English Medium इयत्ता १० - CBSE Important Questions for Mathematics

A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. We would like to find out the number of toys produced on that day.

A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.

A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

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

Solve for x :

`1/(x + 1) + 3/(5x + 1) = 5/(x + 4), x != -1, -1/5, -4`

Solve for x :

`1/(2x - 3) + 1/(x - 5) = 1 1/9 , X != 3/2, 5`

Solve for x

`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 2, "where x" != -1/2, 1`

A pole has to be erected at a point on the boundary of a circular park of diameter 13 meters in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 meters. Is it the possible to do so? If yes, at what distances from the two gates should the pole be erected?

If the quadratic equation (c² – ab) x² – 2 (a² – bc) x + b² – ac = 0 in x, has equal roots, then show that either a = 0 or a³ + b³ + c³ = 3abc ?

Solve the given quadratic equation for x : 9x² – 9(a + b)x + (2a² + 5ab + 2b²) = 0 ?

Find the positive value(s) of k for which quadratic equations x² + kx + 64 = 0 and x² – 8x + k = 0 both will have real roots ?

Solve for x :

x² + 5x − (a² + a − 6) = 0

If x = −2 is a root of the equation 3x² + 7x + p = 1, find the values of p. Now find the value of k so that the roots of the equation x² + k(4x + k − 1) + p = 0 are equal.

If 1 is a root of the quadratic equation 3x² + ax – 2 = 0 and the quadratic equation a(x² + 6x) – b = 0 has equal roots, find the value of b ?

The sum of the squares of two consecutive multiples of 7 is 637. Find the multiples ?

Solve the following quadratic equation for x:

`4sqrt3x^3+5x-2sqrt3=0`

Find the value(s) of k so that the quadratic equation 3x² − 2kx + 12 = 0 has equal roots ?

Solve for x: `3x^2-2sqrt3x+2=0`

Solve the following quadratic equation for x:

x² − 4ax − b² + 4a² = 0

Find the roots of the equation  .`1/(2x-3)+1/(x+5)=1,x≠3/2,5`