroid of ΔABC.
3. If D divides AC in the ratio k : 1, find the value of k.
4. Find the equation of the line BD.

The n^th term of an Arithmetic Progression (A.P.) is given by the relation T_n = 6(7 – n)..

Find:

1. its first term and common difference
2. sum of its first 25 terms

A solid sphere is cut into two identical hemispheres.

Statement 1: The total volume of two hemispheres is equal to the volume of the original sphere.

Statement 2: The total surface area of two hemispheres together is equal to the surface area of the original sphere.

Which of the following is valid?

Find the coordinates of the centroid P of the ΔABC, whose vertices are A(–1, 3), B(3, –1) and C(0, 0). Hence, find the equation of a line passing through P and parallel to AB.

An Arithmetic Progression (A.P.) has 3 as its first term. The sum of the first 8 terms is twice the sum of the first 5 terms. Find the common difference of the A.P.

A manufacturing company prepares spherical ball bearings, each of radius 7 mm and mass 4 gm. These ball bearings are packed into boxes. Each box can have a maximum of 2156 cm³ of ball bearings. Find the:

1. maximum number of ball bearings that each box can have.
2. mass of each box of ball bearings in kg.
   (Use π = `22/7`)