English Medium कक्षा १० - CBSE Important Questions

If 7 times the seventh term of the AP is equal to 5 times the fifth term, then find the value of its 12^th term.

In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021-22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year.

Based on the above information answer the following questions.

1. Find the production in the 1^st year
2. Find the production in the 12^th year.
3. Find the total production in first 10 years.
   [OR]
   In how many years will the total production reach 31200 cars?

In an A.P. if the sum of third and seventh term is zero. Find its 5^th term.

If the last term of an A.P. of 30 terms is 119 and the 8^th term from the end (towards the first term) is 91, then find the common difference of the A.P. Hence, find the sum of all the terms of the A.P.

If the first term of an A.P. is 5, the last term is 15 and the sum of first n terms is 30, then find the value of n.

In an A.P., the sum of first n terms is `n/2 (3n + 5)`. Find the 25^th term of the A.P.

Find the sum of all 11 terms of an A.P. whose 6^th term is 30.

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 30^th installment? What amount of loan has he paid after 30^th installment?

Read the following passage:

1. In which year, the production is 29,200 sets?
2. Find the production in the 8^th year.
   OR
   Find the production in first 3 years.
3. Find the difference of the production in 7^th year and 4^th year.

The sum of the 4^th and 8^th term of an A.P. is 24 and the sum of the 6^th and 10^th term of the A.P. is 44. Find the A.P. Also, find the sum of first 25 terms of the A.P.

Solve the equation:

– 4 + (–1) + 2 + 5 + ... + x = 437

Three numbers in A.P. have the sum of 30. What is its middle term?

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.

Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right-angled isosceles triangle.

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.

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.

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.

Two vertices of an isosceles triangle are (2, 0) and (2, 5). Find the third vertex if the length of the equal sides is 3.

Find the points on the x-axis, each of which is at a distance of 10 units from the point A(11, –8).

Point A lies on the line segment PQ joining P(6, -6) and Q(-4, -1) in such a way that `(PA)/( PQ)=2/5` . If that point A also lies on the line 3x + k( y + 1 ) = 0, find the value of k.