AIEEE Questions and Answers with Explanation

Q:

Consider 5 independent Bernoulli’s trials each with probability of success p. If the probability of at least one failure is greater than or equal to 31/32 , then p lies in the interval ?

A) [1, 32]	B) (0, 1)
C) [1, 1/2]	D) (1, 1/2]

Answer & Explanation Answer: C) [1, 1/2]

Explanation:

Probability of atleast one failure
= 1 - no failure > 31/32
= 1 - $P^{5}$ > 31/32
= $P^{5} <$ 1/32
= p < 1/2
Also p > 0
Hence p lies in [0,1/2].

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Q:

If the price of diesel increases by 25% and Karthik intends to spend only an additional 15% on diesel, by how much % will he reduce the quantity of diesel purchased ?

A) 6.67 %	B) 8 %
C) 7.41 %	D) 9 %

Answer & Explanation Answer: B) 8 %

Explanation:

Let the price of 1 litre of diesel be Rs.x and let Karthik initially buy 'y' litres of diesel.
Therefore, he would have spent Rs. xy on diesel.

When the price of diesel increases by 25%, the new price per litre of diesel is 1.25x.

Karthik intends to increase the amount he spends on diesel by 15%.
i.e., he is willing to spend xy + 15% of xy = 1.15xy

Let the new quantity of diesel that he can get be 'q'.
Then, 1.25x x q = 1.15xy
Or q = (1.15/1.25)y = 0.92y.

As the new quantity that he can buy is 0.92y, he gets 0.08y lesser than what he used to get earlier.

Or a reduction of 8%.

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Filed Under: Percentage
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Q:

If $\log_{3} (30)$ = $\frac{1}{a}$ and $\log_{5} (30) = \frac{1}{b}$ then the value of $3 \log_{30} (2)$ is:

A) 3(1+a+b)	B) 2(1-a-b)
C) 3(1-a-b)	D) 3(1+a-b)

Answer & Explanation Answer: C) 3(1-a-b)

Explanation:

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Filed Under: Logarithms
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Q:

One who hates marriage is called

A) Misogamist	B) Philogynist
C) Hater	D) Synder

Answer & Explanation Answer: A) Misogamist

Explanation:

One who hates marriage is called misogamist.

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Q:

Ajay and his wife Reshmi appear in an interview for two vaccancies in the same post. The Probability of Ajay's selection is 1/7 and that of his wife Reshmi's selection is 1/5. What is the probability that only one of them will be selected?

A) 5/7	B) 1/5
C) 2/7	D) 2/35

Answer & Explanation Answer: C) 2/7

Explanation:

P( only one of them will be selected) = p[(E and not F) or (F and not E)]

= $P [(E \cap F) \cup (F \cap E)]$

= $P (E) P (F) + P (F) P (E)$

= $\frac{1}{7} \times \frac{4}{5} + \frac{1}{5} \times \frac{6}{7} = \frac{2}{7}$

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Q:

Which ionization process requires the most energy?

A) C3+ (g) → C4+ (g) + e-	B) C (g) → C+ (g) + e-
C) C2+ (g) → C3+ (g) + e-	D) C+ (g) → C2+ (g) + e-

Answer & Explanation Answer: A) C3+ (g) → C4+ (g) + e-

Explanation:

We know that each successive IE is greater than the previous one, because each ionization process removes one electron and hence increases the total attractive force on the remaining electrons from the nucleus. Hence, C3+ (g) → C4+ (g) + e- needs more energy.

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Filed Under: Chemistry
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Q:

$4 \frac{4}{5}$ of 259.99 = ? % of 1247.9

A) 96	B) 100
C) 78	D) 88

Answer & Explanation Answer: B) 100

Explanation:

Given

$4 \frac{4}{5}$ of 259.99 = ? % of 1247.9

24/5 x 260 = ? x 1248/100

? = 1248 x 100/1248

? = 100.

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Q:

State in which the few govern the many?

A) Autocracy	B) Monarchy
C) Plutocracy	D) Oligarchy

Answer & Explanation Answer: D) Oligarchy

Explanation:

Oligarchy is a form of government in which the power rests with the small group of people.

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