AMCAT Previous Years Questions on Numbers, decimal fractions and power



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Expected Ques

Basic Mathematics


       6 - 8 Questions


Applied Mathematics



      8 - 10 Questions


Engineering Mathematics


       8 - 10 Questions




Ques. There are four prime numbers written in ascending order of magnitude. The product of first three
is 385 and that of last three is 1001. Find the first number.
Op 1: 5
Op 2: 7
Op 3: 11
Op 4: 17
Op 5:

Correct Op : 1

Ques. A rectangular courtyard 3.78 meters long and 5.25 meters wide is to be paved exactly with square
tiles ,all of the same size. What is the largest size of the tile which could be used for the purpose?
Op 1: 14 cm
Op 2: 21 cm
Op 3: 42 cm
Op 4: None of these
Op 5:

Correct Op : 2

Ques. The largest four digit number which is a multiple of 8, 10,12 and 15 is:
Op 1: 120
Op 2: 9600
Op 3: 9840
Op 4: 9960
Op 5:

Correct Op : 4


Ques. Rajeev multiplies a number by 10, the log (to base 10) of this number will change in what way?
Op 1: Increase by 10
Op 2: Increase by 1
Op 3: Multiplied by 10
Op 4: None of these
Op 5:

Correct Op : 2

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
Op 5:

Correct Op : 3

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

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

Ques. The value of 21/2 upto three places of decimal is
Op 1: 1.41
Op 2: 1.412
Op 3: 1.413
Op 4: 1.414
Op 5:

Correct Op : 4



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

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
Op 5:

Correct Op : 2

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

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

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

Ques. If x = 1+21/2 and y=1-21/2, then x2+y2 is -
Op 1: 2
Op 2: 3
Op 3: 6
Op 4: 0
Op 5:

Correct Op : 3

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 : 2

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

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

Ques. If xy = yx and x = 2y, the value of y is:
Op 1: 1
Op 2: 2
Op 3: 3
Op 4: 4
Op 5: None of these

Correct Op : 2

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 500 ?

Op 1: 0

Op 2: 1

Op 3: 50

Op 4: None of these

Op 5:

Correct Op : 2

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

Ques. What is the value of 0-10 ?

Op 1: 0

Op 2: 1

Op 3: -10

Op 4: None of these

Op 5:

Correct Op : 4

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

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

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

Ques. What is the value of: x1.5 * x2 ?

Op 1: x3

Op 2: x3.5

Op 3: x0.75

Op 4: None of these

Op 5:

Correct Op : 2

Ques. What is the value of: (33*812*20)/95 ?

Op 1: 0

Op 2: 3

Op 3: 1/3

Op 4: None of these

Op 5:

Correct Op : 2

Ques. What number should be divided by (0.81)1/2 to give the result as 81?

Op 1: 9

Op 2: 81

Op 3: 72.9

Op 4: 0.9

Op 5:

Correct Op : 3

Ques. If 6(x-3) = 36(x-5), then what is the value of x?

Op 1: 2

Op 2: No value will agree

Op 3: -1

Op 4: 7

Op 5:

Correct Op : 4

Ques. Which is the largest among 21/2, 51/3 and 41/4 ?

Op 1: (2)1/2

Op 2: 51/3

Op 3: 41/4

Op 4: None of these

Op 5:

Correct Op : 2

Ques. What is the value of 10009/1004?

Op 1: 1005

Op 2: 105

Op 3: 1019

Op 4: None of these

Op 5:

Correct Op : 3

Ques. Which of the following fractions is less than 7/8 and greater than 1/3 ?

Op 1: 1/4

Op 2: 23/24

Op 3: 11/12

Op 4: 11/24

Op 5:

Correct Op : 4

Ques. 892.7 - 573.07 - 95.007 = ?

Op 1: 224.623

Op 2: 224.777

Op 3: 233.523

Op 4: 414.637

Op 5:

Correct Op : 1

Ques. Which is the closest approximation to the product 0.3333 x 0.25 x 0.499 x 0.125 x 24 ?

Op 1: 1/8

Op 2: 3/4

Op 3: 3/8

Op 4: 2/5

Op 5:

Correct Op : 1

Ques. Find the value of X :

0.009/X = 0.01

Op 1: 0.0009

Op 2: 0.09

Op 3: 0.9

Op 4: 9

Op 5:

Correct Op : 3

Ques. The least among the following is:

Op 1: 0.2

Op 2: 1/0.2

Op 3: 0.22222222

Op 4: (0.2)2

Op 5:

Correct Op : 4

Ques. In the following expression, there are two missing digits: * and #. Find the value of *.

1*5#4 / 148 = 78

Op 1: 1

Op 2: 4

Op 3: 6

Op 4: 8

Op 5: None of these

Correct Op : 1

Ques. What is the value of (-5)(4)(2)(-1/2)(3/4) ?

Op 1: -30

Op 2: -15

Op 3: 15

Op 4: 30

Op 5:

Correct Op : 3

Ques. If x * y = x2 + y2 - xy, then the value of 9 * 11 is:

Op 1: 93

Op 2: 103

Op 3: 113

Op 4: 121

Op 5:

Correct Op : 2

Ques. If a = 0.1039, then the value of (4a2 - 4a + 1)1/2 + 3a is:

Op 1: 0.1039

Op 2: 0.2078

Op 3: 1.1039

Op 4: 2.1039

Op 5:

Correct Op : 3

Ques. If a, b, c, d, e are five consecutive odd numbers, their average is:

Op 1: 5 (a + 4)

Op 2: (abcde/5)

Op 3: 5 (a + b + c + d + e)

Op 4: None of these

Op 5:

Correct Op : 4

Ques. (x % of 932) + 30 = 309.6

Find x.

Op 1: 25

Op 2: 30

Op 3: 35

Op 4: 40

Op 5:

Correct Op : 2

Ques. Which of the following multipliers will cause a number to be increased by 29.7% ?

Op 1: 1.297

Op 2: 12.97

Op 3: 129.7

Op 4: 1297

Op 5:

Correct Op : 1

Ques. If 2A = 3B and 4B = 5C, then A: C is:

Op 1: 4 : 3

Op 2: 8 : 15

Op 3: 15 : 8

Op 4: 3 : 4

Op 5:

Correct Op : 3

Ques. 0.4777 . . . is the recurring decimal for the fraction:

Op 1: 4777/100000

Op 2: 477/100

Op 3: 437/1000

Op 4: 43/90

Op 5:

Correct Op : 4

Ques. 0.8888 ÷ 0.011 is equal to:

Op 1: 8.08

Op 2: 80.8

Op 3: 0.808

Op 4: None of these

Op 5:

Correct Op : 2

Ques. The ascending order of rational numbers -7/10, 5/-8, 2/-3 is:

Op 1: -7/10, 2/-3, 5/-8

Op 2: -7/10, 5/-8, 2/-3

Op 3: 5/-8, -7/10, 2/-3

Op 4: 2/-3, 5/-8, -7/10

Op 5:

Correct Op : 1

Ques. If A is real and 1 + A + A2 + A3 = 40, then A is equal to:

Op 1: -3

Op 2: -1

Op 3: 1

Op 4: 3

Op 5:

Correct Op : 4

Ques. (1 + 3 + 5 + ... + 3983) / 1992 = ?

Op 1: 1988

Op 2: 1992

Op 3: 1990

Op 4: None of these

Op 5:

Correct Op : 2

Ques. Which one of the following should be added to 25p2 + 16q2, so that the resulting sum becomes a

perfect square?

Op 1: 20pq

Op 2: 30pq

Op 3: 40pq

Op 4: 50p2q2

Op 5:

Correct Op : 3

Ques. (1.0816) 1/2= ?
Op 1: 0.14
Op 2: 1.4
Op 3: 1.004
Op 4: 1.04
Op 5:

Correct Op : 4

Ques. If the digit in the units place of a square natural number is 6, then the digit in the tens place will
be:
Op 1: 1
Op 2: 3
Op 3: Even
Op 4: Odd
Op 5:

Correct Op : 4

Ques. (a+b)3-(a-b)3 can be factorized as:
Op 1: 2b(3a2+b2)
Op 2: 2a(3a2+b2)
Op 3: 2b(3b2+a2)
Op 4: 2a(a2+3b2)
Op 5:

Correct Op : 1

Ques. If 9x2+3px+6q when divide by 3x+1 leaves a remainder -3/4 and qx2+4px+7 is exactly divisible by
x+1, then the values of p and q respectively will be:
Op 1: 0, 7/4
Op 2: -7/4, 0
Op 3: Same
Op 4: 7/4, 0
Op 5:

Correct Op : 4

Ques. The equations 2x+3y-7=0 and 10x+15y-35=0 are:
Op 1: Consistent and have unique solution
Op 2: Consistent and have infinitely many solutions
Op 3: inconsistent
Op 4: none of these
Op 5:

Correct Op : 2

Ques. The solution of the simultaneous equations (1/2)x + (1/3)y = 2 and x+y=1 is:
Op 1: x = 0, y = 1
Op 2: x = 1, y = 0
Op 3: x = 2/3, y = 3/2
Op 4: x = 10, y = -9
Op 5:

Correct Op : 4

Ques. If the equation x2-2(k+1)x+(9/2)k=0 has two identical roots then the values of k are:
Op 1: k=1, 2
Op 2: k=2 or 1/2
Op 3: k=3, 1/2
Op 4: none of these
Op 5:

Correct Op : 2

Ques. The number which should be subtracted from 5a2-3ab+7b2 to make it equal to a2+ab+b2, is:
Op 1: 4a2-4ab+6b2
Op 2: 4a2-4ab+5b2
Op 3: 4a2+4ab+6b2
Op 4: 4a2-3ab+6b2
Op 5: None of these

Correct Op : 1

Ques. If x = (1/2) (2p+2q-r), y = (1/3) (-p-2q+3r) and z=(1/5) (3p-4r+5q), then the value of 2x-3y-5z is:
Op 1: 0
Op 2: -q
Op 3: 2
Op 4: None of these
Op 5:

Correct Op : 2

Ques. The roots of the quadratic equation 6x2-5x+1=0 are:
Op 1: 2,3
Op 2: 1/2,1/3
Op 3: 3,4
Op 4: 1/3,1/4
Op 5: None of these

Correct Op : 2

Ques. If a = 16, b=25, the value of 1/(a-1/2 - b-1/2) is:
Op 1: 10
Op 2: 15
Op 3: 20
Op 4: 25
Op 5: 30

Correct Op : 3

Ques. 3a2 (ab+bc+ca) =
Op 1: 3a2+3a2bc+3a3c
Op 2: 3a3b+3a2bc+3c
Op 3: 3a3b+3a2bc+3a3c
Op 4: a3b+abc+a2c
Op 5: None of these

Correct Op : 3

Ques. x4y-xy4 =
Op 1: xy(x-y)(x2 + xy + y2)
Op 2: xy(x+y)(x2-xy+y4)
Op 3: x(xy-1)(x2-xy+y)
Op 4: (x3+y2)xy
Op 5: None of these

Correct Op : 1

Ques. Factors of 6a2-25a+4 are:
Op 1: (a+4) (a-6)
Op 2: (a-4) (6a+1)
Op 3: (a-4)(6a-1)
Op 4: (a-6) (a-4)
Op 5: None of these

Correct Op : 3

Ques. The correct relationship after eliminating x, y and z from x+y = a, y+z=b and z+x = c and x+y+z = m,
is:
Op 1: m=x+y+z
Op 2: 2m=a+b+c
Op 3: m=x-y-z
Op 4: 2m=x-y-z
Op 5: None of these

Correct Op : 2

Ques. If r = at2 and s = 2at, the relation among s, r and a is:
Op 1: s2=4ar
Op 2: s=ar
Op 3: s=2ar
Op 4: s2=ar
Op 5: None of these

Correct Op : 1

Ques. If a+b=6, ab=5, the value of a-b is:
Op 1: 4
Op 2: 5
Op 3: 6
Op 4: 7
Op 5: 9

Correct Op : 1

Ques. |X - 5| + 4 > 0 and |X2| < 4. Then x can be:
Op 1: 4
Op 2: 2
Op 3: 0.5
Op 4: All of these
Op 5:

Correct Op : 3

Ques. If f(x) = sum of all the digits of x, where x is a natural number, then what is the value of
f(101)+f(102)+f(103)+ .. +f(200)?
Op 1: 1000
Op 2: 784
Op 3: 999
Op 4: 1001
Op 5:

Correct Op : 4

Ques. Pawan is a very confused person. Once he wrote 1+2+3+4+5+6+7+8+9+10 = 100. In how many
places you need to change '+' with ' * ' to make the equality hold good ?
Op 1: 2
Op 2: 4
Op 3: 3
Op 4: None of these
Op 5:
Correct Op : 3
Explanation - Apart from the mathematical correction, through the logical reasoning, the answer is 1×2+3×4+5+6+7×8+9+101×2+3×4+5+6+7×8+9+10 =2+12+5+6+56+9+10=2+12+5+6+56+9+10 =14+11+65+10=14+11+65+10 =25+65+10=25+65+10 =100

Ques. What is the highest power of 82 contained in 83!-82! ?
Op 1: 3
Op 2: 2
Op 3: 164
Op 4: None of these
Op 5:

Correct Op : 1

Ques. If x = 0.75, then what is the value of the expression (1+x+x2) + x3/(1-x) ?
Op 1: 0.25
Op 2: 4
Op 3: 1.75
Op 4: 1
Op 5:

Correct Op : 2

Ques. If a lies between 2 and 3, both included, and b lies between 4 and 6, both included, then what is
the ratio of minimum and maximum limits of a2-b2?
Op 1: -4
Op 2: 4
Op 3: 32/7
Op 4: - 28/6
Op 5:

Correct Op : 3

Ques. If a, b, c are roots of the equation 1x3-4x2+6.5x + 3.5 = 0, then what is the value of a2 + b2 + c2?
Op 1: 1
Op 2: 64
Op 3: 169
Op 4: 3
Op 5:

Correct Op : 4

Ques. If |x| + |y| = 7, then what is the sum of minimum and maximum values of x + y?
Op 1: 3/2
Op 2: -7
Op 3: 7
Op 4: 0
Op 5:

Correct Op : 4

Ques. 832.58-242.31 =779.84- ?
Op 1: 179.57
Op 2: 199.57
Op 3: 295.05
Op 4: None of these
Op 5:

Correct Op : 4

Ques. Which is the closest approximation to the product 0.3333 * 0.25 * 0.499 * 0.125 * 24 ?
Op 1: 1/8
Op 2: 3/4
Op 3: 3/8
Op 4: 2/5
Op 5:

Correct Op : 1

Ques. The simplification of (0.2 * 0.2 + 0.02 * 0.02 - 0.4 * 0.02) / 0.36
Op 1: 0.009
Op 2: 0.09
Op 3: 0.9
Op 4: 9
Op 5:

Correct Op : 2

Ques. If 13 + 23+ 33+ ..........+ 93 = 2025 ,then the value of (0.11)3 + (0.22)3 + ....+ (0.99)3 is close to:
Op 1: 0.2695
Op 2: 0.3695
Op 3: 2.695
Op 4: 3.695
Op 5:

Correct Op : 3

Ques. In a purse there are 30 coins, twenty one-rupee and remaining 50-paise coins. Eleven coins are
picked simultaneously at random and are placed in a box. If a coin is now picked from the box, find the
probability of it being a rupee coin?
Op 1: 4/7
Op 2: 1/2
Op 3: 2/3
Op 4: 5/6
Op 5:

Correct Op : 3

Ques. Which among the following is greatest: 51/2, 111/3, 1231/6 ?
Op 1: 51/2
Op 2: 111/3
Op 3: 1231/6
Op 4: All are equal
Op 5:

Correct Op : 1

Ques. What are the unit's digits of 369, 6864, 4725 respectively ?
Op 1: 9,6 and 6
Op 2: 6, 6 and 6
Op 3: 3,6 and 4
Op 4: None of these
Op 5:

Correct Op : 3

Ques. A = 11 * 22 * 33 * 44 * 55 * ........1010. How many zeroes will be there at the end of A ?
Op 1: 6
Op 2: 15
Op 3: 10
Op 4: None of these
Op 5:

Correct Op : 2

Ques. If x = 3 + 31/2, then what is the value of x2 + 9/x2 ?
Op 1: 15 + 3 * 31/2
Op 2: 18 + 3 * 31/2
Op 3: 27 + 3 * 31/2
Op 4: None of these
Op 5:
Correct Op : 4

Ques. If x4 + 1/x4 = 47, then find the value of x3 + 1/x3
Op 1: 18
Op 2: 27
Op 3: 9
Op 4: 12
Op 5:

Correct Op : 1


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