List of top Mathematics Questions asked in CBSE X

A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in Fig. 11.9. Find : 
(i) the total length of the silver wire required.
(ii) the area of each sector of the brooch.

Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope (see Fig. 11.8). Find (i) the area of that part of the field in which the horse can graze. (ii) the increase in the grazing area if the rope were 10 m long instead of 5 m. (Use π = 3.14)

The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.

A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle. (Use π = 3.14 and \(\sqrt3\) = 1.73)

In triangle ABC, right-angled at B, if tan A =\(\frac{ 1}{\sqrt{3}}\). find the value of:
(i) sin A cos C + cos A sin C
(ii) cos A cos C – sin A sin C

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

If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ∠POA is equal to

In \(Δ\)PQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.

From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm². [Use \(\pi=\frac{22}{ 7}\)]

In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110°, then ∠PTQ is equal to

From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is

State whether the following are true or false. Justify your answer.
(i) The value of tan A is always less than 1.
(ii) sec A = \(\frac{12}{5}\) for some value of angle A.
(iii) cos A is the abbreviation used for the cosecant of angle A.
(iv) cot A is the product of cot and A.
(v) sin \(\theta\) = \(\frac{4}{3}\) for some angle \(\theta\).

A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q so that OQ = 12 cm. Length PQ is :

A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs 500 per m². (Note that the base of the tent will not be covered with canvas.) [Use \(\pi =\frac{22 }{7}\)]

A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding : (i) minor segment (ii) major sector. (Use π = 3.14)

Fill in the blanks :

1. A tangent to a circle intersects it in ____ point(s).
2. A line intersecting a circle in two points is called a ____ .
3. A circle can have ____ parallel tangents at the most.
4. The common point of a tangent to a circle and the circle is called ____ .

A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

How many tangents can a circle have?

In \(ΔABC\) right angled at B, AB = 24 cm, BC = 7 m. Determine 
(i) sin A, cos A
(ii) sin C, cos C

Which term of the AP : 3, 15, 27, 39, ……… will be 132 more than its 54^th term?

The 17^th term of an AP exceeds its 10^th term by 7. Find the common difference.

If the 3^rd and the 9^th terms of an AP are 4 and –8 respectively, which term of this AP is zero?

A straight highway leads to the foot of a tower. A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°. Find the time taken by the car to reach the foot of the tower from this point.

An AP consists of 50 terms of which 3^rd term is 12 and the last term is 106. Find the 29^th term.