English Medium इयत्ता १० - CBSE Question Bank Solutions for Mathematics

The volume of a hemisphere is 19404 cm³. The total surface area of the hemisphere is

Match the following columns:

Find the point on the y-axis which is equidistant from the points (S, - 2) and (- 3, 2).

The line segment joining the points A(2, 1) and B (5, - 8) is trisected at the points P and Q such that P is nearer to A. If P also lies on the line given by  2x - y + k= 0  find the value of k.

Find the coordinates of point A, where AB is a diameter of the circle with centre (–2, 2) and B is the point with coordinates (3, 4).

Find the point on the y-axis which is equidistant from the points (5, −2) and (−3, 2).

A bucket open at the top is in the form of a frustum of a cone with a capacity of 12308.8 cm³. The radii of the top and bottom of the circular ends of the bucket are 20 cm and 12 cm respectively. Find the height of the bucket and also the area of the metal sheet used in making it. (Use π = 3.14)

Write the number of zeroes in the end of a number whose prime factorization is 2² × 5³ × 3² × 17.

The point R divides the line segment AB, where A(−4, 0) and B(0, 6) such that AR=34AB.">AR = `3/4`AB. Find the coordinates of R.

Let ∆ ABC ∽ ∆ DEF and their areas be respectively, 64 cm² and 121 cm². If EF = 15⋅4 cm, find BC.

A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere and hence find the surface area of this sphere.

A container opened at the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container, at the rate of ₹ 50 per litre. Also find the cost of metal sheet used to make the container, if it costs ₹ 10 per 100 cm². (Take π = 3⋅14)

Five years ago, a woman’s age was the square of her son’s age. Ten years hence, her age will be twice that of her son’s age. Find:

1. the age of the son five years ago.
2. the present age of the woman.

The line segment joining the points (3, -1) and (-6, 5) is trisected. The coordinates of point of trisection are ______.

The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally in the ratio ______.

sin (45° + θ) – cos (45° – θ) is equal to ______.

If `sqrt2 sin (60° – α) = 1` then α is ______.

The value of sin² 30° – cos² 30° is ______.

If cos (40° + A) = sin 30°, then value of A is ______.

If cosec θ - cot θ = `1/3`, the value of (cosec θ + cot θ) is ______.