Mathmetics

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

Q31.
The L.C.M and H.C.F of two numbers are 660 and 10 respectively. If the sum of the numbers is 170, what is the difference between the numbers ?
1) 50 2) 56
3) 60 4) 64
5)None of these
Answer : 50
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Q32.
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
Answer : 1 : 5
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
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Q33.
1) 8 2) 9
3) 10 4) 12
5)None of these
Answer : 10
Explanation :
Given, x2 + 9/x = 6x
Or x2 - 6x = 9
Or (x-3)2 = 0  
Or x = 3
So, x2 + 9/x= 10
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Q34.
If  a = 4/3, then, what is the value of 27a3 -108a+ 144a - 317  ?
1) 221 2) -231
3) -253 4) 0
5)None of these
Answer : -253
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
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Q35.
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 :
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 .
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Q36.
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
Answer : 43 years
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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Q37.
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
Answer : 100.8 sq cm
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Q38.
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 :
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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Q39.
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
Answer : 10 cm
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
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Q40.
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
Answer : 41
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