English Medium इयत्ता १० - CBSE Important Questions for Mathematics

Prove that the lengths of the tangents drawn from an external point to a circle are equal.

Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

Prove that a parallelogram circumscribing a circle is a rhombus.

Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

Prove that, if a line is drawn parallel to one side of a triangle to intersect the other two sides, then the two sides are divided in the same ratio.

Prove that, if a line is drawn parallel to one side of a triangle to intersect the other two sides, then the two sides are divided in the same ratio.

Prove that, if a line is drawn parallel to one side of a triangle to intersect the other two sides, then the two sides are divided in the same ratio.

Prove that `sqrt(5)` is an irrational number. 

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2∠OPQ.

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segments joining the points of contact to the centre.

If AD and PM are medians of triangles ABC and PQR, respectively where ΔABC ~ ΔPQR, prove that `("AB")/("PQ") = ("AD")/("PM")`.

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 circular ends are 20 cm and 12 cm, respectively. Find the height of the bucket and the area of metal sheet used in making the bucket. (use π = 3.14)

A pole 6 m high casts a shadow `2sqrt(3)` m long on the ground, then the Sun’s elevation is ______.

In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find the length of the arc.  (Use π = `22/7`)

In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find the area of the sector formed by the arc. (Use π = `22/7`)

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.

Prove that `(sin "A" - 2sin^3 "A")/(2cos^3 "A" - cos "A") = tan "A"`

As observed from the top of a 100 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships. [Use `sqrt3` = 1.732]