Mathmetics
ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams
Q31. 

1)  1 : 6  2)  1 : 5 
3)  1 : 25  4)  1 : 125 
5)  None of these 
Answer : 1 : 5
Explanation :
Explanation :
The volume of the larger cube = 53 = 125 cm^{3}.
The volume of each of the smaller cubes = 13 = 1 cm^{3}.
Therefore, one would get 125 smaller cubes.
The surface area of the larger cube = 6a^{2} = 6(52) = 6 25 = 150
The surface area of each of the smaller cubes = 6 (12) = 6.
Therefore, surface area of all of the 125, 1 cm^{3} cubes = 125 6 = 750.
Therefore, the required ratio = 150 : 750 = 1 : 5
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Q32. 
1)  8  2)  9 
3)  10  4)  12 
5)  None of these 
Answer : 10
Explanation :
Explanation :
Given, x^{2} + 9/x = 6x
Or x^{2}  6x = 9
Or (x3)^{2} = 0
Or x = 3
So, x^{2} + 9/x^{2 }= 10
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Q33. 

1)  221  2)  231 
3)  253  4)  0 
5)  None of these 
Answer : 253
Explanation :
Explanation :
Given, a = 4/3
Or 3a = 4
Or 3a  4 = 0
Or (3a4)^{3} = 27a^{3}  108a^{2} + 144a  64 = 0^{3}
Or 27a^{3}  108a^{2} + 144a  317 = (27a^{3}  108a^{2} + 144a 64)  153 = 0  253 =  253
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Q34.  A fort has provisions for 250 soldiers for 35 days. After 5 days a reinforcements of 25 soldiers were arrived. Again after 10 days, 25 soldiers left the fort. How long will the remaining provisions lasting ? 
1)  12  2)  16 
3)  18  4)  19 
5)  None of these 
Answer : 19
Explanation :
Explanation :
Short Cut Methods:
ND (No. of days) = N_{1}D_{1} + N_{2}D_{2} = total amount of food after 5 days.
or ( 250 X 30) = ( 250 + 25) X 10 + 250 X x
or x = 19 days .
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Q35. 

1)  33 years  2)  40 years 
3)  43 years  4)  48 years 
5)  None of these 
Answer : 43 years
Explanation :
Explanation :
Present age of C = 85 – 7 = 78 years
Present age of B = 78 – 12 = 66 years
Present age of A = 3
11 66 = 18 years
Present age of A’s father = 18 + 25 = 43 years
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Q36. 

1)  100.8 sq cm  2)  112.4 sq cm 
3)  104.2 sq cm  4)  Cannot be determined 
5)  None of these 
Answer : 100.8 sq cm
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Q37.  The ratio of the adjacent angles of a parallelogram is 7 : 8. Also, the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ? 
1)  136°  2)  156° 
3)  168°  4)  208° 
5)  None of these 
Answer : 168°
Explanation :
Explanation :
Sum of the adjacent angles of a parallelogram is 180°.
Smaller angle of the parallelogram = 7/15 × 180 = 84°
Second largest angle of the quadrilateral = 7/30 × 360 = 84°
Required sum = 84 + 84 = 168°
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Q38.  The smallest side of a rightangled triangle is 8 cm less than the side of a square of perimeter 56 cm. The second largest side of the rightangled triangle is 4 cm less than the length of the rectangle of area 96 sq cm and breadth 8 cm. What is the largest side of the rightangled triangle ? 
1)  10 cm  2)  12 cm 
3)  15 cm  4)  18 cm 
5)  None of these 
Answer : 10 cm
Explanation :
Explanation :
Side of the square = 56/4 = 14 cm
smallest side of the triangle = 14 – 8 = 6 cm
Length of the rectangle = 96/ 8 = 12 cm
Second largest side of the triangle = 112 – 4 = 8 cm
So, Largest side of the triangle = square root of 6^{2} + 8^{2 } = 10 cm
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Q39. 

1)  26  2)  27 
3)  41  4)  56 
5)  None of these 
Answer : 41
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Q40. 

1)  2420  2)  2880 
3)  3260  4)  4840 
5)  None of these 
Answer : 2880
Explanation :
Explanation :
Treating the group of four vowels (E, I O and U) as one distinct letter then total number of letters will be 8  4 + 1 = 5 [i.e. P, R, V, S and (E, I, O, U)].
The five letters can be arranged in 5! = 120 ways The vowels among themselves can be arranged in 4! = 24 ways,
The letters of the word ‘PREVIOUS’ can be arranged in 120 × 24 = 2880 ways such that vowels always come together.
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