English Medium Class 10 - CBSE Question Bank Solutions for Mathematics

Find the roots of the following quadratic equation by factorisation: 

`2x^2 – x + 1/8 = 0`

Find the roots of the following quadratic equation by factorisation:

100x² – 20x + 1 = 0

John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.

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.

Find two numbers whose sum is 27 and product is 182.

 Find two consecutive positive integers, sum of whose squares is 365.

The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

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.

In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects

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.

In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine:

sin A, cos A

In ΔABC right angled at B, AB = 24 cm, BC = 7 m. Determine:

sin C, cos C

 In Given Figure, find tan P – cot R.

If sin A = `3/4`, calculate cos A and tan A.

Given sec θ = `13/12`, calculate all other trigonometric ratios.

If ∠A and ∠B are acute angles such that cos A = cos B, then show that ∠A = ∠B.

If cot θ =` 7/8` evaluate `((1+sin θ )(1-sin θ))/((1+cos θ)(1-cos θ))`

If cot θ = `7/8`, evaluate cot² θ.

In ΔABC, right angled at B. If tan A = `1/sqrt3` , find the value of

1.  sin A cos C + cos A sin C
2. cos A cos C − sin A sin C

In ΔPQR, right angled at Q, PR + QR = 25 cm and PQ = 5 cm. Determine the values of sin P, cos P and tan P.