English Medium कक्षा १० - CBSE Question Bank Solutions

The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.

A ladder has rungs 25 cm apart. (See figure). The rungs decrease uniformly in length from 45 cm at the bottom to 25 cm at the top. If the top and bottom rungs are 2 `1/2` m apart, what is the length of the wood required for the rungs?

[Hint: number of rungs = `250/25+ 1`]

A small terrace at a football field comprises 15 steps, each of which is 50 m long and built of solid concrete. Each step has a rise of `1/4` m and a tread of `1/2` m (See figure). Calculate the total volume of concrete required to build the terrace.

[Hint: Volume of concrete required to build the first step = `1/4 xx 1/2 xx 50  m^3`]

Find how many integers between 200 and 500 are divisible by 8.

Find the value of k for which the equation x² + k(2x + k − 1) + 2 = 0 has real and equal roots.

If the sum of first m terms of an A.P. is the same as the sum of its first n terms, show that the sum of its first (m + n) terms is zero

If the pth term of an A. P. is `1/q` and qth term is `1/p`, prove that the sum of first pq terms of the A. P. is `((pq+1)/2)`.

Find the value of p, for which one root of the quadratic equation px² – 14x + 8 = 0 is 6 times the other.

Which term of the progression 20, 19`1/4`,18`1/2`,17`3/4`, ... is the first negative term?

If ad ≠ bc, then prove that the equation (a² + b²) x² + 2 (ac + bd) x + (c² + d²) = 0 has no real roots.

If the ratio of the sum of the first n terms of two A.Ps is (7n + 1) : (4n + 27), then find the ratio of their 9^th terms.

Find the sum of first 8 multiples of 3

Find all zeroes of the polynomial `(2x^4 - 9x^3 + 5x^2 + 3x - 1)` if two of its zeroes are `(2 + sqrt3)`  and `(2 - sqrt3)`

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

`p(x) = x^2 + 2sqrt2x + 6`

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

`q(x)=sqrt3x^2+10x+7sqrt3`

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

`f(x)=x^2-(sqrt3+1)x+sqrt3`

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

`g(x)=a(x^2+1)-x(a^2+1)`

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α - β

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/alpha-1/beta`

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/alpha+1/beta-2alphabeta`