It's a Question of your Career!

Correct Answer: 13 days

Solution : A, B, and C can do work separately in 18, 36, and 54 days 
Let the total work = LCM (18, 36, and 54) = 108 units
Efficiency = $\frac{\text{Total work}}{\text{Number of days}}$
So, Efficiency of A = $\frac{108}{16}$ = 6
Efficiency of B

Correct Answer: IMPORTANT

Solution : Given:
IMPROVEMENT

Let's compare all the option words with the word IMPROVEMENT –
First option: ROPE; All the letters of ROPE are present in the word IMPROVEMENT.
Second option: TRIM; All the letters of TRIM are present in the word IMPROVEMENT.
Third option: IMPORTANT; Only

Correct Answer: Negative

Solution :
The slope of this graph will be negative.
Reason:
Slope = m = $\tan\theta$
Here the $\theta > 90^{\circ}$ i.e., in the second quadrant.
$\therefore\tan\theta$ is negative in the second quadrant.
Hence, the correct answer is negative.

Correct Answer: $\frac{x^{2}}{y\sqrt{y^{2}-x^{2}}}$

Solution : Given:
$\cos 21^{\circ}=\frac{x}{y}$
So, $\cos 69^{\circ}=\cos (90^{\circ}-21^{\circ})=\sin 21^{\circ}= \sqrt{1-\cos^2 21º}=\sqrt{1-\frac{x^2}{y^2}}=\frac{\sqrt{y^2-{x^2}}}{y}$
Also, $\operatorname{cosec21^{\circ}}=\frac{1}{\sin 21^{\circ}}=\frac{y}{\sqrt{y^2-{x^2}}}$
Now, $(\operatorname{cosec21^{\circ}}-\cos 69^{\circ})=\frac{y}{\sqrt{y^2-{x^2}}}-\frac{\sqrt{y^2-{x^2}}}{y}$
⇒ $(\operatorname{cosec21^{\circ}}-\cos 69^{\circ})=\frac{y^2-(y^2-x^2)}{y\sqrt{y^2-{x^2}}}=\frac{x^{2}}{y\sqrt{y^{2}-x^{2}}}$
Hence, the correct answer is $\frac{x^{2}}{y\sqrt{y^{2}-x^{2}}}$.

Correct Answer: 26 cm

Solution :
Let the radius of the circle as \(r\) and the length of the chord OP as \(L\).
Given that the diameter of the circle is 20 cm, the radius is \(r = \frac{20}{2} = 10\) cm.
Use the Pythagorean theorem to find the length

Correct Answer: 10%

Solution : As per the given graph,
The number of students in school C is more than the number of students in school B by
$=\frac{( 79.2 − 72 )}{72}$ × 100%
$= 10$%
Hence, the correct answer is 10%

Correct Answer: 229: 217

Solution : The average of total students from school A 2008, 2012, and 2013 = 640 + 900 + 750 = 2290
The average of total students from school B in 2009, 2010, and 2011 =  820 + 600 + 750 = 2170
The required ratio

Correct Answer: Veteran

Solution : The correct choice is the third option. 

A veteran is a person who has considerable experience or has been involved in a particular activity, profession, or occupation for a long time. They are highly skilled or knowledgeable due to their extensive experience.

The meanings

Correct Answer: Had just swallowed

Solution : The third option is the correct answer, since "had just swallowed" is the correct verb form to be used here as per past perfect tense. The sentence indicates that the baby had recently swallowed a safety pin before the person brought it

Correct Answer: 40 cm

Solution : Let the height and radius of the cylinder be $x$.
Given volume = $64\pi$ litres = $64000\pi$ cm³
We know that,
Volume of the cylinder = $\pi r^2h$
So, $\pi\times x^2\times x=64000\pi$
⇒ $x^3=64000$
$\therefore x= 40$
Hence, the correct answer is 40