List of top Mathematics Questions asked in CBSE Class X

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.
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
a circle with the two tangents TP and TQ
Fig. 10.11
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 \(\theta\).
For the following APs, write the first term and the common difference:
(i) 3, 1, − 1, − 3 …
(ii) − 5, − 1, 3, 7 …
(iii) \(\frac{1}{3}, \frac{5}{3},\frac{9}{3},\frac{13}{3}\) ,…
(iv) 0.6, 1.7, 2.8, 3.9 …
Draw a circle and two lines parallel to a given line such that one is a tangent and the other, a secant to the circle.
Write first four terms of the A.P. when the first term a and the common difference d are given as follows
(1) a = 10, d = 10
(2) a = − 2, d = 0
(3) a = 4, d = − 3
(4) a = − 1 d =\(\frac{1}{2}\)
(5) a = − 1.25, d = − 0.25
A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle. (Use \(\pi = 3.14\) and \(\sqrt3 = 1.73\))
In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find: 
(i) the length of the arc (ii) area of the sector formed by the arc (iii) area of the segment formed by the corresponding chord
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 :
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 ____ .
How many tangents can a circle have?
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)
In which of the following situations, does the list of numbers involved make as arithmetic progression and why?
(1) The taxi fare after each km when the fare is Rs 15 for the first km and Rs 8 for each additional km.
(2) The amount of air present in a cylinder when a vacuum pump removes \(\frac{1}{4}\) of the air remaining in the cylinder at a time.
(3) The cost of digging a well after every metre of digging, when it costs Rs 150 for the first metre and rises by Rs 50 for each subsequent metre.
(4) The amount of money in the account every year, when Rs 10000 is deposited at compound interest at 8% per annum.

Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, – 3) and B is (1, 4).

If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

Which term of the AP : 3, 15, 27, 39, ……… will be 132 more than its 54th term?
The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
If the 3rd and the 9th 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 3rd term is 12 and the last term is 106. Find the 29th term.

Find the ratio in which the line segment joining A(1, – 5) and B(– 4, 5) is divided by the x-axis. Also find the coordinates of the point of division.

Find the \(31^{st}\) term of an AP whose \(11^{th}\) term is 38 and the \(16^{th}\) term is 73.

A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30° (see Fig. 9.13). Find the distance travelled by the balloon during the interval.

A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground.

Find the ratio in which the line segment joining the points (– 3, 10) and (6, – 8) is divided by (– 1, 6).