ALGEBRIC IDENTITIES
1.
If
a2 + 
= 98(a 
),
then the value of a3 + 
will be
= 98(a ),
then the value of a3 + will be
(1) 535 (2) 1030 (3) 790 (4) 970
2.
If 4x
= 18y, then the value of (
) is
) is
(1) 
(2) 
(3) 
(4) 
(2) (3) (4)
3.
If
x2 + y2 - 4x - 4y + 8 = 0, then the value of x – y is
(1) 4 (2) -4 (3) 0 (4) 8
4.
If
x2 – 3x + 1 = 0, then the value of x3 + 
is
is
(1) 9 (2)
18 (3) 27 (4) 1
5.
If
the sum of 
and its reciprocal is 1 and a 
0, b 0, then the value of a3 + b3
is
and its reciprocal is 1 and a 0, b 0, then the value of a3 + b3
is
(1) 2 (2) -1 (3) 0 (4) 1
6.
If
x – y = 
= 
,
the numerical value of xy is
= ,
the numerical value of xy is
(1) 
(2) 
(3) 
(4)
(2) (3) (4)
7.
If
(a - 3)2 + (b - 4)2 + (c - 9)2 = 0, then the
value of 
is
is
(1) -4 (2) 4 (3) 
4 (4) 
2
4 (4) 2
8.
If
x + 
= 2, x 0 then the value of x2 + is equal to
= 2, x 0 then the value of x2 + is equal to
(1) 1 (2) 2 (3) 3 (4) 4
9.
If
a2 + b2 + c2 + 3 = 2 (a + b + c) then the
value of (a + b +c) is
(1) 2 (2) 3 (3) 4 (4) 5
10.
If
x varies inversely as (y2 - 1) and is equal to 24 when y = 10, then
the value of x when y = 5 is
(1) 99 (2) 12 (3) 24 (4) 100
11.
If
x + y = 2z, then the value of 
+ 
is
+ is
(1) 1 (2) 3 (3) 
(4) 2
(4) 2
12.
If
p + q = 10 and pq = 5, then the numerical value of 
+ 
will be
+ will be
(1) 16 (2) 20 (3) 22 (4) 18
13.
If
x3 + y3 = 35 and x + y = 5, then the value of + 
will be
+ will be
(1) (2) 
(3) 6 (4)
(2) (3) 6 (4)
14.
If
x + = 5, then the value of 
= 5, then the value of
(1) 
(2) 
(3) 
(4) 
(2) (3) (4)
15.
If
x = 1 + 
+ 
,
then the value of (2x4 – 8x3 – 5x2 + 26x - 28)
is
+ ,
then the value of (2x4 – 8x3 – 5x2 + 26x - 28)
is
(1) 6
(2) 0 (3) 3 (4) 2
(2) 0 (3) 3 (4) 2
16.
If 
+ 
= 
+ 
, b a, then the value of x is
+ = + , b a, then the value of x is
(1) 
(2) 
(3) 1 (4) 
(2) (3) 1 (4)
17.
If
x = 
, y = 
then the value of 
+ 
is
, y = then the value of + is
(1) (2) (3) 1 (4) 
(2) (3) 1 (4)
18.
If
xa . xb . xc = 1 then the value of a3
+ b3 + c3 is
(1) 9 (2) abc (3) a + b + c (4) 3abc
19.
If
a + 
+ 2 = 0, then the value of (a37 - 
)
is
+ 2 = 0, then the value of (a37 - )
is
(1) 0 (2) -2 (3) 1 (4) 2
20.
If
x = 2 - 
+ 
,
then the value of x3 – 6x2 + 18x + 18 is
+ ,
then the value of x3 – 6x2 + 18x + 18 is
(1) 22 (2) 33 (3) 40 (4) 45
21.
If
2x = 3y = 6-z then (
+ 
) is equal to
+ ) is equal to
(1) 0 (2) 1 (3) 
(4)
(4)
22.
If
a * b = 2a – 3b + ab, then 3 * 5 + 5 * 3 is equal to
(1) 22 (2) 24 (3) 26 (4) 28
23.
Two
numbers x and y(x 
) are such that their sum is equal to three times their difference. Then
value of 
will be
) are such that their sum is equal to three times their difference. Then
value of will be
(1) 1.0 (2) 0.5 (3) 0.6 (4) 1.1
24.
For
what value(s) of a is x + 
+ a2 a perfect square
+ a2 a perfect square
(1) 18 (2) 
(3) -
(4) 
18 (2) (3) - (4)
25.
If 
+ 
+ 
= 1, then the value of 
+ 
+ 
is
+ + = 1, then the value of + + is
(1) 1 (2) 2 (3) 3 (4) 4
26.
If
a2x + 2 = 1, where a is a positive real number other than 1, then x
is equal to
(1) -2 (2) -1 (3) 0 (4) 1
27.
The
value of (1 + )(1 + )( 1 + 
)( 1 + 
) is
)(1 + )( 1 + )( 1 + ) is
(1) (1 + 
) (2) x+4 (3) (4) 
) (2) x+4 (3) (4)
28.
If
1
x2,
then the value of 
+ 
is
x2,
then the value of + is
(1) 1 (2) 2 (3) 3 (4) 2x – 4
29.
If
47.2506 = 4A + 
+ 2C + 
+ 6E, then the value of 5A + 3B + 6C + D + 3E
is
+ 2C + + 6E, then the value of 5A + 3B + 6C + D + 3E
is
(1) 53.6003 (2) 53.603 (3) 153.6003 (4) 213.0003
30.
If
55x + 5 = 1, then x equals to
(1) 0 (2) -1 (3) 1 (4) -
31.
If
………
=
,
the value of x is
………=,
the value of x is
(1) 31 (2) 32 (3) 36 (4) 37
32.
If
= 
= 
= 3, then the value of
= ?
= = = 3, then the value of = ?
(1) 2 (2) 3 (3) 4 (4) 9
33.
If
x = 7 - 4,
then 
+ 
is equal to
,
then + is equal to
(1) 1
(2) 2
(3) 3 (4) 4
34.
The
third proportional to (
+ 
) and 
is
+ ) and is
(1) xy (2) 
(3) 
(4) 
(3) (4)
35.
Let
a = - 
,
b = - 2, c = 2 - ,
Then point out the correct alternative among the four alternatives given below.
- ,
b = - 2, c = 2 - ,
Then point out the correct alternative among the four alternatives given below.
(1) b
(2) a
(3) b
(4) a
(2) a (3) b (4) a
36.
If 
= a, 
= b, and 
= c, where a, b, c are all non-zero numbers,
then x equals to
= a, = b, and = c, where a, b, c are all non-zero numbers,
then x equals to
(1) 
(2) 
(3) 
(4) 
(2) (3) (4)
37.
If
a + b + c = 0, then the value of (
+ 
+ 
)(
+ 
+ 
)
is
+ + )( + + )
is
(1) 8 (2) -3 (3) 9 (4) 0
38.
If
x2 – 3x + 1 = 0, then the value of x2 + x + + 
is
+ is
(1) 10 (2) 2 (3) 6 (4) 8
39.
If
+ 
+ 
= 4(a+b+c) , then x is equal to
+ + = 4(a+b+c) , then x is equal to
(1) (a+b+c)2 (2) a2+b2+c2 (3) ab+bc+ca (4) a2+b2+c2-ab-bc-ca
40.
If
a + b = 1, c + d = 1 and a – b =
, then the value of c2 - d2
, then the value of c2 - d2
(1) 
(2) 
(3) 1 (4) -1
(2) (3) 1 (4) -1
41.
If
= 
,
then the value of (x +
)
is
= ,
then the value of (x +)
is
(1) 15 (2) 10 (3) 20 (4) 5
42.
The
simplest form of the expression 
is
is
(1) 2p2 (2) 
(3) p+3 (4) 
(3) p+3 (4)
43.
If
p : q = r : s = t : u = 2 : 3, then (mp+nr+ot) : (mq+ns+ou) equals
(1) 3 : 2 (2) 2 : 3 (3) 1 : 3 (4) 1 : 2
44.
If
[p] means the greatest integer less than or equal to p, then [-]
+ [4]
+ [3] is equal to
]
+ [4]
+ [3] is equal to
(1) 4 (2) 5 (3) 6 (4) 7
45.
If
is an operation such thaALGEBRIC IDENTITIES
is an operation such thaALGEBRIC IDENTITIES
1.
If
a2 + = 98(a ),
then the value of a3 + will be
= 98(a ),
then the value of a3 + will be
(1) 535 (2) 1030 (3) 790 (4) 970
2.
If 4x
= 18y, then the value of () is
) is
(1) (2) (3) (4)
(2) (3) (4)
3.
If
x2 + y2 - 4x - 4y + 8 = 0, then the value of x – y is
(1) 4 (2) -4 (3) 0 (4) 8
4.
If
x2 – 3x + 1 = 0, then the value of x3 + is
is
(1) 9 (2)
18 (3) 27 (4) 1
5.
If
the sum of and its reciprocal is 1 and a 0, b 0, then the value of a3 + b3
is
and its reciprocal is 1 and a 0, b 0, then the value of a3 + b3
is
(1) 2 (2) -1 (3) 0 (4) 1
6.
If
x – y = = ,
the numerical value of xy is
= ,
the numerical value of xy is
(1) (2) (3) (4)
(2) (3) (4)
7.
If
(a - 3)2 + (b - 4)2 + (c - 9)2 = 0, then the
value of is
is
(1) -4 (2) 4 (3) 4 (4) 2
4 (4) 2
8.
If
x + = 2, x 0 then the value of x2 + is equal to
= 2, x 0 then the value of x2 + is equal to
(1) 1 (2) 2 (3) 3 (4) 4
9.
If
a2 + b2 + c2 + 3 = 2 (a + b + c) then the
value of (a + b +c) is
(1) 2 (2) 3 (3) 4 (4) 5
10.
If
x varies inversely as (y2 - 1) and is equal to 24 when y = 10, then
the value of x when y = 5 is
(1) 99 (2) 12 (3) 24 (4) 100
11.
If
x + y = 2z, then the value of + is
+ is
(1) 1 (2) 3 (3) (4) 2
(4) 2
12.
If
p + q = 10 and pq = 5, then the numerical value of + will be
+ will be
(1) 16 (2) 20 (3) 22 (4) 18
13.
If
x3 + y3 = 35 and x + y = 5, then the value of + will be
+ will be
(1) (2) (3) 6 (4)
(2) (3) 6 (4)
14.
If
x + = 5, then the value of
= 5, then the value of
(1) (2) (3) (4)
(2) (3) (4)
15.
If
x = 1 + + ,
then the value of (2x4 – 8x3 – 5x2 + 26x - 28)
is
+ ,
then the value of (2x4 – 8x3 – 5x2 + 26x - 28)
is
(1) 6 (2) 0 (3) 3 (4) 2
(2) 0 (3) 3 (4) 2
16.
If + = + , b a, then the value of x is
+ = + , b a, then the value of x is
(1) (2) (3) 1 (4)
(2) (3) 1 (4)
17.
If
x = , y = then the value of + is
, y = then the value of + is
(1) (2) (3) 1 (4)
(2) (3) 1 (4)
18.
If
xa . xb . xc = 1 then the value of a3
+ b3 + c3 is
(1) 9 (2) abc (3) a + b + c (4) 3abc
19.
If
a + + 2 = 0, then the value of (a37 - )
is
+ 2 = 0, then the value of (a37 - )
is
(1) 0 (2) -2 (3) 1 (4) 2
20.
If
x = 2 - + ,
then the value of x3 – 6x2 + 18x + 18 is
+ ,
then the value of x3 – 6x2 + 18x + 18 is
(1) 22 (2) 33 (3) 40 (4) 45
21.
If
2x = 3y = 6-z then ( + ) is equal to
+ ) is equal to
(1) 0 (2) 1 (3) (4)
(4)
22.
If
a * b = 2a – 3b + ab, then 3 * 5 + 5 * 3 is equal to
(1) 22 (2) 24 (3) 26 (4) 28
23.
Two
numbers x and y(x ) are such that their sum is equal to three times their difference. Then
value of will be
) are such that their sum is equal to three times their difference. Then
value of will be
(1) 1.0 (2) 0.5 (3) 0.6 (4) 1.1
24.
For
what value(s) of a is x + + a2 a perfect square
+ a2 a perfect square
(1) 18 (2) (3) - (4)
18 (2) (3) - (4)
25.
If + + = 1, then the value of + + is
+ + = 1, then the value of + + is
(1) 1 (2) 2 (3) 3 (4) 4
26.
If
a2x + 2 = 1, where a is a positive real number other than 1, then x
is equal to
(1) -2 (2) -1 (3) 0 (4) 1
27.
The
value of (1 + )(1 + )( 1 + )( 1 + ) is
)(1 + )( 1 + )( 1 + ) is
(1) (1 + ) (2) x+4 (3) (4)
) (2) x+4 (3) (4)
28.
If
1x2,
then the value of + is
x2,
then the value of + is
(1) 1 (2) 2 (3) 3 (4) 2x – 4
29.
If
47.2506 = 4A + + 2C + + 6E, then the value of 5A + 3B + 6C + D + 3E
is
+ 2C + + 6E, then the value of 5A + 3B + 6C + D + 3E
is
(1) 53.6003 (2) 53.603 (3) 153.6003 (4) 213.0003
30.
If
55x + 5 = 1, then x equals to
(1) 0 (2) -1 (3) 1 (4) -
31.
If
………=,
the value of x is
………=,
the value of x is
(1) 31 (2) 32 (3) 36 (4) 37
32.
If
= = = 3, then the value of = ?
= = = 3, then the value of = ?
(1) 2 (2) 3 (3) 4 (4) 9
33.
If
x = 7 - 4,
then + is equal to
,
then + is equal to
(1) 1
(2) 2
(3) 3 (4) 4
34.
The
third proportional to ( + ) and is
+ ) and is
(1) xy (2) (3) (4)
(3) (4)
35.
Let
a = - ,
b = - 2, c = 2 - ,
Then point out the correct alternative among the four alternatives given below.
- ,
b = - 2, c = 2 - ,
Then point out the correct alternative among the four alternatives given below.
(1) b (2) a (3) b (4) a
(2) a (3) b (4) a
36.
If = a, = b, and = c, where a, b, c are all non-zero numbers,
then x equals to
= a, = b, and = c, where a, b, c are all non-zero numbers,
then x equals to
(1)
(2) (3) (4)
(2) (3) (4)
37.
If
a + b + c = 0, then the value of ( + + )( + + )
is
+ + )( + + )
is
(1) 8 (2) -3 (3) 9 (4) 0
38.
If
x2 – 3x + 1 = 0, then the value of x2 + x + + is
+ is
(1) 10 (2) 2 (3) 6 (4) 8
39.
If
+ + = 4(a+b+c) , then x is equal to
+ + = 4(a+b+c) , then x is equal to
(1) (a+b+c)2 (2) a2+b2+c2 (3) ab+bc+ca (4) a2+b2+c2-ab-bc-ca
40.
If
a + b = 1, c + d = 1 and a – b =, then the value of c2 - d2
, then the value of c2 - d2
(1) (2) (3) 1 (4) -1
(2) (3) 1 (4) -1
41.
If
= ,
then the value of (x +)
is
= ,
then the value of (x +)
is
(1) 15 (2) 10 (3) 20 (4) 5
42.
The
simplest form of the expression is
is
(1) 2p2 (2) (3) p+3 (4)
(3) p+3 (4)
43.
If
p : q = r : s = t : u = 2 : 3, then (mp+nr+ot) : (mq+ns+ou) equals
(1) 3 : 2 (2) 2 : 3 (3) 1 : 3 (4) 1 : 2
44.
If
[p] means the greatest integer less than or equal to p, then [-]
+ [4]
+ [3] is equal to
]
+ [4]
+ [3] is equal to
(1) 4 (2) 5 (3) 6 (4) 7
45.
If
is an operation such that a * b = 2a when a 
b
is an operation such that a * b = 2a when a b
=a + b when ab
b
=a2 when a = b,
Then
[
]
is equal to
]
is equal to
(1) (2) 
(3) (4) 
(2) (3) (4)
46.
A
General of army wants to form a square from 36562 armies. After arrangement, he
found some armies left. How many armies were left?
(1) 81 (2)
36 (3) 97 (4) 65
47.
If
the product of two positive numbers is 1575 and their ratio is 7 : 9. Then the
greater number is
(1) 45 (2) 35 (3) 135 (4) 63
48.
The
term, that should be added to (4x2+8x) so that resulting expression
be a perfect square, is
(1) 2
(2) 4 (3) 2x (4) 1
49.
A
man is born in the year 1896 A.D. If in the year x2 A.D. his age is
x-4, the value of x is
(1) 40
(2) 44 (3) 36 (4) 42
50.
If
a2 + a + 1 = 0, then the value of a5 + a4 +1
is
(1) a2 (2) 1 (3) 0 (4) a
+ 1
51.
If 
= 7 then the value 
=
= 7 then the value =
(1)
433 (2) 322 (3) 343
(4)
432t a * b = 2a when a b
b
=a + b when ab
b
=a2 when a = b,
Then
[]
is equal to
]
is equal to
(1) (2) (3) (4)
(2) (3) (4)
46.
A
General of army wants to form a square from 36562 armies. After arrangement, he
found some armies left. How many armies were left?
(1) 81 (2)
36 (3) 97 (4) 65
47.
If
the product of two positive numbers is 1575 and their ratio is 7 : 9. Then the
greater number is
(1) 45 (2) 35 (3) 135 (4) 63
48.
The
term, that should be added to (4x2+8x) so that resulting expression
be a perfect square, is
(1) 2
(2) 4 (3) 2x (4) 1
49.
A
man is born in the year 1896 A.D. If in the year x2 A.D. his age is
x-4, the value of x is
(1) 40
(2) 44 (3) 36 (4) 42
50.
If
a2 + a + 1 = 0, then the value of a5 + a4 +1
is
(1) a2 (2) 1 (3) 0 (4) a
+ 1
51.
If = 7 then the value =
= 7 then the value =
(1)
433 (2) 322 (3) 343
(4)
432
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