Maximum Value of AB, If A + B = Constant

Q.

A mixture of 40 litres of milk and water contains 10$\%$ water. How much water must be added to make water 20$\%$ in the new mixture?

1. 8 lts

2. 5 lts

3. 7.5 lts

4. 6 lts

5. 9 lts

Q.

A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?

1. 74

2. 88

3. 68

4. 40

5. 34

Q.

If a + b + c = 18, find the maximum value of $a^3{b}^{2}c$ given that a, b & c are positive numbers.

1. 78732
2. 78736
3. 78722
4. 78746

Q.

Find the maximum volume of a right circular cylinder if the sum of the radius and the height of the given cylinder is 6?

1. 28 p

2. 32 p

3. 40 p

4. 64 p

Q.

An outgoing batch of students want to gift a PA system worth Rs 4, 200 to their school. If the teachers offer to pay 50% more than the students and an external benefactor gives three times the teacher's contribution, then how much should the teachers donate?

1. 600

2. 420

3. 2700

4. none

5. 900

Q.

X and Y are two cylinders of the same height. The base of X has diameter that is half the diameter of the base of Y. If the height of X is doubled, the volume of X becomes:

1. Equal to the volume of Y

2. Double the volume of Y

3. Half the volume of Y

4. Greater than the volume of Y

5. None of these

Q. Length of a rectangular garden is 10m and its breadth is 8m. If a road of uniform width of xm is surrounded outside the park, find the area of the road in term of x

Q.

The third proportional to $x^2-y^2$ and $(x-y)$ is :

1. none

2. 

3. 

4. 

5. 

Q. 15 9 8 12 36 170
19 (a) (b) (c) (d) (e)
What will come in the place of (b)?

1. 18
2. 22
3. 24
4. 16
5. None of these

Q. If a + b + c = 13, what is the maximum value of (a - 3)(b - 2)(c + 1) ?

1. 26
2. 30
3. 19
4. 27

Q.

In each of the following questions a number series is given. After the series a number is given followed by (A), (B), (C), (D) and (E). Complete the series starting with the number given following the sequence of the given series. Then, answer the question given below each:
1, 9, 65, 393,
2, (A), (13), (C), (D), (E)
Which of the following numbers will come in place of (C)?

1. 490
2. 729
3. 854
4. 734
5. None of the above

Q. p, q and r are three non - negative integers such that p + q + r = 10. The maximum value of pq+ qr + pr + pqr is

1. $\ge$ 70 and < 80
2. $\ge$ 60 and < 70
3. $\ge$ 50 and < 60
4. $\ge$ 40 and < 50

Q.

Preeti thought of a two-digit number and divided the number by the sum of the digits of the number. She found that the remainder is 3. Sarosh also thought of a two-digit number and divided the number by the sum of the digits of the number. He also found that the remainder is 3. Find the probability that the two digit number thought by Preeti and Sarosh is same?

1. None of these

2. 

3. 

4. 

5. 

Q. The radius of a cylinder is 5 m more than its height. If the curved surface area of the cylinder is 792 $m^2$. What is the volume of the cylinder? (in $m^3$)

1. 5244
2. 5712
3. 5544
4. 5462
5. 5306

Q. If three sides of a rectangular park have a total length of 400ft, then the area of the park is maximum when the length (in ft) of its longer side is (in ft.)___

Q. Given that the sum of two non-negative quantities is 200, the probability that their product is not less than $\frac{3}{4}$ times their greatest product value is:

1. none of these
2. $\frac{99}{200}$
3. $\frac{101}{200}$
4. $\frac{87}{100}$

Q.

Of three positive numbers, the product of the first and second number is 42, that of the second and third is 56 and that of third and first is 48. Six times the third number is ?

1. 6

2. 42

3. 48

4. 36

5. None of these

Q. If a, b, c and d are four positive numbers such that a + b + c + d = 4, then what is the maximum value of (a + 1)(b + 1) (c + 1)(d + 1) ?

1. 16
2. 81
3. 32
4. 8

Q. Veena's monthly income is equal to the cost of 34 kg of nuts. Cost of 10 kg of nuts is equal to the cost of 20 kg of apples. If the cost of 12 kg of apples is Rs 1500, what is Veena's annual salary?(In some places, annual income and in some places, monthly income are given)

1. Rs 1 lakh 20 thousand
2. Rs 1 lakh 2 thousand
3. Rs 2 lakh 20 thousand
4. Cannot be determined
5. None of the above

Q. AVR cinema hall has 500 seats. Cost of each ticket is Rs.300 per seat. At this price, the owner will be able to fill the entire hall. If the price of the ticket goes up by Re.1, the number of seats sold goes down by 1. At what price of the ticket, will he maximize his revenue?

1. 450

2. 350

3. none of these

4. 425

Q.

A metal rod is melted and reshaped such that the radius of the rod is reduced to one – fourth.
The new length of the rod is how many times the original length?

1. 16 times

2. 8 times

3. 4 times

4. times

5. Remains the same

Q. In which year the monthly rent in Churchgate increase more than 100% from the previous year?

1. 2006
2. 2007
3. 2008
4. 2009
5. 2010

Q. If the quantity of coriander sold is increased by 200% and the price per kg is reduced by 8%, what will be the total cost of coriander sold?

1. Rs 38460
2. Rs 36480
3. Rs 38640
4. Rs 36840
5. None of these

Q. If a 100m wire is made available to fence 3 sides of a hockey ground which is rectangular in shape, taking wall as the fourth side, what is the maximum possible area of the field? ___

Q.

If a + b = 18, find the maximum value of (a - 4)(b + 1) given that a & b are positive numbers.

1. 55
2. 56.25
3. 56.5
4. 56

Q. The number of Phones produced by Company A is what percent of the total number of products produced by Company B?

1. $25\%$
2. $33\%$
3. $37\%$
4. $29\%$
5. None of these

Q.

Gopika decided to donate 13% of her salary to an NGO, but on the day of donation she changed her mind and donated Rs.3607.50, which was 75% of the amount she had decided to donate earlier. How much is Gopika’s salary?

1. Rs.37, 000

2. Rs.35, 000

3. None of these

4. Rs.39, 000

5. Cannot be determined

Q. Find the maximum volume of a right circular cylinder if the sum of the radius and the height of the given cylinder is 6.

1. 32 $\pi$
2. 64 $\pi$
3. 40 $\pi$
4. 28 $\pi$

Q.

Find the number of non-negative integers below 10000 which when divided by 7 and 89 leaves a remainder 1?

1. 17

2. 15

3. 14

4. 16

Q.

In a 50 over game, the run rate in the first 10 overs was only 3.9. What should be the run rate in the remaining 40 overs to reach a target of 289 runs?

1. 6

2. 6.25

3. 7

4. None of these