(English Medium) ICSE Class 10 - CISCE Important Questions for Mathematics

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

In the given figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region.

If the quadratic equation px² − 2√5px + 15 = 0 has two equal roots then find the value of p.

In the following figure, in ΔPQR, seg RS is the bisector of ∠PRQ. If PS = 6, SQ = 8, PR = 15, find QR.

Radha deposited ₹ 400 per month in a recurring deposit account for 18 months. The qualifying sum of money for the calculation of interest is ______.

In the given figure, if A(P-ABC) = 154 cm²  radius of the circle is 14 cm, find

(1) `∠APC` 

(2) l ( arc ABC) .

Given, `x + 2 ≤ x/3 + 3` and x is a prime number. The solution set for x is ______.

Solve the following inequation, write the solution set and represent it on the real number line.

`5x - 21 < (5x)/7 - 6 ≤ -3 3/7 + x, x ∈ R`

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`)

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`)

Prove the identity (sin θ + cos θ)(tan θ + cot θ) = sec θ + cosec θ.

Which of the following equations has 2 as a root?

Prove the following trigonometry identity:

(sin θ + cos θ)(cosec θ – sec θ) = cosec θ ⋅ sec θ – 2 tan θ

The roots of equation (q – r)x² + (r – p)x + (p – q) = 0 are equal.

Prove that 2q = p + r; i.e., p, q, and r are in A.P.

Given that the sum of the squares of the first seven natural numbers is 140, then their mean is ______.

Using step-deviation method, find mean for the following frequency distribution:

A bag contains 3 red and 2 blue marbles. A marble is drawn at random. The probability of drawing a black marble is ______.

If x, y and z are in continued proportion, Prove that:

`x/(y^2.z^2) + y/(z^2.x^2) + z/(x^2.y^2) = 1/x^3 + 1/y^3 + 1/z^3`

A mixture of paint is prepared by mixing 2 parts of red pigments with 5 parts of the base. Using the given information in the following table, find the values of a, b and c to get the required mixture of paint.

While factorizing a given polynomial using the remainder and factor theorem, a student finds that (2x + 1) is a factor of 2x³ + 7x² + 2x – 3.

1. Is the student’s solution correct in stating that (2x + 1) is a factor of the given polynomial?
2. Give a valid reason for your answer.

Also, factorize the given polynomial completely.