**MATHEMATICS QUESTIONNAIRE – X CLASS**

**1. REAL NUMBERS **

Hi
friends and my dear students! In this post, I have covered **Important questions
for 10 ^{th} class maths chapter-1 Real numbers, Chapter wise previous
year Questions. **After
Reading Please do share it with your friends.

**Learn Maths for All Classes here.**

1 MARK QUESTIONS:

1. State Euclid’s division algorithm

2. Expand
(i) log p^{2}q^{3}/r (ii) log15 (iii) logx2y3z4 (iv) log343/125
(v) log 125/625

(vi) log√x^{3}/y^{3}(vii) log 64/243

3. Explain
why i) 17x11x^{2}+17x11x5

ii) 7x11x13+13 iii)7x6x5x4x3x2x1+5 is a
composite number

4. Determine
i. Log_{2} 512

ii. log _{x}√ x

iii. log_{2}1/16

iv.
2^{2 +} ^{log}_{2}^{3}

v.
log_{2}0.0001

vi. log_{10}cos0

vii
. 2^{2 +} ^{log }_{2}^{6}

viii
log_{1}1

ix.
6^{log}_{6}^{7}

x.
5^{2 +} ^{log }_{5}^{10}

xi.
2log3+3log2+log5-log12

xii
log_{10} 3+ log_{10} 4+ log_{10} 4- log_{10} 6

xiii. log_{12}18+log_{12}8

xiv.
log(a^{2}xb^{3})-log(a^{3}/b^{2})^{ }

xv.
log_{b}a.log_{c}b.log_{a}c^{2/3}

5. Write
the following in exponential form

i.
log_{10} 32= x

ii. log_{5 }625= y

iii.
log_{10 }1000= z

iv.
log_{7} ^{1/343}= -a

v.
log_{10}0.001=-4

vi.log_{5}125=3

6. Find
the HCF of the smallest composite number and the smallest prime number?

7. If
HCF (306,657) = 9,find LCM

8. Write
the condition to be satisfied by ‘q’ so that a rational number p/q has a
terminating decimal expansion?

**2 MARK QUESTIONS: **

9. Find the LCM and HCF of (i) 12, 18 (ii) 12,15,21 (iii) 2^{3}
x 3^{2} and 2^{4} x 3 by prime factorization method

10. Use Euclid’s algorithm to find the HCF of (i) 900,270 (ii) 96,72

11. Find the HCF and LCM of 75 and 160 by the fundamental theorem of
Arithmetic and verify LCM x HCF =product of two numbers

12. Solve i. 3^{x}=5^{x-2}

ii. 2^{x+1}=3^{1-x }

iii. 3^{x}=5^{x+2
}

13. Show that

i. 7 √5

ii. 3√2

iii. 3+2√5

iv. 5-√3

v. 1/√2

vi. √26 is irrational

14. Write i. 2log3+3log5-5log

ii. log 10+2log3-log2

iii. 2logx+3log4+log2

iv. 2log3-1/2log16+log12

as a single logarithm

15. Show that i. 4^{n} ii. 6^{n} iii.12^{n},n€N can never end with the
digit 0

16. State whether the following are terminating or non- terminating
repeating decimal without actual division

i.29/343 ii.23/2252 iii.6/15 iv.35/50 v.7/8
vi.13/3125 vii. 9/15 viii. 77/210

17. Find the value of a+b+c+d if product of first ten natural numbers
is written as 2^{a}x3^{b}x5^{c}x7^{d}

18. If the prime factorization of natural number (n) is 2^{3}x3^{2}x5^{2}x7.
How many consecutive zeroes will it have at the end of it justify your answer?

19. If log2(x^{2}-4x+7)=2
find the value of ’x’

**Also Check**

**Introduction to Knowing Our Numbers Key Points**

**SSC (10th class) Trigonometry Exercise - 11.1 Solution**

**SSC(10th class) Trigonometry Exercise - 11.1 Solutions**

**4 MARK QUESTIONS:**

1. Use Euclid’s division lemma to show that any
positive odd integer is of the form 6q+1 or 6q+3 or 6q+5 where q is integer

2. Use Euclid’s lemma to show that square of any
positive integer is of form 3p,3p+1

3. Show that i.

are irrationals.

4. If log(x+y/3) =1/2(logx+logy) then find the
value of x/y+y/x.

5. If i.x^{2}+y^{2}=25xy then
show that 2log(x+y)=3log3+logx+logy ii.x2+y2=6xy then show that
2log(x+y)=3log2+logx+logy

6. (2.3)x=(0.23)y = 1000 then find the value of
1/x-1/y

7. Show that a positive odd integer is of the
form 4q+1 or 4q+3 where q is an integer

8. Show that If x^{2}+y^{2} =3xy
then 2log(x-y) = logx + logy ii.x^{2}+y^{2}=10xy,
2log(x+y)=logx+logy+2log2+log3

9. If a^{2}+b^{2}=7ab then
log(a+b/3)=1/2(loga+logb)

10. Use Euclid’s division
lemma to show that the cube of any positive integer is of the form 9m,9m+1,9m+8

** PRIORITY-II**

**1 MARK QUESTIONS: **

1. Sate fundamental theorem
of arithmetic

2. If LCM of two numbers
’a’ and ‘b’ is 24 and their HCF is ‘1’ then find the numbers

3. If log_{10}x=a,
write 10^{2a-3} value in terms of x

4. Define logarithm of a
natural number?

5. Is log_{1}10 defined? Why?

6. Write any rational number between 2/3 & 3/5?

7.
Find the value of log108 when log2=0.3010

8.
Can you find the HCF of 7 and 9 without using prime factorization method?
Justify your answer?

9.
If x=9, y=log32 then find xy

10. What can you
say about the LCM and HCF of any two consecutive numbers and prime numbers?

**2
MARK QUESTIONS: **

11. Write any four
laws of logarithms?

12. Is i. log2 ii.
log3 iii. log100 iv ∏
. a rational or irrational? justify your
answer

13. Do you think
that sum of two irrational and product of two irrational is again an
irrational? Justify your answer

14. Find ‘x’ if i.2 log+1/2 log9-log3=logx

ii. log_{x}^{10} = -3

iii. log_{10}^{x-9}
log_{10}^{x}=1

15. Why 6^{n}+5^{n}
always end with 1? Explain

16. Prove that log_{a}^{a}=1

17. What is the
difference between rational and irrational numbers expressed in decimal form?

18. Show that
log27540=2log2+4log3+log5+log17

19. Insert 4
rational numbers between ¾ and 1 without using the a+b/2 formula

20. A number when divided by 61 gives 21 as
quotient and 32 as remainder find the number

21. Check whether (2√3+√5) (2√3-√5 is rational or irrational? Justify your answer

**4 MARK QUESTIONS:**

1. Show that one and one out of n,n+2, or n+4 is divisible by
3 where ‘n’ is any positive integer

2. Show that every positive even integer is of the form 2q
and that every positive odd integer is of the form 2q+1 where ‘q’ is some
integer

3. Plot√2,√3,√5on number
line

4. Prove that logaxy=logax+logay

5. Use Euclid’s division lemma to show
that the cube of any positive integer is of the form 7m or 7m+1 or 7m+6

**1
MARK QUESTIONS:**

1. State
Euclid’s division algorithm

2. Expand
(i) log p^{2}q^{3}/r (ii) log15 (iii) logx2y3z4 (iv) log343/125
(v) log 125/625(vi) log√ x^{3}/y^{3}(vii) log 64/243

3. Explain
why i) 17x11x^{2}+17x11x5

ii) 7x11x13+13 iii)7x6x5x4x3x2x1+5 is a
composite number

4. Determine
i. Log_{2} 512

ii. log _{x}√ x

iii. log_{2}1/16

iv.
2^{2 +} ^{log}_{2}^{3}

v.
log_{2}0.0001

vi. log_{10}cos0

vii
. 2^{2 +} ^{log }_{2}^{6}

viii
log_{1} 1

ix.
6^{log}_{6}^{7}

x.
5^{2 +} ^{log }_{5}^{10}

xi.
2log3+3log2+log5-log12

xii
log_{10} 3+ log_{10} 4+ log_{10} 4- log_{10} 6

xiii. log_{12}18+log_{12}8

xiv.
log(a^{2}xb^{3})-log(a^{3}/b^{2})^{ }

xv.
log_{b}a.log_{c}b.log_{a}c^{2/3}

5. Write
the following in exponential form

i.
log_{10} 32= x

ii. log_{5 }625= y

iii.
log_{10 }1000= z

iv.
log_{7} ^{1/343}= -a

v.
log_{10}0.001=-4

vi.log_{5}125=3

6. Find
the HCF of the smallest composite number and the smallest prime number?

7. If
HCF (306,657) = 9,find LCM

8. Write the condition to be satisfied by ‘q’ so that a rational number p/q has a terminating decimal expansion?

## IITJEE 7th class Introduction to Algebra Notes

**Introduction to integers (7th class)**

## Introduction to Real number

**Trigonometry Do This & Try this solution**

**2 MARK QUESTIONS: **

9. Find the LCM and HCF of (i) 12, 18 (ii) 12,15,21 (iii) 2^{3}
x 3^{2} and 2^{4} x 3 by prime factorization method

10. Use Euclid’s algorithm to find the HCF of (i) 900,270 (ii) 96,72

11. Find the HCF and LCM of 75 and 160 by fundamental theorem of
Arithmetic and verify LCM x HCF =product of two numbers

12. Solve i. 3^{x}=5^{x-2}

ii. 2^{x+1}=3^{1-x }

iii. 3^{x}=5^{x+2
}

13. Show that i. 7 √5

ii. 3√2

iii. 3+2√5

iv. 5-√3

v. 1/√2

vi. √26 is irrational

14. Write i. 2log3+3log5-5log

ii. log 10+2log3-log2

iii. 2logx+3log4+log2

iv. 2log3-1/2log16+log12

as a single logarithm

15. Show that i. 4^{n} ii. 6^{n} iii.12^{n},n€N can never end with the
digit 0

16. State whether the following are terminating or non- terminating
repeating decimal without actual division

i.29/343 ii.23/2252 iii.6/15 iv.35/50 v.7/8
vi.13/3125 vii. 9/15 viii. 77/210

17. Find the value of a+b+c+d if the product of the first ten natural numbers
is written as 2^{a}x3^{b}x5^{c}x7^{d}

18. If the prime factorization of natural number (n) is 2^{3}x3^{2}x5^{2}x7.
How many consecutive zeroes will it have at the end of it justify your answer?

19. If log2(x^{2}-4x+7)=2
find the value of ’x’

**4 MARK QUESTIONS: **

1. Use Euclid’s division lemma to show that any
positive odd integer is of the form 6q+1 or 6q+3 or 6q+5 where q is integer

2. Use Euclid’s lemma to show that square of any
positive integer is of form 3p,3p+1

3. Show that i.

are irrationals.

4. If log(x+y/3) =1/2(logx+logy) then find the
value of x/y+y/x.

5. If i.x^{2}+y^{2}=25xy then
show that 2log(x+y)=3log3+logx+logy ii.x2+y2=6xy then show that
2log(x+y)=3log2+logx+logy

6. (2.3)x=(0.23)y = 1000 then find the value of
1/x-1/y

7. Show that a positive odd integer is of the
form 4q+1 or 4q+3 where q is integer

8. Show that If x^{2}+y^{2} =3xy
then 2log(x-y) = logx + logy ii.x^{2}+y^{2}=10xy,
2log(x+y)=logx+logy+2log2+log3

9. If a^{2}+b^{2}=7ab then
log(a+b/3)=1/2(loga+logb)

10. Use Euclid’s division
lemma to show that the cube of any positive integer is of the form 9m,9m+1,9m+8

**PRIORITY-II**

**1 MARK QUESTIONS: **

1. Sate fundamental theorem
of arithmetic

2. If LCM of two numbers
’a’ and ‘b’ is 24 and their HCF is ‘1’ then find the numbers

3. If log_{10}x=a,
write 10^{2a-3} value in terms of x

4. Define logarithm of a
natural number?

5. Is log_{1}10 defined? Why?

6. Write any rational number between 2/3 & 3/5?

7.
Find the value of log108 when log2=0.3010

8.
Can you find the HCF of 7 and 9 without using prime factorization method?
Justify your answer?

9.
If x=9, y=log32 then find xy

10. What can you say about the LCM and HCF of any two consecutive numbers and prime numbers?

**2
MARK QUESTIONS:**

11. Write any four
laws of logarithms?

12. Is i. log2 ii.
log3 iii. log100 iv ∏
. a rational or irrational? justify your
answer

13. Do you think
that sum of two irrational and product of two irrational is again an
irrational? Justify your answer

14. Find ‘x’ if i.2 log+1/2 log9-log3=logx

ii. log_{x}^{10} = -3

iii. log_{10}^{x-9}
log_{10}^{x}=1

15. Why 6^{n}+5^{n}
always end with 1? Explain

16. Prove that log_{a}^{a}=1

17. What is the
difference between rational and irrational number expressed in decimal form?

18. Show that
log27540=2log2+4log3+log5+log17

19. Insert 4
rational numbers between ¾ and 1 without using a+b/2 formula

20. A number when divided by 61 gives 21 as
quotient and 32 as remainder find the number

21. Check whether (2√3+√5) (2√3-√5 is rational or irrational? Justify your answer

**4 MARK QUESTIONS:**

1. Show that one and one out of n,n+2 or n+4 is divisible by
3 where ‘n’ is any positive integer

2. Show that every positive even integer is of the form 2q
and that every positive odd integer is of the form 2q+1 where ‘q’ is some
integer

3. Plot√2,√3,√5on number
line

4. Prove that logaxy=logax+logay

5. Use Euclid’s division lemma to show
that the cube of any positive integer is of the form 7m or 7m+1 or 7m+6

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