Question 1 :
In an AP, given $a_3 = 15, S_{10} = 125$, find d and $a_{10}$.
Question 2 :
In an AP, given l = 28, S = 144, and there are total 9 terms. Find a.
Question 3 :
In an AP, given $a = 7, a_{13} = 35$, find d and $S_{13}$.
Question 4 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 3rd term ?
Question 5 :
The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x.
Question 6 :
30th term of the AP: 10, 7, 4, . . . , is
Question 7 :
Find the sum of the following AP: $\frac{1}{15}, \frac{1}{12}, \frac{1}{10}, . .$ , to 11 terms
Question 8 :
The sum of the 4th and 8th terms of an AP is 24 and the sum of the 6th and 10th terms is 44. Find the first three terms of the AP.
Question 9 :
Find the sum of the first 40 positive integers divisible by 6.
Question 11 :
The 17th term of an AP exceeds its 10th term by 7. Find the common difference.
Question 12 :
Does $a_1, a_2, . . ., a_n, . . $ form an AP where $a_n = 9 – 5n$?
Question 13 :
In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, e.g., a section of Class I will plant 1 tree, a section of Class II will plant 2 trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students?
Question 14 :
Find the sum of the following AP: 0.6, 1.7, 2.8, . . ., to 100 terms.
Question 15 :
Find the sum of the following AP: 7 + 10.5 + 14 + . . . + 84
Question 16 :
Check whether – 150 is a term of the AP : 11, 8, 5, 2 . . .
Question 17 :
Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.
Question 18 :
Ramkali saved Rs. 5 in the first week of a year and then increased her weekly savings by Rs. 1.75. If in the nth week, her weekly savings become Rs. 20.75, find n.
Question 19 :
Find the sum of the following AP: –37, –33, –29, . . ., to 12 terms.
Question 20 :
Subba Rao started work in 1995 at an annual salary of Rs. 5000 and received an increment of Rs. 200 each year. In which year did his income reach Rs. 7000?
Question 21 :
The first and the last terms of an AP are 17 and 350 respectively. If the common difference is 9, what is the sum of the AP?
Question 22 :
If the sum of the first n terms of an AP is $4n – n^2$, What is the 10th term ?
Question 23 :
In an AP, given $a_n = 4, d = 2, S_n = –14$, find n and a.
Question 24 :
In an AP, given $a = 8, a_n = 62, S_n = 210$, find n and $d$.
Question 25 :
Find the sum of the following AP: –5 + (–8) + (–11) + . . . + (–230)
Question 26 :
Find the sum of the odd numbers between 0 and 50.
Question 27 :
Find the sum of the following AP: 2, 7, 12, . . ., to 10 terms.
Question 28 :
If the sum of the first n terms of an AP is $4n – n^2$, what is the first term (that is $S_1$)?
Question 29 :
Find the number of terms in the following AP :18, 15.5, 13, . . . , – 47
Question 30 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bc6273b230584979a13.JPG' />
In the above fig. A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, . . . as shown in above figure. What is the total length of such a spiral made up of thirteen consecutive semicircles?
Question 31 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b46273b23058497996a.PNG' />
In the above figure, if PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and $\angle BQR = 70^{\circ}$, then $\angle AQB$ is equal to
Question 32 :
A tangent to a circle intersects it in how many point(s)?
Question 33 :
If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of $80^{\circ}$, then $\angle POA$ is equal to
Question 34 :
Is it TRUE or FALSE, that the angle between two tangents to a circle may be $0^{\circ}$?
Question 35 :
A chord PQ of a circle is parallel to the tangent drawn at a point R of the circle. Does R bisects the arc PRQ?
Question 36 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b4f273b230584979976.PNG' />
According to the above figure, Is it TRUE or FALSE that BOA is a diameter of a circle and the tangent at a point P meets BA extended at T. If $\angle PBO = 30^{\circ}$, then $\angle PTA$ is equal to $30^{\circ}$?
Question 37 :
In two concentric circles , the chord of the larger circle , which touches the smaller circle , is bisected at the point of contact . Is this statement true ?
Question 38 :
What is the common point of a tangent to a circle and the circle called?
Question 39 :
What is a line intersecting a circle in two points called?
Question 40 :
Is it TRUE or FALSE, that if a chord AB subtends an angle of $60^{\circ}$ at the centre of a circle, then angle between the tangents at A and B is also $60^{\circ}$?
Question 41 :
Does a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A?
Question 42 :
Is it TRUE or FALSE, that AB is a diameter of a circle and AC is its chord such that $\angle BAC = 30^{\circ}$. If the tangent at C intersects AB extended at D, then BC = BD?
Question 43 :
From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is
Question 44 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bcc273b230584979a1a.JPG' />
The above image represents two tangents TP and TQ drawn to a circle with centre O from an external point T . Then
Question 45 :
State true or false. Lengths of tangents from an external point to a circle are equal.
Question 46 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b49273b23058497996f.PNG' />
In the above figure, tangents PQ and PR are drawn to a circle such that $\angle RPQ = 30^{\circ}$. A chord RS is drawn parallel to the tangent PQ. What is the value of $\angle RQS$?
Question 47 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b44273b230584979967.PNG' />
In the above figure, AT is a tangent to the circle with centre O such that OT = 4 cm and $\angle OTA = 30^{\circ}$. Then AT is equal to
Question 48 :
How many parallel tangents at the most can a circle have?
Question 49 :
The opposite sides of a quadrilateral circumscribing a circle subtend ________ angles at the centre of the circle.
Question 50 :
Is it TRUE or FALSE, that if angle between two tangents drawn from a point P to a circle of radius a and centre O is $90^{\circ}$, then OP = $a \sqrt{2}$ ?
Question 51 :
If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is
Question 53 :
State true or false. Tangent is perpendicular to the radius through the point of contact.
Question 54 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bcc273b230584979a1b.JPG' />
PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T (see the above image). Find the length TP.
Question 55 :
If angle between two radii of a circle is $130^{\circ}$, the angle between the tangents at the ends of the radii is :
Question 56 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19b4f273b230584979977.PNG' />
According to the above figure, Is it TRUE or FALSE that PQL and PRM are tangents to the circle with centre O at the points Q and R, respectively and S is a point on the circle such that $\angle SQL = 50^{\circ}$ and $\angle SRM = 60^{\circ}$. Then $\angle QSR$ is equal to $40^{\circ}$?
Question 57 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a4b273b230584979916.jpg' />
In the above figure, XY and X′Y′ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X′Y′ at B. ∠ AOB = ?
Question 58 :
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 .
Question 59 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19bcb273b230584979a19.PNG' />
In the above case, PQ is called a non-intersecting line with respect to the circle . TRUE OR FALSE ?
Question 60 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b19a4b273b230584979917.JPG' />
In the above figure, a triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the sides AB and AC.
