English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

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 zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:

`q(x) = sqrt(3)x^2 + 10x + 7sqrt(3)`

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 zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients:

g(x) = a(x² + 1) – x(a² + 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`

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α²β + αβ²

If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α⁴ + β⁴ 

If α and β are the zeroes of the quadratic polynomial f(x) = ax² + bx + c, then evaluate `1/(aalpha + b) + 1/(abeta + b)`.

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

If α and β are the zeros of the quadratic polynomial f(x) = ax² + bx + c, then evaluate `a(α^2/β + β^2/α) + b(α/β + β/α)`.