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Q:

The amount of water (in ml) that should be added to reduce 9 ml lotion, containing 50% alcohol, to a lotion containing 30% alcohol is ?

A) 6 ml	B) 11 ml
C) 15 ml	D) 9 ml

Answer & Explanation Answer: A) 6 ml

Explanation:

Let us assume that the lotion has 50% alcohol and 50% water.
ratio = 1:1
As the total solution is 9ml
alcohol = water = 4.5ml
Now if we want the quantity of alcohol = 30%
The quantity of water = 70%
The new ratio = 3:7
Let x ml of water be added
We get,
$\frac{4.5}{4.5 + x} = \frac{3}{7}$
=> x=6
Hence 6ml of water is added.

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Filed Under: Alligation or Mixture
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Q:

Bhim has assembled a basket of fruit as a holiday gift for each of his friends- Santosh, Tarun, Ujjwal, and Varun. A total of fifteen pieces of fruits-five apples, five oranges and five pears are distributed among the four baskets according to the following conditions: Santosh , Tarun and Ujjwal will each receive exactly two different types of fruit. Varun will receive only apples. Tarun will receive more pieces of fruit than Santosh. Each basket includes at least three pieces of fruit.

1. If Varun’s basket contains more pieces of fruit than Tarun’s basket, then Tarun’s basket must contain:
I. Four pieces of fruit.
II. At least one orange.
III. At least one pear.

(a) I only (b) III only (c) Botha I and II (d) Both II and III

2. If Ujjwal’s basket contains more pieces of fruit than Tarun’s basket, all of the following must be false EXCEPT:

(a) Only Varun will receive apple

(b) Varun will receive exactly four apple.

(c) Ujjwal will receive exactly two apple.

(d) Tarun will receive exactly four pear.

Answer

1. Answer (b)

Santosh , Ujjwal and Varun must each receive at least three pieces, but Tarun must receive at least four pieces. The maximum number of pieces that any person may receive is six ( 6 + 3+ 3+3 = 15 ), and only Tarun may receive six pieces. Ujjwal and Varun each may receive as many as five pieces, while Santosh may receive only four pieces at maximum.
At least one pear.

2. Answer (c)

Varun may receive no more than five pieces and Tarun may receive no fewer than four pieces. As a result, if Varun receives more pieces than Tarun, then Varun must receive five pieces, and Tarun must receive four pieces. Thus, statement (a) must be true. Since Varun will receive five pieces, none of the other three friends will receive any apple, accordingly, each of the other three friends must receive at least one orange and at least one pear. Thus, statement (b) and (d) must be true.

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Subject: Deriving Conclusions From Passages Exam Prep: AIEEE , Bank Exams , CAT , GATE , GRE
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Q:

One type of liquid contains 25 % of benzene, the other contains 30% of benzene. A can is filled with 6 parts of the first liquid and 4 parts of the second liquid. Find the percentage of benzene in the new mixture.

A) 27 %	B) 26 %
C) 29 %	D) 21 %

Answer & Explanation Answer: A) 27 %

Explanation:

Let the percentage of benzene = X
(30 - X)/(X- 25) = 6/4 = 3/2
=> 5X = 135
X = 27

So, required percentage of benzene = 27 %

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Filed Under: Alligation or Mixture
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Q:

A box contains 5 green, 4 yellow and 5 white pearls. Four pearls are drawn at random. What is the probability that they are not of the same colour ?

A) 11/91

B) 4/11

C) 1/11

D) 90/91

A) Option A	B) Option B
C) Option C	D) Option D

Answer & Explanation Answer: D) Option D

Explanation:

Let S be the sample space. Then,
n(s) = number of ways of drawing 4 pearls out of 14

= $C_{4}^{14}$ ways = $\frac{14 \times 13 \times 12 \times 11}{4 \times 3 \times 2 \times 1}$ = 1001

Let E be the event of drawing 4 pearls of the same colour.
Then, E = event of drawing (4 pearls out of 5) or (4 pearls out of 4) or (4 pearls out of 5)

$\Rightarrow C_{1}^{5} + C_{4}^{4} + C_{1}^{5}$ = 5+1+5 =11

P(E) = $\frac{n (E)}{n (S)} = \frac{11}{1001} = \frac{1}{91}$

Required probability = $1 - \frac{1}{91} = \frac{90}{91}$

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Filed Under: Permutations and Combinations
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Q:

A container contains 50 litres of milk. From that 8 litres of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container ?

A) 24.52 litres	B) 29.63 litres
C) 28.21 litres	D) 25.14 litres

Answer & Explanation Answer: B) 29.63 litres

Explanation:

Given that container has 50 litres of milk.

After replacing 8 litres of milk with water for three times, milk contained in the container is:

$\Rightarrow [50 {(1 - \frac{8}{50})}^{3}]$

$\Rightarrow (50 \times \frac{42}{50} \times \frac{42}{50} \times \frac{42}{50})$ = 29.63 litres.

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Filed Under: Alligation or Mixture
Exam Prep: CAT
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Q:

Trichloroacetaldehyde was subject to Cannizzaro's reaction by using NaOH. The mixture of the products contains sodium trichloroacetate and another compound. The other compound is :

A) Chloroform	B) 2, 2, 2-Trichloroethanol
C) Trichloromethanol	D) 2, 2, 2-Trichloropropanol

Answer & Explanation Answer: B) 2, 2, 2-Trichloroethanol

Explanation:

$\begin{matrix} C l \\ | \\ C l & - & C & - & C H O \\ | \\ C l \end{matrix}$ $\to_{C a n n i z z a r o' s R e a c t i o n}^{N a O H}$ $\begin{matrix} C l \\ | \\ C l & - & C & - & C O O N a \\ | \\ C l \end{matrix}$ $+$ $\begin{matrix} C l \\ | \\ C l & - & C & - & C H_{2} \\ | 2 & 1 \\ C l \end{matrix}$ $- O H$

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Filed Under: Chemistry
Exam Prep: AIEEE

Q:

Which containers use a FlowLayout as their default layout ?

Answer

The Panel and Applet classes use the FlowLayout as their default layout.

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Subject: Java

Q:

Which containers use a border Layout as their default layout ?

Answer

The window, Frame and Dialog classes use a border layout as their default layout.

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Subject: Java

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