Mathematics 2011 | Study Mode

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Question 41
A
6!
B
7!
C
5!
D
8!
Explanation
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 42
A
24
B
60
C
12
D
120
Explanation
The first person will sit down and the remaining will join.

i.e. (n - 1)!

= (5 - 1)! = 4!

= 24 ways

Correct option: A
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Question 43
A
\(\frac{2}{3}\)
B
\(\frac{1}{3}\)
C
\(\frac{2}{9}\)
D
\(\frac{7}{9}\)
Explanation
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
\(\frac {\sin\theta}{\cos\theta}\)

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

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

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

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

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

Correct option: A
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Question 45
A
{a, b, d, e}
B
{b, d}
C
{a, e}
D
{c}
Explanation

Explanation not provided, please join discuss, your contributions are welcomed


Correct option: D
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Question 46
A
30%
B
25%
C
35%
D
20%
Explanation
\(\frac{70}{360} \times 36 = \frac{70}{10}\)

= 7

Correct option: D
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Question 47
A
180
B
135
C
210
D
105
Explanation

Explanation not provided, please join discuss, your contributions are welcomed


Correct option: A

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