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Q:

Ten years ago, A was half of B in age. If the ratio of their present ages is 3:4, then what will be the total of their present ages?

Answer

Let A's age 10 years ago be x years

Then B's age 10 years ago be 2x yeats

$\inline \Rightarrow \frac{x+10}{2x+10}=\frac{3}{4}$

$\inline \Rightarrow 4(x+10)=3(2x+10)$

$\inline \Rightarrow x=5$

$\inline \therefore$ Total of their present ages = $x+10+2x+10$

= $3x+20$

= 35 years

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Subject: Problems on Ages

Q:

Where is the secretariat office of Birdlife International?

A) Geneva	B) Cambridge UK
C) Suva, Fiji	D) Mumbai,India

Answer & Explanation Answer: B) Cambridge UK

Explanation:

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Filed Under: World Geography

Q:

If the letters of the word VERMA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word VERMA is :

A) 108	B) 117
C) 810	D) 180

Answer & Explanation Answer: A) 108

Explanation:

The number of words beign with A is 4!

The number of words beign with E is 4!

The number of words beign with M is 4!

The number of words beign with R is 4!

Number of words beign with VA is 3!

Words beign with VE are VEAMR

VEARM

VEMAR

VEMRA

VERAM

VERMA

Therefore, The Rank of the word VERMA = 4 x 4! + 3! + 6 = 96 + 6 + 6 =108

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Filed Under: Permutations and Combinations
Exam Prep: CAT , Bank Exams , AIEEE
Job Role: Bank PO , Bank Clerk

Q:

The number of signals that can be generated by using 5 differently coloured flags, when any number of them may be hoisted at a time is:

A) 235	B) 253
C) 325	D) None of these

Answer & Explanation Answer: C) 325

Explanation:

Required number of signals = $5 P_{1} + 5 P_{2} + 5 P_{3} + 5 P_{4} + 5 P_{5}$

= 5 + 20 + 60 + 120 + 120 = 325

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Filed Under: Permutations and Combinations
Exam Prep: AIEEE , Bank Exams , CAT
Job Role: Bank Clerk , Bank PO

Q:

What is the total no of ways of selecting atleast one item from each of the two sets containing 6 different items each?

A) 2856	B) 3969
C) 480	D) None of these

Answer & Explanation Answer: B) 3969

Explanation:

We can select atleast one item from 6 different items = $2^{6} - 1$

Similarly we can select atleast one item from other set of 6 different items in $2^{6} - 1$ ways.

Required number of ways = $(2^{6} - 1) (2^{6} - 1) = {(2^{6} - 1)}^{2}$ = 3969

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Filed Under: Permutations and Combinations
Exam Prep: GATE , CAT , Bank Exams , AIEEE
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Q:

If a+b+c =21 what is the total number of positive integral solutions?

A) 109	B) 190
C) 901	D) 910

Answer & Explanation Answer: B) 190

Explanation:

Number of positive integral solutions = $n - 1_{C_{r - 1}}$ = ${}^{20}C_{2}$ = 190

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Filed Under: Permutations and Combinations
Exam Prep: CAT , Bank Exams , AIEEE
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Q:

If a+b+c = 21, what is the total number of non - negative integral solutions?

A) 123	B) 253
C) 321	D) 231

Answer & Explanation Answer: B) 253

Explanation:

Number of non - negative integral solutions = $n + r - 1 C_{r - 1} = {}^{23}C_{2}$ = 253

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Filed Under: Permutations and Combinations
Exam Prep: CAT , Bank Exams , AIEEE
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Q:

In how many different ways can 6 different balls be distributed to 4 different boxes, when each box can hold any number of ball?

A) 2048	B) 1296
C) 4096	D) 576

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