Properties of Set Operation

Q. Akhil and Sanjeev were given two baskets of mangoes of equal number. Akhil added 2 mangoes to his basket while Sanjeev also added 2 mangoes to his basket. After some time their friend Sarath counted the number of mangoes in the two boxes. Which of the following will be true, in terms of the number of mangoes?

1. The number of mangoes in Akhil's basket is more than that of Sanjeev.
2. The number of mangoes in Sanjeev's basket is more than that of Akhil.
3. The number of mangoes in both the baskets are equal.
4. The number of mangoes in Sarath's basket is more than that of Akhil.

Q.

Question 1

Both u and v vary directly with each other. When u is 10, v is 15, which of the following is not a possible pair of corresponding values of u and v?
(a) 2 and 3
(b) 8 and 12
(c) 15 and 20
(d) 25 and 37.5

Q. Mangoes are packed in boxes, each weighing 4 kg 500g.How many such boxes can be loaded in a tempo which cannot carry beyond 900 kg ?

Q.

A father with $8$ children takes $3$ at a time to the Zoological gardens, as often as he can without taking the same $3$ children together more than once.

The number of times he will go to the garden is?

1. $56$

2. $21$

3. $112$

4. None of these

Q. A survey show that 63% of the american likes cheese whereas 76% of the american like apples if x% of the american like both cheese and apples find the value of x.

Q. Which of the following statements are not well defined?​

$\text{I}.$ Set of best cricketers in the Indian cricket team
$\text{II}.$ Set of odd natural numbers divisible by $2$
$\text{III}.$ Set of letters in the word $\text{BYJUS}$
$\text{IV}.$ Set of large numbers

1. $\text{I and II}$
2. $\text{I and IV}$
3. $\text{II and III}$
4. $\text{II and IV}$

Q. If $n(A\cup B\cup C)=100,n\left(A\right)=4x,n\left(B\right)=6x,n\left(C\right)=5x,n(A\cap B)=20,n(B\cap C)=15,n(A\cap C)=25$ and $n(A\cap B\cap C)=10$ , then find the value of $x$.
$\left[5\right]$

Q. In || gm ABCD, it is given that AB = 10 cm, DL ⊥ AB and BM ⊥ AD such that DL = 6 cm and BM = 8 cm. Then, AD = ?
(a) 7.5 cm
(b) 8 cm
(c) 12 cm
(d) 14 cm

Q. Referring to the given Venn diagram, the number of total students, who took History or Mathematics or Science, is:

1. $183$
2. $190$
3. $148$
4. $430$

Q. Find the number of students that had taken Only one of the subjects.

Q. Using DeMorgan's law, which of the following is equivalent to the statement $C\cap (B\cup A\text{'}){}^{\prime }$ ?

1. $C\cap (B{}^{\prime }\cup A){}^{\prime }$
2. $C{}^{\prime }\cap (B{}^{\prime }\cup A{}^{\prime })$
3. $(C\cup B)\cap A{}^{\prime }$
4. $C\cap (B{}^{\prime }\cap A)$

Q. If A = {b, c, e, g, h}, B = {a, c, d, g, i} and C = {a, d, e, g, h}, then show that A – (B ∩ C) = (A – B) ∪ (A – C).

Q. $\frac{24.23\times 1.423\times 34.21}{521.3\times 413.32\times 2.53}$ is same is

1. $\frac{2423\times 1423\times 3421}{5213\times 41332\times 253}$
2. $\frac{2423\times 1423\times 3421}{5213\times 4133.2\times 2.53}$
3. $\frac{2.423\times 14.23\times 342.1}{521.3\times 4133.2\times 2.53}$
4. $\frac{24.23\times 14.23\times 3.421}{5.213\times 41332\times 0.253}$

Q. A village having a population of 4000 requires 150 litres of water per head per day. It has a tank measuring 20 m × 15 m × 6 m. For how many days will the water of this tank last?