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In an A.P., the sum of first n terms is `n/2 (3n + 5)`. Find the 25th term of the A.P.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Find the sum of all 11 terms of an A.P. whose 6th term is 30.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Rohan repays his total loan of ₹ 1,18,000 by paying every month starting with the first installment of ₹ 1,000. If he increases the installment by ₹ 100 every month, what amount will be paid by him in the 30th installment? What amount of loan has he paid after 30th installment?
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Read the following passage:
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India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs. The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 16000 sets in 6th year and 22600 in 9th year. |
- In which year, the production is 29,200 sets?
- Find the production in the 8th year.
OR
Find the production in first 3 years. - Find the difference of the production in 7th year and 4th year.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
The sum of the 4th and 8th term of an A.P. is 24 and the sum of the 6th and 10th term of the A.P. is 44. Find the A.P. Also, find the sum of first 25 terms of the A.P.
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Solve the equation:
– 4 + (–1) + 2 + 5 + ... + x = 437
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
Three numbers in A.P. have the sum of 30. What is its middle term?
Concept: Sum of First ‘n’ Terms of an Arithmetic Progressions
If A(4, 3), B(-1, y) and C(3, 4) are the vertices of a right triangle ABC, right-angled at A, then find the value of y.
Concept: Distance Formula
If the point P(x, y) is equidistant from the points A(a + b, b – a) and B(a – b, a + b). Prove that bx = ay.
Concept: Distance Formula
If the point P(2, 2) is equidistant from the points A(–2, k) and B(–2k, –3), find k. Also, find the length of AP.
Concept: Distance Formula
In a classroom, 4 friends are seated at the points A, B, C and D as shown in the following figure. Champa and Chameli walk into the class and after observing for a few minutes, Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees.
Using distance formula, find which of them is correct.
Concept: Distance Formula
For what values of k are the points (8, 1), (3, –2k) and (k, –5) collinear ?
Concept: Distance Formula
The long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of the distances travelled by their tips in 24 hours. (Use π = 3.14) ?
Concept: Distance Formula
If A and B are the points (−6, 7) and (−1, −5) respectively, then the distance
2AB is equal to
Concept: Distance Formula
Find the value of y for which the distance between the points A (3, −1) and B (11, y) is 10 units.
Concept: Distance Formula
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is ______.
Concept: Distance Formula
Find the distance between the points (a, b) and (−a, −b).
Concept: Distance Formula
The points (– 4, 0), (4, 0), (0, 3) are the vertices of a ______.
Concept: Distance Formula
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Case Study Trigonometry in the form of triangulation forms the basis of navigation, whether it is by land, sea or air. GPS a radio navigation system helps to locate our position on earth with the help of satellites. |
- Make a labelled figure on the basis of the given information and calculate the distance of the boat from the foot of the observation tower.
- After 10 minutes, the guard observed that the boat was approaching the tower and its distance from tower is reduced by 240(`sqrt(3)` - 1) m. He immediately raised the alarm. What was the new angle of depression of the boat from the top of the observation tower?
Concept: Distance Formula
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In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.
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Based on the above information answer the following questions using the coordinate geometry.
- Find the distance between Lucknow (L) to Bhuj (B).
- If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
- Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P)
[OR]
Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).
Concept: Distance Formula
