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

1)  I only  2)  I and II only 
3)  II and III only  4)  I and III only 
5)  None of these 
Answer : I only
Explanation :
Explanation :
Explanation:
P = Rs. 5000 & T = 2 years.
I. S.I. on Rs. 5000 in 5 years is Rs. 2000.
(5000 x R x 5)/100 = 2000 or R = 8.
Thus I only gives the answer.
Correct answer is (1).
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Q32. 

1)  I and II only  2)  II and III only 
3)  All I, II and III  4)  Any two of the three 
5)  None of these 
Answer : All I, II and III
Explanation :
Explanation :
Explanation:
I. Material cost = Rs. 2.50 per m^{2}
II. Labour cost = Rs. 3500.
III. Total cost = Rs. 14,500.
Let the area be A sq. metres.
Material cost = Rs. (14500  3500) = Rs. 11,000.
5A/2 = 11000 or A = (11000 x 2 )/5 = 4400 m^{2}.
Thus, all I, II and III are needed to get the answer.
Correct answer is (3).
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Q33.  A person invested some amount at the rate of 12% simple interest and a certain amount at the rate of 10% simple interest. He received yearly interest of Rs. 130. But if he had interchanged the amounts invested, he would have received Rs.4 more as interest. How much did he invest at 12% simple interest ? 
1)  Rs.400  2)  Rs.500 
3)  Rs.700  4)  Rs.800 
5)  None of these 
Answer : Rs.700
Explanation :
Explanation :
Explanation :
Let the amount invested at 12% be x and the amount invested at 10% be y respectively
( x x 12 x 1)/100 +( y x 10 x 1)/100 = 130
1.2x + y = 1300
Similarly, 1.2y + x = 1340
or (1.2x) x 1.2 + 1.2y = 1300 x 1.2
x +1.2y = 1340
or 0.44x = 1560  1340 = 220
or x = (220/0.44)  Rs. 500
or y = 1300  1.2 x 500 = Rs. 700
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Q34.  A person invested some amount at the rate of 12% simple interest and a certain amount at the rate of 10% simple interest. He received yearly interest of Rs. 130. But if he had interchanged the amounts invested, he would have received Rs.4 more as interest. How much did he invest at 12% simple interest ? 
1)  Rs.400  2)  Rs.500 
3)  Rs.700  4)  Rs.800 
5)  None of these 
Answer : Rs.700
Explanation :
Explanation :
Explanation :
Let the amount invested at 12% be x and the amount invested at 10% be y respectively
( x x 12 x 1)/100 +( y x 10 x 1)/100 = 130
1.2x + y = 1300
Similarly, 1.2y + x = 1340
or (1.2x) x 1.2 + 1.2y = 1300 x 1.2
x +1.2y = 1340
or 0.44x = 1560  1340 = 220
or x = (220/0.44)  Rs. 500
or y = 1300  1.2 x 500 = Rs. 700
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Q35. 

1)  36 pie m3  2)  48 pie m3 
3)  50 pie m3  4)  54 pie m3 
5)  None of these 
Answer : 36 pie m3
Explanation :
Explanation :
Explanations:
Volume of the oil = 22/7x 62 x 14 = 504 x 22/7 m3.
Base radius of all the containers = 7 m
Volume of the spherical can = (4/3) x (22/7)x 63 m3.
Volume of the conical can = (1/3) x (22/7) x 62 x 6 m3 = 72 x (22/7)
Balance oil = Volume of the cylindrical can
= 504 (22/7)  288 (22/7) 72(22/7) = 144(22/7) m3.
Oil dropped = 1/4 th of the cylindrical can
= 1/4x 144 = 36 (22/7) m3.
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Q36. 

1)  2 : 3  2)  1 : 3 
3)  1 : 2  4)  1 : 4 
5)  None of these 
Answer : 1 : 2
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Q37.  If 2x^{2 }7xy +3y^{2 }= 0 ,then the value of x:y = ? 
1)  3:2  2)  2:3 
3)  3:1 and 1:2  4)  5:6 
5)  None of these 
Answer : 3:1 and 1:2
Explanation : Given, 2x^{2 }7xy +3y^{2 }= 0
Explanation : Given, 2x^{2 }7xy +3y^{2 }= 0
or 2(x/y)^{2}7(x/y)+ 3 = 0
So, x/y=3/1 and x/y=1/2
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Q38.  If a,b and c are real numbers such that ab+c <1 , a+b+c >1 and 9a+3b+c < 4, then what is the sign of 'a'? 
1)  + only  2)   only 
3)  + or   4)  Can't be said 
5)  None of these 
Answer :  only
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Q39.  If a,b and c are the two roots of a quadratic equation such that a+b =24 and ab = 8, the quadratic equation having a and b as its roots is . 
1)  x2+2x+8=0  2)  x24x+8=0 
3)  x224x+128=0  4)  2x2+8x+9=0 
5)  None of these 
Answer : x224x+128=0
Explanation : Given, a+b =24 and ab = 8
Explanation : Given, a+b =24 and ab = 8
So,solving from two equations,we get a =16 and b=8
Therefore,ab=16 x 8 = 128
Quadratic equations
x^{2}  ( sum of roots)x + products of the roots = 0
or x^{2}24x+128 = 0
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Q40.  What is the value of 'P' , if the following equation has two equal roots ? 
1)  P=6 or P=2  2)  P=4 or P=3 
3)  P=6 or P=3  4)  P=4 or P=2 
5)  None of these 
Answer : P=6 or P=2
Explanation : Here, a=4,b=  (P2); c=1
Explanation : Here, a=4,b=  (P2); c=1
Given, equation has equal roots,then D=0
b^{2} 4ac =0
or p^{2} +4  4p  16 = 0
or p^{2} 6p +2p  12 =0
or p(p6) + 2(p2) = 0
or p=6 or 2
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