Common Admission Test (CAT) Questions and Answers with Explanation

Q:

A duster is of dimension 5x5x7 all in cms, is sinked into a cylindrical vessel of radius 5 cm and height 10 cm. After insertion the level of the water is inccresed by 2.14 cm. Then by what percentage the part of the duster is above the layer ?

A) 96 %	B) 4 %
C) 97 %	D) 3 %

Answer & Explanation Answer: B) 4 %

Explanation:

Imension of the duster is assumed as 5x5x7 cm3

Volume of the duster below the water layer
= volume of water increased
= πxrxrxh = 3.14×52×2.14 ≈ 168 cm3

Total volume of the duster = 5×5×7 = 175 cm3

Percentage of the duster part below the layer = 168×100/175 = 96%

Percentage of the duster part above the layer = 4%

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Q:

A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 110 feet per second. After how many seconds does the ball attain its maximum height?

A) 2.87 sec	B) 3.44 sec
C) 4.65 sec	D) 5.41 sec

Answer & Explanation Answer: B) 3.44 sec

Explanation:

It is launched vertically with an initial speed of 110 ft/sec.

It will reach maximum height when the speed drops to 0.

Vo=110 feet per second

ho=2 feet

So, h(t) = -16t^2 +110t +2

Take the derivative: h'(t) = 110 -32t

The maximum height will be at the inflection when the derivative crosses the x-axis, then h'(t)=0.

So, set h'(t)=0 and solve for t:

0 = 110 -32t

-110 = -32t

t=3.4375

t=3.44 seconds.

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Q:

A sold an article to B at 40% profit and B sold it to C at 50% profit, then what will be profit percent with respect to A ?

A) 97 %	B) 110 %
C) 135 %	D) 115 %

Answer & Explanation Answer: B) 110 %

Explanation:

% Profit with respect to A = 40 + 50 + (40 x 50)/100 = 90 + 20 = 110 %.

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Q:

The Value of $[\log (\tan (1^{0})) + \log (\tan (2^{0})) + \dots \dots + \log (\tan (89^{0}))]$ is

A) -1	B) 0
C) 1/2	D) 1

Answer & Explanation Answer: B) 0

Explanation:

$= [\log \tan (1^{0}) + \log \tan (89^{0})] + [\log \tan (2^{0}) + \log \tan (88^{0})] + \dots \dots + [\log \tan (45^{0})]$

$= \log [\tan (1^{0}) \times \tan (89^{0})] + \log [\tan (2^{0}) \times \tan (88^{0})] + \dots \dots + \log (1)$

$[∵ \tan (90 - θ) = c o t θ a n d \tan (45^{0}) = 1]$

= log 1 + log 1 +.....+log 1

= 0.

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Q:

What is always coming but never arrives?

Answer

It is Tomorrow. It always be tomorrow which represents coming but never arrives.

Workspace

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Q:

A merchant commences with a certain capital and gains annually at the rate of 30 per cent. At the end of 2 years he has worth Rs 10,000. What was the original capital?

A) Rs. 4987	B) Rs. 5148
C) Rs. 5917	D) Rs. 6254

Answer & Explanation Answer: C) Rs. 5917

Explanation:

Let the Original capital amount be Rs. P

Given after 2 years the amount is Rs. 10000

Rate of interest = 30%

According to the question,

$P x \frac{130}{100} x \frac{130}{100} = 10000 = > P = \frac{1000000}{169} = 5917$

Therefore, the capital amount P = Rs. 5917

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Q:

Rice worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs. 153 per kg, then the price of third variety of rice per kg?

A) Rs. 571.25	B) Rs. 175.5
C) Rs. 751.75	D) Rs. 850

Answer & Explanation Answer: B) Rs. 175.5

Explanation:

Let the price of required variety = Rs. P/kg

Then, respective amounts were m kg, m kg and 2m kg

= 126m + 135m + 2pm = 153 x 4m

=> 2p = 351

p = 175.5 / kg

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Q:

Bijapur is known for its what?

A) Statue of Gomateshwara	B) Heavy rainfall
C) Gol Gumbaz	D) Severe Drought area

Answer & Explanation Answer: C) Gol Gumbaz

Explanation:

Bijapur is known for its Gol Gumbaz. Bijapur city is well known for its historical monuments of architectural importance built during the rule of the Adil Shahi dynasty.

What is Gol Gumbaz ::

1. It is the tomb of Mohammed Adil Shah. This is the most famous monument in Bijapur.

2. It is the largest dome ever built in India.

3. A particular attraction in this monument is the central chamber, where every sound is echoed seven times.

4. Another attraction at the Gol Gumbaz is the Whispering Gallery, where even minute sounds can be heard clearly 37 metres away.

Statue of Gomateshwara - Shravanabelagola in Karnataka.

Heavy Rainfall - Cherrapunji in Meghalaya.

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