English Medium कक्षा १० - CBSE Question Bank Solutions for Mathematics

The mean of first ten natural numbers is ______.

The prime factorisation of the number 5488 is ______.

The graph of y = f(x) is shown in the figure for some polynomial f(x). The number of zeroes of f(x) are ______.

The given linear polynomial y = f(x) has

If two positive integers a and b are written as a = x³y² and b = xy³, where x, y are prime numbers, then the result obtained by dividing the product of the positive integers by the LCM (a, b) is ______.

A point (x, y) is at a distance of 5 units from the origin. How many such points lie in the third quadrant?

National Art convention got registrations from students from all parts of the country, of which 60 are interested in music, 84 are interested in dance and 108 students are interested in handicrafts. For optimum cultural exchange, organisers wish to keep them in minimum number of groups such that each group consists of students interested in the same artform and the number of students in each group is the same. Find the number of students in each group. Find the number of groups in each art form. How many rooms are required if each group will be allotted a room?

1. At an instance, the midfielders and forward formed a parallelogram. Find the position of the central midfielder (D) if the position of other players who formed the parallelogram are :- A(1, 2), B(4, 3) and C(6, 6)
2. Check if the Goal keeper G(–3, 5), Sweeper H(3, 1) and Wing-back K(0, 3) fall on a same straight line.
   [or]
   Check if the Full-back J(5, –3) and centre-back I(–4, 6) are equidistant from forward C(0, 1) and if C is the mid-point of IJ.
3. If Defensive midfielder A(1, 4), Attacking midfielder B(2, –3) and Striker E(a, b) lie on the same straight line and B is equidistant from A and E, find the position of E.

Three bells toll at intervals of 9, 12 and 15 minutes respectively. If they start tolling together, after what time will they next toll together?

The HCF of two numbers 65 and 104 is 13. If LCM of 65 and 104 is 40x, then the value of x is ______.

If α and β are the zeroes of the polynomial x² + x − 2, then find the value of `alpha/beta+beta/alpha`

If the quadratic equation px² − 2√5px + 15 = 0 has two equal roots then find the value of p.

In an A.P., if S5 + S7 = 167 and S₁₀₌235, then find the A.P., where Sn denotes the sum of its first n terms.

Solve for x: `sqrt(3x^2)-2sqrt(2)x-2sqrt3=0`

Solve for x : ` 2x^2+6sqrt3x-60=0`

Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.

Find the values of k for which the quadratic equation 9x² - 3kx + k = 0 has equal roots.

If -5 is a root of the quadratic equation 2x² + px – 15 = 0 and the quadratic equation p(x² + x)k = 0 has equal roots, find the value of k.

If the ratio of the sum of first n terms of two A.P’s is (7n +1): (4n + 27), find the ratio of their mth terms.

Solve for x: `1/(x+1)+2/(x+2)=4/(x+4), `x ≠ -1, -2, -3