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### Mathmetics

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

##### A 5 cm cube is cut into as many 1 cm cubes as possible. What is the ratio of the surface area of the larger cube to that of the sum of the surface areas of the smaller cubes ?
 1) 1 : 6 2) 1 : 5 3) 1 : 25 4) 1 : 125 5) None of these
Explanation :
The volume of the larger cube = 53 = 125 cm3.
The volume of each of the smaller cubes = 13 = 1 cm3
Therefore, one would get 125 smaller cubes.
The surface area of the larger cube = 6a2 = 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 cm3 cubes = 125  6 = 750.
Therefore, the required ratio = 150 : 750 = 1 : 5
##### Q82.
 1) 8 2) 9 3) 10 4) 12 5) None of these
Explanation :
Given, x2 + 9/x = 6x
Or x2 - 6x = 9
Or (x-3)2 = 0
Or x = 3
So, x2 + 9/x= 10
##### If  a = 4/3, then, what is the value of 27a3 -108a2 + 144a - 317  ?
 1) 221 2) -231 3) -253 4) 0 5) None of these
Explanation :
Given, a = 4/3
Or  3a = 4
Or 3a - 4 = 0
Or (3a-4)3 = 27a3 - 108a2 + 144a - 64 = 03
Or 27a3 - 108a2 + 144a - 317 = (27a3 - 108a2 + 144a -64) - 153 = 0 - 253 = - 253
##### 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
Explanation :
Short- Cut Methods:

ND (No. of days) = N1D1 + N2D2 = total amount of food after 5 days.
or ( 250 X 30) = ( 250 + 25) X 10 + 250 X x
or  x = 19 days .
##### The ratio of the present age of  A  to that of  B is 3 : 11.  B  is 12 years younger than C. C ''s age after 7 years will be 85 years. What is the present age of  A's  father, who is 25 years older than A ?
 1) 33 years 2) 40 years 3) 43 years 4) 48 years 5) None of these
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
##### The length of a rectangle is three-fifths of the side of a square. The radius of a circle is equal to side of the square. The circumference of the circle is 132 cm. What is the area of the rectangle if the breadth of the rectangle is 8 cm ?
 1) 100.8 sq cm 2) 112.4 sq cm 3) 104.2 sq cm 4) Cannot be determined 5) None of these
##### 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
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°
##### The smallest side of a right-angled triangle is 8 cm less than the side of a square of perimeter 56 cm. The second largest side of the right-angled 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 right-angled triangle ?
 1) 10 cm 2) 12 cm 3) 15 cm 4) 18 cm 5) None of these
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 62 + 82  = 10 cm
##### A boy has 3 library tickets and 8 books of his interest in the library. Of these 8, he does not want to borrow Chemistry part II unless Chemistry part I is also borrowed. In how many ways can he choose the three books to be borrowed?
 1) 26 2) 27 3) 41 4) 56 5) None of these