MCQS
Page-4.29
Question 1:
Mark the correct alternative in each of the following:
(1) If , then
(a) 25
(b) 10
(c) 23
(d) 27
(1) If , then
(a) 25
(b) 10
(c) 23
(d) 27
Answer 1:
Given
We shall use the identity
Here put,
Hence the value of is
Hence the correct choice is (c).
Question 2:
If , then
(a) 64
(b) 14
(c) 8
(d) 2
(a) 64
(b) 14
(c) 8
(d) 2
Answer 2:
Given
We shall use the identity
Here putting,
Hence the value of is
Hence the correct choice is (d).
Question 3:
If = 4, then
(a) 196
(b) 194
(c) 192
(d) 190
(a) 196
(b) 194
(c) 192
(d) 190
Answer 3:
Given
We shall use the identity
Here put,
Squaring on both sides we get,
Hence the value of is
Hence the correct choice is (b).
Question 4:
If , then =
(a) 927
(b) 414
(c) 364
(d) 322
(a) 927
(b) 414
(c) 364
(d) 322
Answer 4:
Given
We shall use the identityand
Here put,
Take Cube on both sides we get,
Hence the value of is
Hence the correct choice is (d).
Question 5:
If , then =
(a) 8
(b) 10
(c) 12
(d) 13
(a) 8
(b) 10
(c) 12
(d) 13
Answer 5:
Given
We shall use the identity
Here putting,
Hence the value of is
Hence the correct choice is (b).
Question 6:
If , then
(a) 5
(b) 10
(c) 15
(d) none of these
(a) 5
(b) 10
(c) 15
(d) none of these
Answer 6:
Given
We shall use the identity
Put we get,
Substitute y = 5 in the above equation we get
The Equation satisfy the condition that
Hence the value of is 5
The correct choice is (a).
Question 7:
If , then
(a) 5
(b) 4
(c) 3
(d) 2
(a) 5
(b) 4
(c) 3
(d) 2
Answer 7:
Given
We shall use the identity
Put we get,
Substitute y = 2 in above equation we get,
The Equation satisfy the condition that
Hence the value of is 2
Hence the correct choice is (d).
Question 8:
If a + b + c = 9 and ab + bc + ca = 23, then a2 + b2 + c2 =
(a) 35
(b) 58
(c) 127
(d) none of these
(a) 35
(b) 58
(c) 127
(d) none of these
Answer 8:
Given
Using identity we get,
By transposing +46 to left hand side we get,
Hence the value of is
The correct choice is (a).
Question 9:
(a − b)3 + (b − c)3 + (c − a)3 =
(a) (a + b + c) (a2 + b2 + c2 − ab − bc − ca)
(b) (a − b) (b − c) (c − a)
(c) 3(a − b) ( b− c) (c − a)
(d) none of these
(a) (a + b + c) (a2 + b2 + c2 − ab − bc − ca)
(b) (a − b) (b − c) (c − a)
(c) 3(a − b) ( b− c) (c − a)
(d) none of these
Answer 9:
Using identity
Here
Hence the Value of is
The correct choice is .
Question 10:
If , then a3 − b3 =
(a) 1
(b) −1
(c)
(d) 0
(a) 1
(b) −1
(c)
(d) 0
Answer 10:
Taking Least common multiple in we get,
Using identity
Hence the value of is
The correct choice is (d).
Question 11:
If a − b = −8 and ab = −12, then a3 − b3 =
(a) −244
(b) −240
(c) −224
(d) −260
(a) −244
(b) −240
(c) −224
(d) −260
Answer 11:
Given
Using identity
Here we get
Transposing -288 to left hand side we get
Hence the value of is -224
The correct choice is .
Question 12:
If the volume of a cuboid is 3x2 − 27, then its possible dimensions are
(a) 3, x2, − 27x
(b) 3, x − 3, x + 3
(c) 3, x2, 27x
(d) 3, 3, 3
(a) 3, x2, − 27x
(b) 3, x − 3, x + 3
(c) 3, x2, 27x
(d) 3, 3, 3
Answer 12:
Given: volume of cuboid
Take 3 as common factor
Using identity
We get,
Here the dimension of cuboid is 3,
The correct alternate is .
Question 13:
75 × 75 + 2 × 75 × 25 + 25 × 25 is equal to
(a) 10000
(b) 6250
(c) 7500
(d) 3750
(a) 10000
(b) 6250
(c) 7500
(d) 3750
Answer 13:
Using identity
Here
Hence the product of is 10,000
The correct choice is .
Question 14:
(x − y) (x + y) (x2 + y2) (x4 + y4) is equal to
(a) x16 − y16
(b) x8 − y8
(c) x8 + y8
(d) x16 + y16
(a) x16 − y16
(b) x8 − y8
(c) x8 + y8
(d) x16 + y16
Answer 14:
Using the identity
Hence is equal to
The correct choice is .
Question 15:
If , then
(a) 27
(b) 25
(c)
(d)
(a) 27
(b) 25
(c)
(d)
Answer 15:
Given
We shall use the identity
Here put,
We shall use the identitywe get,
Taking square root on both sides we get,
Hence the value of is
Hence the correct choice is (c).
Question 16:
If then
(a) 76
(b) 52
(c) 64
(d) none of these
(a) 76
(b) 52
(c) 64
(d) none of these
Answer 16:
Using identity
Here,
Again using identity
Here
Substituting
Using identity
Here
Hence the value of is
The correct choice is (b).
Question 17:
If , then =
(a) 4
(b)
(c)
(d)
(a) 4
(b)
(c)
(d)
Answer 17:
Given
We shall use the identity
Here putting,
Substitute in we get,
Hence the value of is
Hence the correct choice is (b).
Question 18:
If , then
(a) 25
(b) 35
(c) 49
(d) 30
(a) 25
(b) 35
(c) 49
(d) 30
Answer 18:
Given
Using identity we get,
Here
Substituting we get,
By transposing left hand side we get,
Again using identity we get,
Substituting we get
Using identity we get
Here
Substituting we get,
The value of is
The correct choice is (b)
Question 19:
If a2 + b2 + c2 − ab − bc − ca =0, then
(a) a + b + c
(b) b + c = a
(c) c + a = b
(d) a = b = c
(a) a + b + c
(b) b + c = a
(c) c + a = b
(d) a = b = c
Answer 19:
Multiplying both sides by 2 we get,
Therefore the sum of positive quantities is zero if and only if each quantity is zero.
If, then
The correct choice is (d).
Question 20:
If a + b + c = 0, then
(a) 0
(b) 1
(c) −1
(d) 3
(a) 0
(b) 1
(c) −1
(d) 3
Answer 20:
Given
Using identity
Hence the value of
The correct choice is (d).
Question 21:
If a1/3 + b1/3 + c1/3 = 0, then
(a) a + b + c = 0
(b) (a + b + c)3 =27abc
(c) a + b + c = 3abc
(d) a3 + b3 + c3 = 0
(a) a + b + c = 0
(b) (a + b + c)3 =27abc
(c) a + b + c = 3abc
(d) a3 + b3 + c3 = 0
Answer 21:
Using identity we get
Here
Taking Cube on both sides we get,
Hence the value of is
The correct choice is .
Question 22:
If a + b + c = 9 and ab + bc + ca =23, then a3 + b3 + c3 − 3abc =
(a) 108
(b) 207
(c) 669
(d) 729
(a) 108
(b) 207
(c) 669
(d) 729
Answer 22:
Given
Using identity we get,
By transposing +46 to left hand side we get,
Using identity
The value of is
Hence the correct choice is .
Question 23:
(a) 3(a + b) ( b+ c) (c + a)
(b) 3(a − b) (b − c) (c − a)
(c) (a − b) (b − c) (c − a)
(d) none of these
Answer 23:
Using Identity we get,
Hence the value of is
The correct choice is .
Question 24:
The product (a + b) (a − b) (a2 − ab + b2) (a2 + ab + b2) is equal to
(a) a6 + b6
(b) a6 − b6
(c) a3 − b3
(d) a3 + b3
(a) a6 + b6
(b) a6 − b6
(c) a3 − b3
(d) a3 + b3
Answer 24:
Using identity
We can rearrange as
Again using the identity
Here
Hence the product of is
The correct choice is .
Question 25:
The product (x2−1) (x4 + x2 + 1) is equal to
(a) x8 − 1
(b) x8 + 1
(c) x6 − 1
(d) x6 + 1
(a) x8 − 1
(b) x8 + 1
(c) x6 − 1
(d) x6 + 1
Answer 25:
Using identity
Here
Hence the product value of is
The correct alternate is .
Question 26:
If , then a3 + b3 =
(a) 1
(b) −1
(c)
(d) 0
(a) 1
(b) −1
(c)
(d) 0
Answer 26:
Using identity we get,
Hence the value of is .
The correct choice is (d).
Question 27:
If 49a2 − b = , then the value of b is
(a) 0
(b)
(c)
(d)
(a) 0
(b)
(c)
(d)
Answer 27:
Given
Using identity
We get
Equating ‘b’ on both sides we get
Hence the value of b is
The correct choice is .
Question 28:
One of the factors of (25x2 – 1) + (1 + 5x)2 is
(a) 5 + x
(b) 5 – x
(c) 5x – 1
(d) 10x
(a) 5 + x
(b) 5 – x
(c) 5x – 1
(d) 10x
Answer 28:
Question 29:
If , then the value of b is
(a) 0
(b)
(c)
(d)
(a) 0
(b)
(c)
(d)
Answer 29:
Question 30:
The coefficient of x in (x + 3)3 is
(a) 1
(b) 9
(c) 18
(d) 27
(a) 1
(b) 9
(c) 18
(d) 27
Answer 30:
Question 31:
(a) 1
(b) 477
(c) 487
(d) 497
Answer 31:
Question 32:
Which of the following is a factor of (x + y)3 – (x3 + y3)?
(a) x2 + 2xy + y2
(b) x2 – xy + y2
(c) xy2
(d) 3xy
(a) x2 + 2xy + y2
(b) x2 – xy + y2
(c) xy2
(d) 3xy
Answer 32:
Question 33:
If , the value of x3 – y3 is
(a) 1
(b) –1
(c) 0
(d)
(a) 1
(b) –1
(c) 0
(d)
Answer 33:
Question 34:
If , the value of x3 + y3 is
(a) 1
(b) –1
(c) 0
(d)
(a) 1
(b) –1
(c) 0
(d)
Answer 34:
Question 35:
If x2 + y2 + xy = 1 and x + y = 2, then xy =
(a) –3
(b) 3
(c)
(d) 0
(a) –3
(b) 3
(c)
(d) 0
Answer 35:
Question 36:
If a, b, c are natural numbers such that a2 + b2 + c2 = 29 and ab + bc + ca = 26, and a + b + c = ______.
(a) 9
(b) 6
(c) 7
(d) 10
(a) 9
(b) 6
(c) 7
(d) 10
Answer 36:
Question 37:
If
(a) 1008
(b) 168
(c) 106
(d) none of these
(a) 1008
(b) 168
(c) 106
(d) none of these
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