October 23, 2020
MATHEMATICS QUESTIONNAIRE – X CLASS
1. REAL NUMBERS
Hi friends and my dear students! In this post, I have covered Important questions for 10th 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 p2q3/r (ii) log15 (iii) logx2y3z4 (iv) log343/125 (v) log 125/625
(vi) log√x3/y3(vii) log 64/243
3. Explain
why i) 17x11x2+17x11x5
ii) 7x11x13+13 iii)7x6x5x4x3x2x1+5 is a
composite number
4. Determine
i. Log2 512
ii. log x√ x
iii. log21/16
iv.
22 + log23
v.
log20.0001
vi. log10cos0
vii
. 22 + log 26
viii
log11
ix.
6log67
x.
52 + log 510
xi.
2log3+3log2+log5-log12
xii
log10 3+ log10 4+ log10 4- log10 6
xiii. log1218+log128
xiv.
log(a2xb3)-log(a3/b2)
xv.
logba.logcb.logac2/3
5. Write
the following in exponential form
i.
log10 32= x
ii. log5 625= y
iii.
log10 1000= z
iv.
log7 1/343= -a
v.
log100.001=-4
vi.log5125=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) 23
x 32 and 24 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. 3x=5x-2
ii. 2x+1=31-x
iii. 3x=5x+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. 4n ii. 6n iii.12n,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 2ax3bx5cx7d
18. If the prime factorization of natural number (n) is 23x32x52x7.
How many consecutive zeroes will it have at the end of it justify your answer?
19. If log2(x2-4x+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.x2+y2=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 x2+y2 =3xy
then 2log(x-y) = logx + logy ii.x2+y2=10xy,
2log(x+y)=logx+logy+2log2+log3
9. If a2+b2=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 log10x=a,
write 102a-3 value in terms of x
4. Define logarithm of a
natural number?
5. Is log110 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. logx10 = -3
iii. log10x-9
log10x=1
15. Why 6n+5n
always end with 1? Explain
16. Prove that logaa=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 p2q3/r (ii) log15 (iii) logx2y3z4 (iv) log343/125
(v) log 125/625(vi) log√ x3/y3(vii) log 64/243
3. Explain
why i) 17x11x2+17x11x5
ii) 7x11x13+13 iii)7x6x5x4x3x2x1+5 is a
composite number
4. Determine
i. Log2 512
ii. log x√ x
iii. log21/16
iv.
22 + log23
v.
log20.0001
vi. log10cos0
vii
. 22 + log 26
viii
log1 1
ix.
6log67
x.
52 + log 510
xi.
2log3+3log2+log5-log12
xii
log10 3+ log10 4+ log10 4- log10 6
xiii. log1218+log128
xiv.
log(a2xb3)-log(a3/b2)
xv.
logba.logcb.logac2/3
5. Write
the following in exponential form
i.
log10 32= x
ii. log5 625= y
iii.
log10 1000= z
iv.
log7 1/343= -a
v.
log100.001=-4
vi.log5125=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) 23
x 32 and 24 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. 3x=5x-2
ii. 2x+1=31-x
iii. 3x=5x+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. 4n ii. 6n iii.12n,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 2ax3bx5cx7d
18. If the prime factorization of natural number (n) is 23x32x52x7.
How many consecutive zeroes will it have at the end of it justify your answer?
19. If log2(x2-4x+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.x2+y2=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 x2+y2 =3xy
then 2log(x-y) = logx + logy ii.x2+y2=10xy,
2log(x+y)=logx+logy+2log2+log3
9. If a2+b2=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
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 log10x=a,
write 102a-3 value in terms of x
4. Define logarithm of a
natural number?
5. Is log110 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. logx10 = -3
iii. log10x-9
log10x=1
15. Why 6n+5n
always end with 1? Explain
16. Prove that logaa=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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