Multiple choice questions on Mathematics for competitive examination Test 4
This is Test 4 on Mathematics consisting of 20 questions for self check of your preparedness for the competitive examination.
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This is a set of multiple choice questions on Mathematics for competitive examination
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Sr No Question Answer Remarks 1 The population of Sundergarh in 2001 was found to be 308429, an increase of 72958 as compared to 1991 census. What is the percentage increase? 0.309 Population in 2001: 308429; Population in 1991: 30842972958=235471. Now the population increase over 235471 is 72958 and percentage increase will be (72958*100)/235471=30.9% 2 Find the greatest number which on dividing 1657 and 2037 leaves a remainder of 6 and 5 respectively. 127 The trick lies in subtracting the number by the remainder i.e. 1651 and 2032 and find HCF which is 127. 3 What is the area of the sector formed by radius of 10 cm with 36 degree angle at the center 10π The area of the full circle is 100*π and that of 36 degree with 36/360 part of the circle i.e. 10π 4 Write the following numbers in descending order: 3/7, 2/11, 4/5, 3/2, 3/13, 3/4, 2/17 3/2, 4/5, 3/4, 3/7, 3/13, 2/11,2/17 The best and correct way is to make the numerator equal by finding the LCM of numerator which is 12. Now the numbers will become 12/28, 12/66, 12/15, 12/8, 12/52, 12/16, 12/102 and now write the numbers in the ascending order of denominator 5 What will be the shape of the surface to obtain maximum perimeter for a given area? rectangle with one minimum possible side When start reducing one dimension of the rectangle, the other starts increasing in multiple and gives the maximum perimeter. 6 The per day salary of two staff were in the ratio of 3:5. Now Rs. 9 per day increment was given to both. The ratio now becomes 12:23. What were the salary of both the staff earlier? 33 and 55 Let the HCF was x, than there earlier salary were 3x and 5x. Now with increase by Rs.9, their salary becomes3x+9 and 5x+9 and the ratio will be 12:23. By solving this equation we get x=11 and their salary were 33 and 55. 7 (1) is multiplied 12 times by itself. What will be the number 1 A negative number when multiplied by a even numbers, it will be positive. 8 The property of the centroid of a triangle is All 9 Find the area of a triangle with two sides of 10 cm and 12 cm and the angle enclosed is 30 degree 30 Recollect SAS method where if two sides and the angle enclosed is known then it is half of the multiple of the sides and sine of the angle enclosed. Therefore it is 1/2*10*12*sin30 or 30 cm² 10 A rectangular park is 45 m long and 30 m wide. A path of 2.5 wide is constructed outside the park. Find the area of the path? 400 m² Area of the outer and inner rectangle will be 50*35 and 45*30 and their difference will be 400 m² 11 The organizers of an essay competition decide that a winner in the
competition gets a prize of Rs 100 and a participant who does not win gets
a prize of Rs 25. The total prize money distributed is Rs 3,000. Find the
number of winners, if the total number of participants is 63.19 Here let the winner are x and participant not getting a prize are y than x+y=63 and 100x+25y=3000 or 4x+y=120. Solving these two equations we get 19 and 44 12 Sum of the six side polygon shown in the figure is 360⁰ than what will be the sum of the exterior angles of five side polygon 360⁰ The sum of the external angles as shown will always be 360 degree irrespective of the number and dimensions of the side 13 Find the smallest perfect square number which is divisible by each of the numbers 6, 9 and 15. 900 First find out the LCM and each of the number of LCM to be multiplied by a prime number which is odd in number to make it even number. Here LCM is 2x3x3x5 =90 and 2 and 5 are in odd number therefore to be multiplied 2×5=10 to make it 900 14 A tire has two punctures. The first puncture alone would have made the tire flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ? (18/5) The leakage rate are 1/9 and 1/6 and of the combined will be 1/9+1/6 or 15/54 and time to flat the tire will be 54/15 minutes 15 A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters a minute. When the tank is full, the inlet is opened and due to the leak the tank is empty in 8 hours. The capacity of the tank (in liters) is 5760 lts emptying rate is 1/61/8=1/24 or the tank will take 24*60 minutes to empty the full tank. Capacity of the tank is 24*60*4=5760 lts. 16 The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Rs 1. Find the sum 625 SI=P*2*4/100 and CI=P[1+4/100]²P or P*8/100+P*16/10000. On subtracting SI we get the difference as P*16*/10000=1 or P=625 17 The value of [x²y³3⁷]³ [x⁶y⁹3²¹] 18 Is the number 214936587 divisible by 9? Yes Divisibility by 3 and 9 is checked by checking the sum of digits and shall be divisible by 9. Here it is 2+1+4+9+3+6+5+8+7=45. Hence divisible 19 What are the factors of a²2ab+b²c² (ab+c)(abc) It is written as (ab)²c² or (ab+c)(abc) 20 Length of the diagonals of a rhombus are a and b, than its area is given by 1/2(a*b) 
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 Answered
 Review

Question 1 of 20
1. Question
The population of Sundergarh in 2001 was found to be 308429, an increase of 72958 as compared to 1991 census. What is the percentage increase?

Question 2 of 20
2. Question
Find the greatest number which on dividing 1657 and 2037 leaves a remainder of 6 and 5 respectively.

Question 3 of 20
3. Question
What is the area of the sector formed by radius of 10 cm with 36 degree angle at the center

Question 4 of 20
4. Question
Write the following numbers in descending order: 3/7, 2/11, 4/5, 3/2, 3/13, 3/4, 2/17

Question 5 of 20
5. Question
What will be the shape of the surface to obtain maximum perimeter for a given area?

Question 6 of 20
6. Question
The per day salary of two staff were in the ratio of 3:5. Now Rs. 9 per day increment was given to both. The ratio now becomes 12:23. What were the salary of both the staff earlier?

Question 7 of 20
7. Question
(1) is multiplied 12 times by itself. What will be the number

Question 8 of 20
8. Question
The property of the centroid of a triangle is

Question 9 of 20
9. Question
Find the area of a triangle with two sides of 10 cm and 12 cm and the angle enclosed is 30 degree

Question 10 of 20
10. Question
A rectangular park is 45 m long and 30 m wide. A path of 2.5 wide is constructed outside the park. Find the area of the path?

Question 11 of 20
11. Question
The organizers of an essay competition decide that a winner in the competition gets a prize of Rs 100 and a participant who does not win gets
a prize of Rs 25. The total prize money distributed is Rs 3,000. Find the number of winners, if the total number of participants is 63. 
Question 12 of 20
12. Question
Sum of the six side polygon shown in the figure is 360⁰ than what will be the sum of the exterior angles of five side polygon

Question 13 of 20
13. Question
Find the smallest perfect square number which is divisible by each of the numbers 6, 9 and 15.

Question 14 of 20
14. Question
A tire has two punctures. The first puncture alone would have made the tire flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?

Question 15 of 20
15. Question
A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters a minute. When the tank is full, the inlet is opened and due to the leak the tank is empty in 8 hours. The capacity of the tank (in liters) is

Question 16 of 20
16. Question
The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Rs 1. Find the sum

Question 17 of 20
17. Question
The value of [x²y³3⁷]³

Question 18 of 20
18. Question
Is the number 214936587 divisible by 9?

Question 19 of 20
19. Question
What are the factors of a²2ab+b²c²

Question 20 of 20
20. Question
Length of the diagonals of a rhombus are a and b, than its area is given by
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I don’t have any study material. One should develop his own study material and may contact the persons who appeared in the last LDCE examination if they have compiled any such material. Thankurli and Nasik training center has issued knowledge book which are helpful in such preparation.