Nothing Special   »   [go: up one dir, main page]
Scribd Logo
Upload

Welcome to Scribd!

  • 3 views

    Solution of Test Qaure Root

    Uploaded by

    Brijesh Yadav

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd

    Solution of Test Qaure Root

    Uploaded by

    Brijesh Yadav
    3 views7 pages

    Copyright

    © © All Rights Reserved

    Available Formats

    DOCX, PDF, TXT or read online from Scribd

    Did you find this document useful?

    Is this content inappropriate?

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    3 views7 pages

    Solution of Test Qaure Root

    Uploaded by

    Brijesh Yadav

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    of 7

    The Pythagorean triplet whose smallest number is 6 is _____.

    Choose the correct answer to fill in the


    blanks.

    A) 6,7,5

    B)7,9,2

    C)6,8,10

    D)6,11,10

    Solution 1

    The correct option is C 6, 8, 10


    For any natural number m>1, the Pythagorean triplet adheres to (2m)2+(m2−1)2=(m2+1)2.
    ∵ smallest number is 6, 2m=6 or m=3.
    m2+1=32+1=9+1=10
    m2−1=32−1=9−1=8
    So, the Pythagorean triplet is 6, 8, 10.

    2.

    Given:

    176×176−124×124

    =1762−1242

    =((176+124)(176−124) [∵a2−b2=(a+b)(a−b)]

    =300×52

    =15600

    ∴176×176−124×124=15600

    Hence, Option B is correct.

    3.Solution

    The correct option is C Coprime


    In a Pythagoras Triple, a,b,c are co-prime or relatively prime.

    Eg: (3,4,5),(5,12,13),(8,15,17),(7,24,25),(20,21,29),(12,35,37),(9,40,41),(28,45,53) etc.

    The correct option is C 12


    Applying the Pythagorean triples rule as a2+b2=c2
    52+x2=132
    25 + x2 = 169
    x2 = 169 - 25
    x2 = 144
    Squaring on both the sides, we get
    x = 12.

    6. The correct option is B 0.63


    √0.160.4=√0.160.40=√1640
    =√410=√0.4=0.63
    7.As we know, between n2 and (n+1)2, the number of non–perfect square numbers are 2n.
    (i) Between 122 and 132 there are 2×12 = 24 natural numbers.

    8. Solution: As 121 = 11 2

    We know that the sum of first n odd natural numbers is n2.


    Therefore, 121 = sum of first 11 odd natural numbers
    = 1 + 3 + 5+ 7 + 9 + 11 +13 + 15 + 17 + 19 + 21

    0.6360.4000−36123400−36934

    3. The correct option is B

    99856

    Section:-B

    2.Greatest 5 digit number = 99999

    We need to find out the smallest number that must be subtracted from 99999 to get a prefect
    square.

    We can observe that 143 is the remainder.

    So, if we subtract 143 from 99999, we will get a perfect square,

    Largest 5 digit perfect square = 99999 - 143

    = 99856

    6. Solution:
    Let the number of rows be, x.
    Therefore, the number of plants in each row = x.
    Total many contributed by all the students = x×x = x2
    Given, x2 = Rs.2025

    x2 = 3×3×3×3×5×5
    ⇒ x2 = (3×3)×(3×3)×(5×5)
    ⇒ x2 = (3×3×5)×(3×3×5)
    ⇒ x2 = 45×45
    ⇒ x = √(45×45)
    ⇒ x = 45
    Therefore,
    Number of rows = 45
    Number of plants in each rows = 45

    4. The correct option is C 41

    Vargamula method
    41
    ____________
    4|1681
    16 ↓
    81|x81
    81
    _______
    x
    ⇒41.
    7.Solution:

    L.C.M of 8, 15 and 20 is (2×2×5×2×3) = 120.


    120 = 2×2×3×5×2 = (2×2)×3×5×2
    Here, 3, 5 and 2 cannot be paired.
    Therefore, we need to multiply 120 by (3×5×2) i.e. 30 to get a perfect square.
    Hence, the smallest squared number which is divisible by numbers 8, 15 and 20 = 120×30 = 3600
    8. Area of square =side x side
    Square root of 441 is 21m
    So, the side will 21 m.

    4. The correct option is B

    49

    Let the no. of rooms be a

    ∴ No. of apartments = a

    Each apartment has 'a' number of rooms. So, total no. of rooms =a×a=a2

    494 240141689 8019 80198 0

    ∴ a2=2401

    a=√2401

    =49.
    ∴ Colony has 49 apartments.

    9. Solution :

    The prime factorization of 5408 is 2×2×2×2×2×13×13

    The number 2 does not have a pair and hence the smallest number that should be multiplied by
    5408 to make it a perfect square is 2.

    Answer : 2

    13. Given:

    Donated money Rs. 2401

    Let the number of students be x.


    ⇒ Money donated by each student =x.

    According to the question,

    x×x=2401

    ⇒x2=2401

    ⇒x=√2401

    724017343749771

    ⇒√2401=√7×7×7×7

    ⇒√2401=√49×49
    ⇒√2401=49

    Hence, the number of students in the class VIII is 49.

    14. Given,

    the area of square is=5184m²

    s×s=5184

    s²=5184

    s=√5184
    s=72

    according to problem,

    l=2x

    b=x
    we know that,

    perimeter of square=perimeter
    of rectangle

    4s=2(l+b)

    4×72=2(2x+x).

    288=6x

    x=288/6

    x=48

    from problem,

    l=2x

    =2×48

    =96

    b=x

    =48

    therefore length is 96
    breadth is 48

    area of rectangle = l × b

    = 96 × 48

    =4608 m²

    15. Answer:

    (1) 10000-9801=199 (2) 323761-322624=1137

    You might also like