English Medium कक्षा १० - CBSE Question Bank Solutions

Which of the following equations has 2 as a root?

If `(1)/(2)` is a root of the equation `x^2 + kx - (5)/(4) = 0`, then the value of k is ______.

The quadratic equation `2x^2 - sqrt(5)x + 1 = 0` has ______.

Which of the following equations has no real roots?

Find whether 55 is a term of the A.P. 7, 10, 13,... or not. If yes, find which term is it.

The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20^th term.

If a_n = 3 – 4n, show that a₁, a₂, a₃,... form an AP. Also find S₂₀.

The sum of first n terms of an A.P. whose first term is 8 and the common difference is 20 equal to the sum of first 2n terms of another A.P. whose first term is – 30 and the common difference is 8. Find n.

Zeroes of a polynomial can be determined graphically. No. of zeroes of a polynomial is equal to no. of points where the graph of polynomial ______.

If p(x) = axr + bx + c, then –`"b"/"a"` is equal to ______.

If 2 and `1/2` are the zeros of px² + 5x + r, then ______.

Case Study -1

The figure given alongside shows the path of a diver, when she takes a jump from the diving board. Clearly it is a parabola.

Annie was standing on a diving board, 48 feet above the water level. She took a dive into the pool. Her height (in feet) above the water level at any time ‘t’ in seconds is given by the polynomial h(t) such that h(t) = -16t² + 8t + k.

The zeroes of the polynomial r(t) = -12t² + (k - 3)t + 48 are negative of each other. Then k is ______.

The sum of the first 15 multiples of 8 is ______.

First four terms of the sequence a_n = 2n + 3 are ______.

If the sum of first n terms of an AP is An + Bn² where A and B are constants. The common difference of AP will be ______.

The sum of the first 2n terms of the AP: 2, 5, 8, …. is equal to sum of the first n terms of the AP: 57, 59, 61, … then n is equal to ______.

If the sum of the first m terms of an AP is n and the sum of its n terms is m, then the sum of its (m + n) terms will be ______.

The sum of first ten natural number is ______.

The sum of first n terms of the series a, 3a, 5a, …….. is ______.

The famous mathematician associated with finding the sum of the first 100 natural numbers is ______.