CBSE-CLASSX-BOARD-IMPORTANT-QUESTIONS-CHAPTERWISE

 CLASS X BOARD EXAM MATHEMATICS 

IMPORTANT QUESTIONS CHAPTE 1-3

CHAPTER 1- REAL NUMBERS

 Short Questions
 1. Explain the Euclid division lemma. 

2. Find the HCF of 135 and 225 using the Euclid division lemma. 

3. Find the HCF of 12, 15, and 21

Long Questions

1. Show that any positive odd integer is of the form 6q + 1, 6q + 3, or 6q + 5.

2. Show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m +8 

3.  Prove that 3 + 2√5 is an irrational number. 

4. Prove that 1/√2 is irrational. 

5.  The greatest number that can divide the number 70 and 125, leaving the remainder 5 and 8, is i) 13  ii)65  iii) 875  iv) 1750

9. Is the square root of 0.4 an irrational or rational number?

10.  The LCM of the prime numbers p & q (p>q) is 221. Then what is the value of 3p-q? 

Solution: Since, p and q are prime numbers, then their LCM = Product of the numbers

Factors of 221 = 13*17 

Click Here So, p = 17 and q = 13 

Hence 3p - q = 17* 3 - 13 = 51 - 13 = 38

Answer = 38 

CHAPTER 2 PLOYNOMIALS 

1.   What is the degree of the polynomial  5x³−7x+95x³−7x+9
2. Write the relation between the product of zeros and coefficients of a quadratic polynomial.

1. If the graph of a polynomial cuts the x-axis at two points, how many zeros does it have?
2. If the graph of a polynomial touches the x-axis at one point, how many zeros does it have?
3. What is the degree of the polynomial x² − x² + 1?
4. What is the constant term of the polynomial 7x³ − 5x + 2?
5. What is the coefficient of x² in 3x³ − 4x² + x − 6?
6. Find the number of zeros from the graph.

7. Find a quadratic polynomial whose sum of the zeros be 1/4 and product of the zeros is -1.

CHAPTER 3 LINEAR EQUATION IN TWO VARIABLES

1.  The coach of a cricket team buys 3 bats and 6 balls for Rs.3900. Later, she buys another bat and 3 more balls of the same kind for Rs.1300. Represent this situation algebraically and geometrically.

2. The cost of 2 kg of apples and 1 kg of grapes on a day was found to be Rs.160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs.300. Represent the situation algebraically and geometrically.

3.  On comparing the ratio, (a1/a2), (b1/b2), and (c1/c2), find out whether the following pair of linear equations are consistent or inconsistent.

(i) 3x + 2y = 5 ; 2x – 3y = 7

(ii) 2x – 3y = 8 ; 4x – 6y = 9

(iii) (3/2)x + (5/3)y = 7; 9x – 10y = 14

(iv) 5x – 3y = 11 ; – 10x + 6y = –22

(v) (4/3)x +2y = 8 ; 2x + 3y = 12

4.  Solve 2x + 3y = 11 and 2x – 4y = – 24 and hence find the value of ‘m’ for which y = mx + 3.

5.  The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

6. The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105, and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?

7. A fraction becomes 9/11 if 2 is added to both the numerator and the denominator. If 3 is added to both the numerator and the denominator, it becomes 5/6. Find the fraction.

8.  The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

9.  A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs.27 for a book kept for seven days, while Susy paid Rs.21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

10.  2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.

11. A train covered a certain distance at a uniform speed. If the train had been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h, it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.

12. Sita Devi wants to make a rectangular pond on the roadside for the purpose of providing drinking water for street animals. The area of the pond will be decreased by 3 square feet if its length is decreased by 2 ft. and breadth is increased by 1 ft. Its area will be increased by 4 square feet if the length is increased by 1 ft. and the breadth remains the same. Find the dimensions of the pond. (2014)

Class 10 Mathematics – Chapter 2: Polynomials

Multiple Choice Questions (MCQs)

1. The relation between the product of zeros and coefficients of a quadratic polynomial ax² + bx + c is:
   (a) −b/a
   (b) c/a
   (c) −c/a
   (d) b/a

   Correct Answer: (b) c/a

2. If the graph of a polynomial cuts the x-axis at two points, the number of zeros is:
   (a) 0
   (b) 1
   (c) 2
   (d) 3

   Correct Answer: (c) 2

3. If the graph of a polynomial touches the x-axis at one point, the number of zeros is:
   (a) 0
   (b) 1
   (c) 2
   (d) Infinite

   Correct Answer: (b) 1

4. The degree of the polynomial x² − x² + 1 is:
   (a) 0
   (b) 1
   (c) 2
   (d) 3

   Correct Answer: (a) 0

5. The constant term of the polynomial 7x³ − 5x + 2 is:
   (a) 7
   (b) −5
   (c) 2
   (d) 0

   Correct Answer: (c) 2

6. The coefficient of x² in 3x³ − 4x² + x − 6 is:
   (a) 3
   (b) −4
   (c) 1
   (d) −6

   Correct Answer: (b) −4

Question: Find the zeros of the following polynomials:

1. 4s² − 4s + 1
2. 4s² − 4s + 1
3. 6x² − 3 − 7