Exam
Question : Select the most appropriate option to improve the underlined segment in the given sentence. If there is no need to improve it, select ‘No improvement required’.
I have withdraw money from the bank.
Option 1: have withdrawing
Option 2: No improvement required
Option 3: have withdrew
Option 4: have withdrawn
Correct Answer: have withdrawn
Solution : The fourth option is the correct choice.
The sentence contains a verb-tense error. When forming the present perfect tense, the past participle of the verb should be used. The past participle of withdraw is withdrawn. The use of the present perfect tense suggests a
Question : If $\tan \theta \cdot \tan 2 \theta=1$, then the value of $\cot 5 \theta$ is:
Option 1: $-1$
Option 2: $1$
Option 3: $-\sqrt{3}$
Option 4: $\sqrt{3}$
Correct Answer: $-\sqrt{3}$
Solution : Given: $\tan \theta \cdot \tan 2 \theta=1$ $⇒\tan2\theta=\cot\theta$ $⇒\tan2\theta=\tan(90°- \theta)$ $⇒2\theta=90°- \theta$ $⇒3\theta=90°$ $\therefore \theta=30°$ $\cot 5\theta=\cot(5×30°)=\cot 150°=\cot(90°+60°)=-\tan60°=-\sqrt3$ Hence, the correct answer is $-\sqrt3$.
Question : What is the Minimum Capital of Private Company?
Option 1: 5 Lakhs
Option 2: 20 Lakhs
Option 3: 1 Lakh
Option 4: 50 Lakhs
Correct Answer: 1 Lakh
Solution : All Private Limited Companies are required to have a minimum capital of Rs. 1 lakh and there is no minimum capital requirement to launch a public limited company.
Hence, the correct answer is option 3.
Question : What is the digit in the unit's place in the number $\frac{15!}{100}$?
Option 1: 5
Option 2: 7
Option 3: 3
Option 4: 0
Correct Answer: 0
Solution : Number of trailing zeroes in $n$! = [$\frac{n}{5}$] + [$\frac{n}{25}$] + [$\frac{n}{125}$] + ....... where [ ] denotes greatest integer function. So, the number of trailing zeroes in 15! = [$\frac{15}{5}$] + [$\frac{15}{25}$] + [$\frac{15}{125}$] + ....... = 3 + 0 + 0 + .....
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