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Q:

Choose the pair which shows the same relation of the given pair from the following options ?

BRISTLE : BRUSH

A) arm : leg	B) key : piano
C) recline : chair	D) stage : curtain

Answer & Explanation Answer: B) key : piano

Explanation:

A bristle is a part of a brush; a key is a part of a piano.

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Filed Under: Analogy
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Q:

Choose the alternative which is closely resembles the water image of the given combination/figure.

ADVANCE

1) download_(1)1492407904.png image 2) download_(2)1492407924.png image 3) download1492407936.png image 4) NONE

A) 1	B) 2
C) 3	D) 4

Answer & Explanation Answer: B) 2

Explanation:

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Filed Under: Analytical Reasoning
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Q:

A potentiometer wire is 100 cm long and a constant potential difference is maintained across it. Two cells are connected in series first to support one another and then in opposite direction. The balance points are obtained at 50 cm and 10 cm from the positive end of the wire in the two cases. The ratio of the emf's is :

A) 3:4	B) 5:4
C) 5:1	D) 3:2

Answer & Explanation Answer: D) 3:2

Explanation:

In series : E1 + E2 = K(50)

In parallel : E1 - E2 = K(10)

E1 + E2 / E1 - E2 = 5/1

=> E1/E2 = 3/2

The emf's are in the ratio of 3:2.

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Filed Under: Physics
Exam Prep: AIEEE

Q:

Which one of the following can be oxidised to the corresponding carbonyl compound:

A) 2-methyl-2-hydroxy propane	B) 2-hydroxy propane
C) o-Nitrophenol	D) Phenol

Answer & Explanation Answer: B) 2-hydroxy propane

Explanation:

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Filed Under: Chemistry
Exam Prep: AIEEE

Q:

What is the maximum velocity with which a body of mass 'm' must enter a vertical loop of radius 'R'so that it can complete the loop?

A) 0 B) gR C) $\sqrt{2} g R$ D) $\sqrt{5 g R}$

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

Answer & Explanation Answer: D) D

Explanation:

To complete the vertical loop, the minimum speed required at the lowest point = $\sqrt{5 g R}$ .

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Filed Under: Physics
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Q:

Solve the equation ${(\frac{1}{2})}^{2 x + 1} = 1$ ?

A) -1/2	B) 1/2
C) 1	D) -1

Answer & Explanation Answer: A) -1/2

Explanation:

Rewrite equation as ${(\frac{1}{2})}^{2 x + 1} = {(\frac{1}{2})}^{0}$

Leads to 2x + 1 = 0

Solve for x : x = -1/2

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Filed Under: Logarithms
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Q:

A box contains 4 different black balls, 3 different red balls and 5 different blue balls. In how many ways can the balls be selected if every selection must have at least 1 black ball and one red ball ?

A) $2^{4} - 1$

B) $2^{4} (2^{5} - 1)$

C) $(2^{4} - 1) (2^{3} - 1) 2^{5}$

D) None

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

Answer & Explanation Answer: C) C

Explanation:

It is explicitly given that all the 4 black balls are different, all the 3 red balls are different and all the 5 blue balls are different. Hence this is a case where all are distinct objects.

Initially let's find out the number of ways in which we can select the black balls. Note that at least 1 black ball must be included in each selection.

Hence, we can select 1 black ball from 4 black balls
or 2 black balls from 4 black balls.
or 3 black balls from 4 black balls.
or 4 black balls from 4 black balls.

Hence, number of ways in which we can select the black balls

= 4C1 + 4C2 + 4C3 + 4C4
= $2^{4} - 1$ ........(A)

Now let's find out the number of ways in which we can select the red balls. Note that at least 1 red ball must be included in each selection.

Hence, we can select 1 red ball from 3 red balls
or 2 red balls from 3 red balls
or 3 red balls from 3 red balls

Hence, number of ways in which we can select the red balls
= 3C1 + 3C2 + 3C3
= $2^{3} - 1$ ........(B)

Hence, we can select 0 blue ball from 5 blue balls (i.e, do not select any blue ball. In this case, only black and red balls will be there)
or 1 blue ball from 5 blue balls
or 2 blue balls from 5 blue balls
or 3 blue balls from 5 blue balls
or 4 blue balls from 5 blue balls
or 5 blue balls from 5 blue balls.

Hence, number of ways in which we can select the blue balls
= 5C0 + 5C1 + 5C2 + … + 5C5
= $2^{5}$ ..............(C)

From (A), (B) and (C), required number of ways
= $2^{5} (2^{4} - 1) (2^{3} - 1)$

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Filed Under: Permutations and Combinations
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Q:

What should come in place of the question mark(?) in the following questions ?

$3 \frac{1}{6} + 4 \frac{1}{2} - 2 \frac{2}{3} - 1 \frac{11}{12} = ?$

A) 1 7/12	B) 1 5/12
C) 3 7/12	D) 3 1/12

Answer & Explanation Answer: D) 3 1/12

Explanation:

? = (3 + 4 - 2 - 1) + ( 1/6 + 1/2 - 2/3 - 11/12)

= 4 + [(2+6-8-11)/12]

= 4 - (11/12 )= 31/12.

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Filed Under: Mathematical Operations
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