AMCAT PREVIOUS QUESTION PAPER AND SOLUTION 2
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7^2=unit digit=9(7*7=49)last unit digit
7^3=unit digit=3(9*7=63)last unit digit
7^4=unit digit=1(3*7=21)last unit digit
7^5=unit digit=7(1*7=7)last unit digit
it repeats for every 4 cycle
so 71/4=remainder=3 it points 3rd cycle whose unit digit is=3
in same vise 6^anything will be resultant 6;
3^1=3
3^2=9(3*3)
3^3=7(9*3)
3^4=1(7*1)
3^5=3(1*3)
same like 7^71 term thus remainder is 1
multiply 3*6*3=24 .
unit digit is 4
> (2y)^y = y^2y
> 2^y * y^y =y^y * y^y
>2^y = y^y
y=2
In Amcat Exam Most of The Question Come From Simplefication Read more Questions
Ques. The unit's digit in the product (771 x 659 x 365) is
Op 1: 1
Op 2: 2
Op 3: 4
Op 4: 6
Correct Op :
Solution:
7^1=unit digit=7
7^2=unit digit=9(7*7=49)last unit digit
7^3=unit digit=3(9*7=63)last unit digit
7^4=unit digit=1(3*7=21)last unit digit
7^5=unit digit=7(1*7=7)last unit digit
it repeats for every 4 cycle
so 71/4=remainder=3 it points 3rd cycle whose unit digit is=3
in same vise 6^anything will be resultant 6;
3^1=3
3^2=9(3*3)
3^3=7(9*3)
3^4=1(7*1)
3^5=3(1*3)
same like 7^71 term thus remainder is 1
multiply 3*6*3=24 .
unit digit is 4
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Ques. 1.52 * 0.02251/2 = ?
Op 1: 0.0375
Op 2: 0.3375
Op 3: 3.275
Op 4: 32.75
Op 5:
Correct Op : 2
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Ques. If x1/2 / 4411/2 = 0.02, the value of x is:
Op 1: 0.1764
Op 2: 1.764
Op 3: 1.64
Op 4: 2.64
Op 5:
Correct Op : 1
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Ques. The value of 21/2 upto three places of decimal is
Op 2: 1.412
Op 3: 1.413
Op 4: 1.414
Op 5:
Correct Op : 4
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Ques. The value of (8-25- 8-26) is:
Op 1: 7 x 8-25
Op 2: 7 x 8-26
Op 3: 8 x 8-26
Op 4: None of these
Op 5:
Correct Op : 2
Solution;
8^-25-8^-26=[(1/8^25)-(1/8^26)]= 7*8^-26
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Ques. If 22n-1 = (1 / 8n-3) then the value of n is:
Op 1: 3
Op 2: 2
Op 3: 0
Op 4: -2
Correct Op : 2
SOLUTION:
Simple put n=2 in both side so in one side
2^2n-1=2^2*2-1=2^3=8----(1)
.
Another Side 1/8^n-3= 1/8^-1= 1/8^-1=8 ----(2)
.
So compare both equation both are equal than value 2 should be satisfied to equation
2^2n-1=2^2*2-1=2^3=8----(1)
.
Another Side 1/8^n-3= 1/8^-1= 1/8^-1=8 ----(2)
.
So compare both equation both are equal than value 2 should be satisfied to equation
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Ques. If 2x = 3y = 6-z, then (1/x + 1/y + 1/z) is equal to:
Op 1: 0
Op 2: 1
Op 3: 3/2
Op 4: -0.5
Op 5:
Correct Op : 1
Solution:
2x = 6 -z Þ 2 = 6-z/x -------------(i)
3y = 6 -z Þ 3 = 6-z/y -------------(ii)
Multiplying (i)and(ii)
2x3 = 6-z/x x 6-z/y
6 = 6(1-z/x) *6(1-z/y)
1 = (-z/x) +(-z/y)
1= -z(1/x +1/y)
1/-z = 1/x +1/y
1/x + 1/y + 1/z = 0
3y = 6 -z Þ 3 = 6-z/y -------------(ii)
Multiplying (i)and(ii)
2x3 = 6-z/x x 6-z/y
6 = 6(1-z/x) *6(1-z/y)
1 = (-z/x) +(-z/y)
1= -z(1/x +1/y)
1/-z = 1/x +1/y
1/x + 1/y + 1/z = 0
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Ques. What is the remainder when 1723 is divided by 16?
Op 2: 1
Op 3: 2
Op 4: 3
Op 5:
Correct Op : 2
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Ques. What will be the remainder when 1336 is divided by 2196?
Op 1: 0
Op 2: 1
Op 3: 12
Op 4: 2195
Op 5:
Correct Op : 2
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Ques. The roots of the equation 4x-3*2x+2+32=0 would include
-Op 1: 2, 3
Op 2: 1, 2, 3
Op 3: 1, 2
Op 4: 4, 8
Op 5:
Correct Op : 1
Solution:
Split the second term and rewrite 4^(x) as 2^(2x):
2^(2x) - 3 * [2^(x) * 2^2] + 32 = 0
2^(2x) - 12 * 2^(x) + 32 = 0
Let's give 2^x a value of y:
y^2 - 12y + 32 = 0
Factor it out:
(y - 8)(y - 4) = 0
y = 4, 8
Now substitute 2^x back for y and solve for each:
2^x = 4
x = 2
2^x = 8
x = 3
Overall:
x = 2, 3
2^(2x) - 3 * [2^(x) * 2^2] + 32 = 0
2^(2x) - 12 * 2^(x) + 32 = 0
Let's give 2^x a value of y:
y^2 - 12y + 32 = 0
Factor it out:
(y - 8)(y - 4) = 0
y = 4, 8
Now substitute 2^x back for y and solve for each:
2^x = 4
x = 2
2^x = 8
x = 3
Overall:
x = 2, 3
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Ques. If ax =b, by=c and cz =a, then the value of xyz is:
Op 1: 0
Op 2: 1
Op 3: 2
Op 4: 3
Op 5:
Correct Op : 2
Solution:
ax=b
by=c
cz=a
=> ax * by * cz = bca
=> xyz = bca/abc=1
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Ques. If x = 1+21/2 and y=1-21/2, then x2+y2 is –
Op 1: 2
Op 3: 6
Op 4: 0
Op 5:
Correct Op : 3
Solution:
x2+y2= (1+2^1/2)^2+ (1-2^1/2)^2
= (a+b)^2+(a-b)^2
so, we get
1+2+2*2^1/2+1+2-2^1/2
1+2+1+2=6 ans.
= (a+b)^2+(a-b)^2
so, we get
1+2+2*2^1/2+1+2-2^1/2
1+2+1+2=6 ans.
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Ques. If 4x+3 = 2x+7, then the value of x is:
Op 1: 3
Op 2: 2
Op 3: 1
Op 4: None of these Op 5:
Correct Op : 3
Ques. 2x+y = 2*(2)1/2 and 2x-y = 21/2,the value of x is:
Op 1: 1
Op 2: 2
Op 3: 3
Op 4: 4
Op 5: None of these Correct Op : 1
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Ques. If x = 8, y = 27, the value of (x4/3+y2/3)1/2 is:
Op 1: 5
Op 2: 6
Op 3: 7
Op 4: 8
Op 5: None of these Correct Op : 1
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Ques. If xy = yx and x = 2y, the value of y is:
Op 1: 1
Op 2: 2
Op 4: 4
Op 5: None of these
Correct Op : 2
Solution:
put x=2y
> (2y)^y = y^2y
> 2^y * y^y =y^y * y^y
>2^y = y^y
y=2
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Ques. If 2x * 3y = 18 and 22x * 3y= 36, the value of x is:
Op 1: 0
Op 2: 1
Op 3: 2
Op 4: 3
Op 5: None of these Correct Op : 2
Ques. What is the value of 50^0 ?
Op 1: 0
Op 2: 1
Op 3: 50
Op 4: None of these
Op 5:
Correct Op : 2
Solution:
anything power zero is zero
50^0=1
50^0=1
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Ques. What is the value of 6-2 ?
Op 1: 1/36
Op 2: 36
Op 3: -36
Op 4: None of these
Op 5:
Correct Op : 1
Solution:
answer is 1/6 *1/6 = 1/36
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Ques. What is the value of 0-10 ?
Op 1: 0
Op 2: 1
Op 3: -10
Op 5:
Correct Op : 4
Solution:
0^-10= 1/(0^10)=1/0= not defined
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Ques. What is the value of 251.5 ?
Op 1: 325
Op 2: 32.5
Op 3: 125
Op 4: None of these
Op 5:
Correct Op : 3
Solution:
25^3/2=(5^2)^3/2 then 5^3=125
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Ques. What is the value of (0.027)1/3?
Op 1: 0.3
Op 2: 0.03
Op 3: 0.003
Op 4: None of these
Op 5:
Correct Op : 1
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Ques. What is the value of (0.016)1/4?
Op 1: 0.2
Op 2: 0.02
Op 3: 0.002
Op 4: None of these
Op 5:
Correct Op : 4
Solution;
(0.016)^1/4 = (16/1000)^1/4 = (2^4/10^3)^1/4 = 2/(10^3/4) = 2/5.62 = 0.355(appx)
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