11.A square and a circle have equal perimeters. The ratio of the area of the square to the area circle is
(1) 1:1 (2) 1:4
(3) pi:2 (4) pi:4
Answer:(4) pi:4
Solution:
Step1:Perimeter of square =4s and perimeter of circle = 2xpixr are equal
=> 4s = 2xpixr
=> s/r=pix2
Step2:Area of square (sxs) / area of circle (Pi x rxr) = sxs/pixrxr = (s/r)^2 /pi
but (s/r) = (pi/2)
=> (s/r)^2 /pi = (pi/2)^2/pi = pi/4
Therefore, the ratio of the area of square and the circle are in the ratio pi:4
12. ABCD is a square with AB = (x + 16) cm and BC = (3x) cm. The
perimeter (in cm) of the square is :
(1) 16 (2) 24
(3) 32 (4) 96
Answer:(3) 32
Since, ABCD is a square this means AB =BC.
=> (x + 16) = 3x
=> 2x = 16
=> x = 8 cm.
Therefore, the length of the square is ( 8 + 16) =3x8 = 24cm.
and the perimeter = 8x4 =32 cm
13.The mean of 10 numbers is 0. If 72 and -12 are included in these
numbers, the new mean will be
(1) 0 (2) 5
(3) 6 (4) 60
Answer: (2) 5
Solution:
Number of number = 10 and their mean = 0.
since two more numbers are added, therefore total numbers = 12.
Using the formula for mean, we have
mean = ( 0 + 72 -12)/12 = 60/12 = 5
14.The circumference of the base of a right circular cylinder is 44 cm and
its height is 15 cm. The volume (in cm3) of the cylinder is (use pi = 22/7)
(1) 770 (2) 1155
(3) 1540 (4) 2310
Answer:(4) 2310
Solution:
Volume of right circular cylinder = (pixrxr)xl
where pi = 22/7 and r is radius of the circular base and l is the length of the cylinder.
Given that perimeter of circular base = 44
=> 2xpxr = 44
=> 2x(22/7)xr = 44
=> r/7=1
=> r =7
Put these values in the formula for volume to get
volume = (22/7)x7x7x15 = 2310
15.The value of 0.001 + 1.01 + 0.11 is
(1) 1.111 (2) 1.101
(3) 1.013 (4) 1.121
Answer: (4) 1.121
Solution:
0.001 + 1.01 + 0.11 = 0.001 + 1.12 = 1.121
16. In 1999, the population of a country was 30.3 million. The number which is the same as 30.3 million is
(1) 303000000 (2)30300000
(3) 3030000 (4)3030000000
Answer: (2)30300000
Solution:
We know, 1 million = 1000000
Then 30.3 million = 30.3 x 1000000 = 30300000
17.
If a^3 = 1 + 7, 3^3= 1 + 7 + b and 4^3 = 1 + 7 + c, where a, b, and c
are different positive integers, then the value of a+b+c is
(1) 58 (2) 68
(2) 77 (4) 79
Answer:(4) 79
Solution:
Step1: a^3 = 1 + 7 = 8 = 2^3
=> a=2
Step2: 3^3 = 1 + 7 + b
=> 27 =8 + b
=> b = 21 - 8 =21
Step3: 4^3 = 1 + 7 + c
=> 64 = 8 + c
=> 56 = c
Therefore, a + b+ c = 21 + 2 + 56 =79
18.We
call a number perfect if it is the sum of all its positive divisors,
except itself. For example,28 is a perfect number because 28 = 1 + 2 + 4
+ 7 +14. Which of the following numbers is a perfect number?
(1) 13 (2) 10
(3) 9 (4) 6
Answer: (4) 6
Solution:
taking each option one by one
(1) 13. There is divisor, other than the number itself, 1. Not a perfect number.
(2) 10. There are three divisors 1,2,5 and their sum = 8.Not a perfect number.
(3) 9. There are two divisors. 1,3 and their sum is 4.Not a perfect number.
(4).6. There are three divisors 1,2,3 and their sum is 6 itself. This is the perfect number we are looking for.
19. Which of the following number is a perfect square?
(1) 548543213 (2) 548543215
(3) 548543251 (4) 548543241
Answer:(4) 548543241
Solution:
A perfect square cannot end with 3. Rejecting option 1.
Again a perfect that has 5 at the unit digit must have 2 in the tenth place.Therefore, rejecting option 2.
Try the division method on option 4 and will get the perfect square.
20. The product of two whole numbers is 24. The smallest possible sum of these numbers is
(1) 8 (2) 9
(3) 10 (4) 12
Answer:
Solution:
The set of pairs of numbers that gives 24 on multiplication are
[(12,2),(8,3),(6,4)]. The sum of these numbers are (14,11,10) respectively.
Therefore the lowest possible sum is 10.
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