If tan A + cot A = 4, find the value of tan^2A + cot^2A

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KPTCL Assistant Exam (Mescom) SLOT-3 2017 click here to view all questions

If tan A + cot A = 4, find the value of tan^2A + cot^2A

A14

B20

C35

D40

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A fair coin is tossed 3 times in succession. If the first to

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PGCET CSE Exam (Karnataka) 2011 click here to view all questions

A fair coin is tossed 3 times in succession. If the first toss produced a head, then the probability of getting exactly two heads in 3 tosses ( including the first toss ) is

A1/8

B3/8

C1/2

D3/4

Akilesh Kharvi ? Dec 8 '2016 at 21:11

Answer:\(\frac{3}{4}\)

Explanation:

P(2 heads in 3 tosses / first toss is a head) 
(H,H,H) 
(H,H,T) 
(H,T,H) 
(H,T,T) 
(T,H,H) 
(T,H,T) 
(T,T,H) 
(T,T,T) 
are the 2^3 = 8 ways in which the coin can roll. 
Since we are given that the first toss is a head, our sample space becomes: 
(H,H,H) 
(H,H,T) 
(H,T,H) 
(H,T,T) 
Of these four possibilities, we want to know how many have exactly 2 heads 
\(= \frac{3}{4}\)

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The probability of two sisters sharing the same birth-month

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PGCET CSE Exam (Karnataka) 2011 click here to view all questions

The probability of two sisters sharing the same birth-month is

A1/144

B1/24

C1/12

D1/6

Akilesh Kharvi ? Dec 8 '2016 at 21:6

Answer: \(\frac{1}{12}\)

Explanation:

The first sister can be born any month, it makes no difference.
The second sister has 1/12 chance of being born in the same month.

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A U B and A B are equal only if

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PGCET CSE Exam (Karnataka) 2011 click here to view all questions

A U B and A B are equal only if

AA is an empty set

BB is an empty set

Cboth A and B are empty sets

Dboth A and B are singleton sets

Akilesh Kharvi ? Dec 8 '2016 at 21:8

Answer: both A and B are empty sets 

Explanation:

Let B = A + X 
A U B = { A, X } 
A ∩ B = { A } 
Thus A U B = A ∩ B only if X is the empty set. 
In that case, A = B

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There are four bus lines between A and B and three between

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There are four bus lines between A and B and three between B and C. The number of ways a person can travel by bus from A to C through B is

A10

B12

C14

D24

Akilesh Kharvi ? Dec 8 '2016 at 20:34

Answer: 12

Explanation:

4 bus lines between a and b.
3 bus lines between b and c. 
the number of possible combinations between a and c going through b are \(4 \times 3 = 12.\)

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