Q.1. The value of is
(a) 0.45
(b)
(c) 45/1000
(d)
Ans.
9900 x = 2300
x = 23/99
Similarly x = 22/99
Q.2. If n is a natural number, then √n is
(a) Always a natural number
(b) Always a rational number
(c) Always a irrational number
(d) Sometimes a natural number and sometimes a surd
Ans. (d)
Q.3. If
prove m-n = 1
Ans.
⇒ 33n - 3m +3 = 30
⇒ 3n - 3m +3 = 0
⇒ n - m +1 = 0
⇒ m- n = 1
Q.4. The value of ((23 + 22)2/3 + (150 - 29)1/2)2 is
(a) 196
(b) 286
(c) 400
(d) 324
Ans. (c)
((23 + 22)2/3 + (150 - 29)1/2)2
((23 + 4)2/3 + (121)1/2)2
((27)2/3 + (121)1/2)2
((33)2/3 + (11))2
(9+11)2 = 202 = 400
Hence option (c) is correct.
Q.5. If
find a2 - b2 , a+ b
Ans.
= -9 - 4√5
a+b = 4√5 - 9 - 9 - 4√5 = -18
a-b = 4√5 - 9 + 9 + 4√5 = 8√5
a2 - b2 = (a+b)(a-b)
= -18 x 8√5
= - 144√5
Q.6. Give any two rational number between the irrational numbers 0.515115111511115.... and 0.53533533353333....
Ans.
Pick any two number between them;
0.521, 0.527
Q.7. Explain the difference between rational number and irrational number with example.
Ans.
Rational number are those numbers expressed in the form of p/q, where p and q are co-primes & q ≠0.
Example: √2, √3, √11 etc.
Irrational numbers can't be expressed in the form mentioned above.
Example: 2, 3/4, 4/3, 0, 1, -2
Rational and Irrational numbers
Q.8. Find a if
Ans.
Squaring both side,
13 - a√10 = 8+5+ 2√40
-a√10 = 2√40
a = -4
Q.9. If x + √13 = 4, find the value of x -1/x
Ans.
Q.10. Find the value of
Ans.
Q.11. Simplify (11+√11)(11-√11)
Ans.
112 - 11 = 121 -11 = 110
Q.12. Find x and y if
Ans.
x = 13, y = -3
Q.13. find the value of
Ans.
Q.14. Simplify
if x = √7 + √6
Ans.
= 13 + 2√42 + 13 - 2√42 - 2
= 24
Q.15. If xy = 1 and x = 7 + 4√3, what is the value of
Ans.
x = 7 + 4√3
1/x = y and y = 1/x,
so,
= (7 - 4√3)2 + (7 + 4√3)2
= 49-48 - 56√3 + 49 + 48 + 56√3
= 194
Q.16. Find x if 4x - 4x-1 = 24.
Ans.
suppose 4x = m
m - m/4 = 24
3m/4 = 24
m = (24 x 4)/3
m = 32
∴ 4x = 32
= 22x = 25
= 2x = 5
= x = 5/2
Q. 17. if x = 2 and y = 4, what is value of (x/y)x-y + (y/x)y-x
Ans. (2/4)-2 + (4/2)4-2 = 22 + 22 = 8
Q.18. Simplify
Ans.
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