MCQS
Page-3.16Question 1:
is equal to
(a) 5
(b) 6
(c)
(d)
(a) 5
(b) 6
(c)
(d)
Answer 1:
Therefore given expression is simplified and correct choice is
Question 2:
is equal to
(a)
(b)
(c)
(d)
(a)
(b)
(c)
(d)
Answer 2:
Therefore given expression is simplified and correct choice is.
Question 3:
The rationalisation factor of is
(a)
(b)
(c)
(d)
(a)
(b)
(c)
(d)
Answer 3:
Question 4:
The rationalisation factor of is
(a)
(b)
(c)
(d)
(a)
(b)
(c)
(d)
Answer 4:
Question 5:
If x = , then equals
(a)
(b) 4
(c) 2
(d)
(a)
(b) 4
(c) 2
(d)
Answer 5:
.We need to find
We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get
Therefore,
Hence the correct option is.
Question 6:
If = , then
(a) a = 2, b =1
(b) a = 2, b =−1
(c) a = −2, b = 1
(d) a = b = 1
(a) a = 2, b =1
(b) a = 2, b =−1
(c) a = −2, b = 1
(d) a = b = 1
Answer 6:
We are asked to find a and b
We know that rationalization factor for is . We will multiply numerator and denominator of the given expression by, to get
On equating rational and irrational terms, we get
Comparing rational and irrational part we get
Hence, the correct choice is.
Question 7:
The simplest rationalising factor of is
(a)
(b)
(c)
(d) none of these
(a)
(b)
(c)
(d) none of these
Answer 7:
The rationalizing factor of is, since when we multiply given expression with this factor we get rid of irrational term.
Therefore, rationalizing factor of the given expression is
Hence correct option is.
Question 8:
The simplest rationalising factor of is
(a)
(b)
(c)
(d)
(a)
(b)
(c)
(d)
Answer 8:
Question 9:
The simplest rationalising factor of − is
(a)
(b)
(c)
(d)
(a)
(b)
(c)
(d)
Answer 9:
Question 10:
If x =, then (x−3)2 =
(a) 1
(b) 3
(c) 6
(d) 7
(a) 1
(b) 3
(c) 6
(d) 7
Answer 10:
We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get
Therefore,
On squaring both sides, we get
Hence the value of the given expression is.
Question 11:
If and xy =1, then
(a) 64
(b) 134
(c) 194
(d) 1/49
(a) 64
(b) 134
(c) 194
(d) 1/49
Answer 11:
Hence is given as
We need to find
We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get
Since so we have
Therefore,
Hence the value of the given expression is.
Question 12:
If then =
(a) 2
(b) 4
(c) 8
(d) 1
(a) 2
(b) 4
(c) 8
(d) 1
Answer 12:
We need to find
We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get
Therefore,
Hence the value of the given expression is 8.Hence correct option is .
Question 13:
If and , then x + y +xy=
(a) 9
(b) 5
(c) 17
(d) 7
(a) 9
(b) 5
(c) 17
(d) 7
Answer 13:
We are asked to find
Now we will rationalize x. We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get
Similarly, we can rationalize y. We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get
Therefore,
Hence the value of the given expression is.
Question 14:
If x= and y = , then x2 + y +y2 =
(a) 101
(b) 99
(c) 98
(d) 102
(a) 101
(b) 99
(c) 98
(d) 102
Answer 14:
We need to find
Now we will rationalize x. We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get
Similarly, we can rationalize y. We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get
Therefore,
Hence the value of the given expression is.
Question 15:
is equal to
(a)
(b)
(c)
(d)
(a)
(b)
(c)
(d)
Answer 15:
We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get
Hence the correct option is.
Question 16:
The value of is
(a)
(b) 4
(c) 3
(d)
(a)
(b) 4
(c) 3
(d)
Answer 16:
We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get
We can factor irrational terms as
Hence the value of given expression is.
Question 17:
If , then
(a) x = 13, y = −7
(b) x = −13, y = 7
(c) x = −13, y = −7
(d) x = 13, y = 7
(a) x = 13, y = −7
(b) x = −13, y = 7
(c) x = −13, y = −7
(d) x = 13, y = 7
Answer 17:
We know that rationalization factor for is . We will multiply numerator and denominator of the given expression by, to get
Since
On equating rational and irrational terms, we get
Hence, the correct choice is.
Question 18:
If x = , then
(a) 2
(b) 4
(c) 8
(d) 9
(a) 2
(b) 4
(c) 8
(d) 9
Answer 18:
We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get
Therefore,
Hence the value of the given expression is.
Question 19:
The value of is
(a)
(b)
(c)
(d)
(a)
(b)
(c)
(d)
Answer 19:
Hence the value of the given expression is.
Question 20:
The value of is
(a)
(b)
(c)
(d) none of these
(a)
(b)
(c)
(d) none of these
Answer 20:
Hence the value of the given expression is.
Question 21:
If then is equal to
(a) 0.1718
(b) 5.8282
(c) 0.4142
(d) 2.4142
(a) 0.1718
(b) 5.8282
(c) 0.4142
(d) 2.4142
Answer 21:
We can rationalize the denominator of the given expression. We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get
Putting the value of , we get
Hence the value of the given expression is 0.14142 and correct choice is.
Question 22:
If then the value of upto three places of decimal is
(a) 0.235
(b) 0.707
(c) 1.414
(d) 0.471
(a) 0.235
(b) 0.707
(c) 1.414
(d) 0.471
Answer 22:
We can factor out from the given expression, to get
Putting the value of, we get
Hence the value of expression must closely resemble be
The correct option is.
Question 23:
The positive square root of is
(a)
(b)
(c)
(d)
(a)
(b)
(c)
(d)
Answer 23:
Hence the square root of the given expression is
Hence the correct option is.
Question 24:
If , then
(a)
(b)
(c) 24
(d) 20
(a)
(b)
(c) 24
(d) 20
Answer 24:
We need to find
We know that rationalization factor for is. We will multiply numerator and denominator of the given expression by, to get
We know that therefore,
Hence the value of the given expression is 20 and correct option is (d).
Question 25:
If
(a) −5
(b) −6
(c) −4
(d) −2
(a) −5
(b) −6
(c) −4
(d) −2
Answer 25:
We need to find a
The given expression can be simplified by taking square on both sides
The irrational terms on right side can be factorized such that it of the same form as left side terms.
Hence,
On comparing rational and irrational terms, we get.Therefore, correct choice is .
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