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Q:

Which one of the following is the cause for a change in the season?

A) Earth’s Rotation and Revolution	B) Earth’s Rotation
C) Earth’s Revolution	D) None of the above

Answer & Explanation Answer: C) Earth’s Revolution

Explanation:

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Filed Under: World Geography

Q:

Which among the following migratory bird species migrates from Arctic to Antarctica every year, making it longest migratory route on nearth?

A) Arctic Tern	B) Black necked swan
C) Bobolink	D) American Robin

Answer & Explanation Answer: A) Arctic Tern

Explanation:

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Filed Under: World Geography

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:

The Number of times the digit 8 will be written when listing the integers from 1 to 1000 is :

A) 100	B) 200
C) 300	D) 400

Answer & Explanation Answer: C) 300

Explanation:

Since 8 does not occur in 1000, we have to count the number of times 8 occurs when we list the integers from 1 to 999. Any number between 1 and 999 is of the form xyz, where $0 \leq x, y, z \leq 9 .$

Let us first count the numbers in which 8 occurs exactly once.

Since 8 can occur atone place in $3 C_{1}$ ways. There are $3 x 9 x 9$ such numbers.

Next, 8 can occur in exactly two places in $3 C_{2} \times 9$ such numbers. Lastly, 8 can occur in all three digits in one number only.

Hence, the number of times 8 occur is

$1 \times (3 \times 9^{2}) + 2 \times (3 \times 9) + 3 \times 1 = 300$

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Filed Under: Permutations and Combinations

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
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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
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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
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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
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