CBSE-NCERT-CLASS-10-BOARD-EXAM-QUESTIONS-CHAPTER-4-6

 CBSE CLASS X MATHEMATICS BOARD EXAM QUESTIONS CHAPTERS 4-6

CHAPTER 4: Quadratic Equations  IMPORTANT QUESTIONS 

 1.  Write the form of the quadratic equation .

2.  What do you mean by roots of the quadratic equation?

3.  Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age?

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

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

6. 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 ` 90, find the number of articles produced and the cost of each article.

Question 1: Find the roots of the quadratic equation:

2x² − 3x − 26 = 0

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Question 2: Find the roots of the following quadratic equations by factorization:

1. x² − 3x − 10 = 0
2. 2x² + x − 6 = 0
3. 2x² + 7x + 5 = 0
4. 2x² − x + ¹⁄₈ = 0
5. 100x² − 20x + 1 = 0

SHORT QUESTIONS

1. Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:

1. 2x² − 3x + 5 = 0
2. 3x² − ⁴⁄₃x + 4 = 0
3. 2x² − 6x + 3 = 0

2. Find the values of k for each of the following quadratic equations so that they have two equal roots:

1. 2x² + kx + 3 = 0
2. kx(x − 2) + 6 = 0

3. Is it possible to design a rectangular mango grove whose length is twice its breadth and whose area is 800 m²? If so, find its length and breadth.

                     CHAPTER 5 ARITHMETIC PROGRESSION

Complete the formulae.

a.an = a + (n-1)...

b. Sn = (n/2){2a +(....-1)d

c. If the last term and common difference is known, 

then, nth term from the last 

Tn = l +(....-1)(-....)

l = last term

Short Questions

1. The cost of digging a well after every meter of digging, when it costs Rs 150 for the first meter and rises by Rs 50 for each subsequent meter. Does this situation represent an A.P.? If yes, then find the 8th term.

Also find the cost of 50 meters.

2.  Write the first four terms of the A.P., 

(1) a = 2.5, d = -1.5

(2) d = 2, Tn = 18 , a = 2

3. Find the missing terms of the following APs

a) 2, ..., 26

b) -4, _ _ _ _ 6

4)  An AP consists of 50 terms, of which the 3rd term is 12 and the last term is 106. Find the 29th term. 

5)  If the 17th term of an AP exceeds the 10th term by 7, then find the common difference.

6) Two APs have the same common difference. The difference between the 100th term is 100. What will be the difference of their 500th term?

7) How many multiples are lying between 10 and 250? 

Long Questions

1) The sum of the 4th and 8th terms of an A.P. is 24, and the sum of the 6th and 10th terms is 44. Find the first three terms of the A.P.

2)  The first and the last terms of an AP are 17 and 350, respectively. If the common difference is 9, how many terms are there, and what is their sum?

3) If the sum of the first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of the first n terms.

4) If the sum of the first n terms of an AP is 4n − n2, what is the first term (that is, S₁)? What is the sum of the first two terms? What is the second term? Similarly, find the 3rd, the10th and the nth terms.

5) Find the sum of the first 15 multiples of 8.

6)  A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.

7)  In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees that each section of each class will plant will be the same as the class in which they are studying, e.g., a section of class I will plant 1 tree, a section of class II will plant 2 trees, and so on till class XII. There are three sections of each class. How many trees will be planted by the students?

8)  200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it, and so on. In how many rows are the 200 logs placed, and how many logs are in the top row?

CHAPTER 6 -TRIANGLES

Short questions 

1. All circles are ________ (congruent, similar).

2. All _____________ triangles are similar (isosceles, equilateral).

3. If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the _____ ratio.

Long Questions

1. Prove that  if  a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

2.  In the given figure

PS/SQ = PT/TR

∠PST = ∠PRQ

Then prove that PRQ is an isosceles triangle.

Question 2: 

DE॥OQ, DF॥OR. Then show that EF॥QR

Question 3: ABCD is a trapezium in which AB∥DC, and its diagonals intersect each other at point O. Show that AO/BO = CO/DO

Question 4: 

S and T are points on sides PR and QR, respectively, of ▵ PQR such that ∠ P = ∠ RTS. Show that ▵ RPQ ∼ ▵ RTS.

Question 6:  ABC and AMP are two right triangles, right-angled at B and M.

Prove that ∆ABC ~ ∆AMP

and CA/PA =  BC/MP

Question 7: A vertical pole of length 6 m casts a shadow 4 m long on the ground, and at the same time a tower casts a shadow 28 m long. Find the height of the tower.

Question 8: If AD and PM are medians of triangles ABC and PQR, respectively, where ∆ABC ~ ∆PQR

Prove that AB/PQ = AD/PM