Irational Numbers (Class-X - AP, TG, CBSE )


1 (i)Prove that  √2 is an irrational number by 
        the method of contraction.  [AP SCERT MP] [CBSE]
 (ii)Prove that  √3 is an irrational number by 
        the method of contraction.  [AP SCERT MP, May 2022] 
 (iii)  Prove that  √5 is an irrational number by 
    the method of contraction.  [AP SSC 2015M] 
(iv) Show that  √11 is an irrational number. 
(v) Show that  √7 is an irrational number.   [ AP SCERT ]
2 (i)Show  that  5-√3 is an irrational number [AP  Aug 2022]
   (ii)Prove that 3+2√5 is an irrational number [AP SCERT MP]
 (iii)Prove that 3-2√5 is an irrational number [AP SCERT MP]
3(i)Prove that √5 + √7 is irrational   [AP SSC 2017J] 
(ii)Prove that √7 + √11 is irrational   [AP SSC 2019J] 
(iii)Prove that  √2 +√5 is an irrational number  [ SCERT MP 2023]

 

Objective Questions (1 Mark )

1. √a +√b is an irrational number. 
        Which of the following is FALSE?   [AP SCERT MP]
         A] a and b are prime    B]  a or b  is prime
         C] a and b are integer  D] a or  b is not a perfect square 
2.Which  of the following is an
     irrational number?   [AP SCERT MP]
        A] 2/3    B] √(16/25)   C] √8 D] √0.04
3. If p is prime, then  √p is ...........  [AP SSC 2016M]
    A] Composite Number    B] Irrational Number  
     C] Positive Integer D] Rational Number

4. Two statements are given below - one labelled Assertion (A) and 
    the other labelled Reason (R). Read the statements carefully
     and choose the option that correctly describes statements
     (A) and (R). [CBSE]
    Assertion (A): 2 is a prime number.
    Reason (R): The square of an irrational number is always a prime number.
    A) Both (A) and (R) are true and (R) is the correct explanation of (A).
    B) Both (A) and (R) are true and (R) is not the correct explanation of (A).
    C) (A) is true but (R) is false.          D) (A) is false but (R) is true.

5. Which of the following is not a real
         number? [AP SCERT]
    A] π     B] √(-9)   C] 3-2√5   D]1.457
 

Comments

Post a Comment

Popular posts from this blog

విద్యా మనోవిజ్ఞాన శాస్త్రం ( Educational Psychology ) - Practice

  1. థార్న్ డైక్‌ CAVD ప్రజ్ఞా పరీక్షలో C అనే అక్షరం సూచించే సామర్థ్యం?      1) వాక్య పూరణం      2) అవగాహన      3) పదజాలం      4) పద ధారాళత 2. వ్యక్తి తన అనుభవాలను, అంతర్గత భావాలను, ఆలోచనలను విశ్లేషించుకుని నివేదించే పద్ధతి?      1) పరిశీలనా పద్ధతి      2) వ్యక్తి చరిత్ర అధ్యయన పద్ధతి      3) ప్రయోగాత్మక పద్ధతి      4) అంతఃపరిశీలనా పద్ధతి 3. ఒక 9 ఏండ్ల బాలుడు.. 8 ఏండ్ల బాలుడికి నిర్దేశించిన అంశాలను మాత్రమే పూర్తిచేయగలిగినట్లయితే అతని ప్రజ్ఞాలబ్ధి?      1) 112.5      2) 88.8      3) 102.5      4) 98.8 4. కింది వాటిలో వికాస లక్షణం కానిది?      1) గుణాత్మకమైనది      2) సమగ్రమైనది      3) అంతర్గతమైన చర్య      4) ఒక ప్రత్యేకాంశానికి పరిమితం 5. ఏ రకమైన బుద్ధిమాంద్యం ఉన్న పిల్లలు సంరక్షకుల అవసరంగల వికలాంగులుగా పరిగణించబడుతారు?      1) స...
Read more

Prime & Composite Numbers

12= 3 x 4, Here 3 is a factor of 12, and 12 is a multiple  of 3.  4 is another factor of 12. In the same way, for 12, there are six factors in all. They are 1,2,3,4,6,12 as 12=1x12, 12=2x6, 12=3x4. A number with exactly two factors-1 and itself is called a prime number .  Example: 2 has only two factors -1 and 2. So, 2 is a prime number. Prime Numbers between 100-200 are  101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199 .[21] A number with at-least   three factors(more than two factors ) is called a Composite number. Example: 12 has six factors-1,2,3,4,6,12. So, 12 is a composite number. 1 has only one factor. i.e. 1. So, 1 is neither a prime number nor a composite number. Even Numbers    : Multiples of 2 or numbers divisible by 2 = {  2,4,6,8,10,.... } Odd  Numbers: numbers which are not multiples of 2 =  { 1,3,5,7,9,........ } Sum of any two even numbers is an even number. Su...
Read more

Why students hate maths?

Demystifying Math Dislike: Understanding Student Perspectives   Explore common reasons why students dislike math. From fear of failure and perceived difficulty to limited relevance and negative experiences, uncover the various factors contributing to students' reluctance to engage with this crucial subject. Anxiety    Math anxiety, characterized by fear or apprehension about math-related tasks, can significantly hinder students' confidence and enjoyment of the subject matter. Boredom    Monotonous teaching methods and a lack of engaging activities can make math lessons feel uninspiring and unappealing to students. Complexity   Mathematics often appears complex and abstract, making it challenging for some students to comprehend and engage with effectively. Fear of Failure    The fear of making mistakes or performing poorly in math can significantly deter students from actively engaging with the subject matter. Lack of Understanding ...
Read more