Mathematics 2011 | Study Mode

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Question 41
A
6! 
B
7! 
C
5! 
D
8! 
Explanation.
Share Answer ELATION
Since there are 7 letters. The first letter can be arranged in 7 ways, , the second letter in 6 ways, the third letter in 5 ways, the 4th letter in four ways, the 3rd letter in three ways, the 2nd letter in 2 ways and the last in one way.

therefore, 7 x 6 x 5 x 4 x 3 x 2 x 1 = 7! ways

Correct Option:
B
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Question 43
A
\(\frac{2}{3}\) 
B
\(\frac{1}{3}\) 
C
\(\frac{2}{9}\) 
D
\(\frac{7}{9}\) 
Explanation.
Share Answer Prime numbers = (43,47,53,59)

N = (43, 44, 45,..., 60)

The universal set contains 18 numbers.

The prime numbers between 43 and 60 are 4

Probability of picking a prime number = \(\frac{4}{18}\)

= \(\frac{2}{9}\)

Correct Option:
C
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Question 44
A
sec2 \(\theta\) 
B
tan \(\theta\) cosec \(\theta\) 
C
cosec \(\theta\)sec \(\theta\) 
D
cosec2\(\theta\) 
Explanation.
Share Answer \(\frac {\sin\theta}{\cos\theta}\)

\(\frac{\cos \theta {\frac{d(\sin \theta)}{d \theta}} - \sin \theta {\frac{d(\cos \theta)}{d \theta}}}{\cos^2 \theta}\)

\(\frac{\cos \theta. \cos \theta - \sin \theta (-\sin \theta)}{cos^2\theta}\)

\(\frac{cos^2\theta + \sin^2 \theta}{cos^2\theta}\)

Recall that sin2 \(\theta\) + cos2 \(\theta\) = 1

\(\frac{1}{\cos^2\theta}\) = sec2 \(\theta\)

Correct Option:
A
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