English Medium इयत्ता १० - CBSE Important Questions for Mathematics

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

The number of zeroes of f(x) is ______.

Find a quadratic polynomial whose zeroes are 6 and – 3.

Find the zeroes of the polynomial x² + 4x – 12.

Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back at the same point in 4 hours 30 minutes. Find the speed of the stream.

In Fig. 1, ABCD is a rectangle. Find the value of x and y.

3 chairs and 1 table cost ₹ 900; whereas 5 chairs and 3 tables cost ₹ 2,100. If the cost of 1 chair is ₹ x and the cost of 1 table is ₹ y, then the situation can be represented algebraically as ______.

Read the following passage:

Based on the above information, answer the following questions:

1. Represent the information given above in terms of x and y.
2. Find the monthly fee paid by a poor child.
   OR
   Find the difference in the monthly fee paid by a poor child and a rich child.
3. If there are 10 poor and 20 rich children in batch II, what is the total monthly collection of fees from batch II?

Read the following passage:

Two schools 'P' and 'Q' decided to award prizes to their students for two games of Hockey ₹ x per student and Cricket ₹ y per student. School 'P' decided to award a total of ₹ 9,500 for the two games to 5 and 4 Students respectively; while school 'Q' decided to award ₹ 7,370 for the two games to 4 and 3 students respectively.

Based on the above information, answer the following questions:

1. Represent the following information algebraically (in terms of x and y).
2. (a) What is the prize amount for hockey?
   OR
   (b) Prize amount on which game is more and by how much?
3. What will be the total prize amount if there are 2 students each from two games?

A lending library has a fixed charge for first three days and an additional charge for each day thereafter. Rittik paid 27 for a book kept for 7 days and Manmohan paid ₹ 21 for a book kept for 5 days. Find the fixed charges and the charge for each extra day.

Find the values of 'a' and 'b' for which the system of linear equations 3x + 4y = 12, (a + b)x + 2(a – b)y = 24 has infinite number of solutions.

Read the following passage:

Lokesh, a production manager in Mumbai, hires a taxi everyday to go to his office. The taxi charges in Mumbai consists of a fixed charges together with the charges for the distance covered. His office is at a distance of 10 km from his home. For a distance of 10 km to his office, Lokesh paid ₹ 105. While coming back home, he took another roµte. He covered a distance of 15 km and the charges paid by him were ₹ 155.

Based on the above information, answer the following questions:

1. What are the fixed charges?
2. What are the charges per km?
3. If fixed charges are ₹ 20 and charges per km are ₹ 10, then how much Lokesh have to pay for travelling a distance of 10 km? 
   OR
   Find the total amount paid by Lokesh for travelling 10 km from home to office and 25 km from office to home. [Fixed charges and charges per km are as in (i) and (ii).

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

If `x=2/3` and x =−3 are roots of the quadratic equation ax² + 7x + b = 0, find the values of a and b.

If x=−`1/2`, is a solution of the quadratic equation 3x²+2kx−3=0, find the value of k

Solve the quadratic equation 2x² + ax − a² = 0 for x.

Find the roots of the following quadratic equation by factorisation:

`sqrt2 x^2 +7x+ 5sqrt2 = 0`

Find the value of k for which the equation x² + k(2x + k − 1) + 2 = 0 has real and equal roots.

If the equation (1 + m²) x² + 2mcx + c² – a² = 0 has equal roots then show that c² = a² (1 + m²)

A train travels at a certain average speed for a distance of 63 km and then travels at a distance of 72 km at an average speed of 6 km/hr more than its original speed. If it takes 3 hours to complete the total journey, what is the original average speed?

The sum of two natural numbers is 15 and the sum of their reciprocals is `3/10`. Find the numbers.