English Medium Class 10 - CBSE Question Bank Solutions

Find the sum of the integers between 100 and 200 that are not divisible by 9.

The ratio of the 11^th term to the 18^th term of an AP is 2 : 3. Find the ratio of the 5^th term to the 21^st term, and also the ratio of the sum of the first five terms to the sum of the first 21 terms.

Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to `((a + c)(b + c - 2a))/(2(b - a))`

Solve the equation

– 4 + (–1) + 2 + ... + x = 437

Jaspal Singh repays his total loan of Rs. 118000 by paying every month starting with the first instalment of Rs. 1000. If he increases the instalment by Rs. 100 every month, what amount will be paid by him in the 30^th instalment? What amount of loan does he still have to pay after the 30^th instalment?

The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 m. The flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?

Find the value of a₂₅ – a₁₅ for the AP: 6, 9, 12, 15, ………..

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.

Find the value of 𝑚 so that the quadratic equation 𝑚𝑥(5𝑥 − 6) = 0 has two equal roots.

Solve for x: 9x² – 6px + (p² – q²) = 0

Find the zeroes of the quadratic polynomial 6x² – 3 – 7x and verify the relationship between the zeroes and the coefficients.

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?

Let p be a prime number. The quadratic equation having its roots as factors of p is ______.

If α and β are the zeros of a polynomial f(x) = px² – 2x + 3p and α + β = αβ, then p is ______.

If the zeroes of the polynomial x² + px + q are double in value to the zeroes of the polynomial 2x² – 5x – 3, then find the values of p and q.

Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.

Find the sum of first 20 terms of an A.P. whose n^th term is given as a_n = 5 – 2n.

Find the nature of the roots of the quadratic equation:

4x² – 5x – 1 = 0

Find the value of 'p' for which the quadratic equation p(x – 4)(x – 2) + (x –1)² = 0 has real and equal roots.

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.