It's a Question of your Career!

Correct Answer: 10

Solution : Given number = $620x976y52$
Co-prime factors of $88 = 8 × 11$
For the smallest possible value of $y$,
$y52$ will be divisible by 8
So, $y$ will be 1 for 152, which is divisible by 8.
As $y = 1$, the possible value of x for which $620x976152$ is divisible by 11.
Sum of even places in number $= 2 + x + 7 + 1 + 2 = 12 + x$
Sum of odd places in number $= 6 + 0 + 9 + 6 + 5 = 26$
For divisibility rule 11: The difference between the sum of digits at odd places and the sum of digits at even places is equal to zero or a multiple of 11.
AT $x=3$, difference = 26 – 15 = 11
$\therefore$ Value of $x^2 + y^2=(3)^2 + 1^2=9 + 1=10$
Hence, the correct answer is 10.

Correct Answer: 150

Solution : Let the total wealth be $x$.
The man wills 40% of his wealth to the wife = 40% of $x$ = 0.4$x$
Wealth for the children = $x$ – 0.4$x$ = 0.6$x$
So, the required percentage $=\frac{\text{wealth for children}}{\text{wealth to the wife}} × 100 = \frac{0.6x}{0.4x} ×100 = 150$%
Hence, the correct answer is 150.

Correct Answer: July 29th

Solution : The correct option is July 29th.

International Tiger Day is observed on July 29th every year. This day is dedicated to raising awareness about tiger conservation and the need to protect the habitats of these magnificent creatures. Various organisations and initiatives use this day to highlight their efforts to conserve tigers and their habitats. This includes projects related to anti-poaching measures, habitat preservation, and community involvement.

Correct Answer: 4 : 5 : 6

Solution : Given: $\frac{1}{2}× A=\frac{2}{5} × B=\frac{1}{3} × C$
⇒ $\frac{1}{2} × A=\frac{2}{5} × B$
⇒ $\frac{A}{B} = \frac{4}{5}$
And, $\frac{2}{5} × B = \frac{1}{3} × C$
⇒ $\frac{B}{C} = \frac{5}{6}$
Taking B as common, the value of B is the same in both cases so that the ratio will be $A : B : C=4:5:6$
Hence, the correct answer is 4 : 5 : 6.

Correct Answer: $\frac{25}{7}$

Solution : We know if $\operatorname{cosec}x + \cot x = a$, then $\operatorname{cosec} x - \cot x = \frac{1}{a}$
Given, $\operatorname{cosec} A+\cot A=7$ ........(1)
⇒ $\operatorname{cosec} A-\cot A=\frac17$ .........(2)
Solving these equations to get the value of $\operatorname{cosec} A$
(1) + (2), we get,
⇒ $\operatorname{cosec} A+\cot A+\operatorname{cosec} A-\cot A=7+\frac{1}{7}$
⇒ $2\operatorname{cosec} A = \frac{49+1}{7}$
⇒ $2\operatorname{cosec} A = \frac{50}{7}$
$\therefore \operatorname{cosec} A = \frac{25}{7}$
Hence, the correct answer is $\frac{25}{7}$.

Correct Answer: 21

Solution : Given: The numbers are 8, 12, and 14.
Let the fourth proportion be $x$.
So, $8:12::14:x$
⇒ $\frac{8}{12} = \frac{14}{x}$
⇒ $x = \frac{14 \times 12}{8}=21$
Hence, the correct answer is 21.

Correct Answer: Only conclusion II follows

Solution : The possible Venn diagram according to the given statements is as follows –

Let's analyze the conclusions –
Conclusion (I): All decagons are hexagons – From the Venn diagram, it is evident that some parts of the circle representing decagons lie inside the circle representing hexagons while some lie outside. Thus, this conclusion does not follow.
Conclusion (II): All hexagons are octagons – From the Venn diagram, it is evident that the circle representing hexagons is completely overlapped by the circle representing octagons. Thus, it can be concluded that all hexagons are octagons.

So, the only conclusion II follows. Hence, the third option is correct.

Correct Answer: 40%

Solution : Let the cost price (CP) be 100.
The gain percentage is 12%.
So, the selling price (SP) = 100 + 100 × $\frac{12}{100}$ = 112
Now, discount = 20%,
So, the marked price (MP) × $\frac{(100-\text{discount percentage})}{100}$ = SP
⇒ MP × $\frac{(100-20)}{100}$ = 112
⇒ MP = $\frac{112×100}{80}$ = 140
Therefore, the required percentage = (140 – 100) = 40%
Hence, the correct answer is 40%.

Correct Answer: Monotonous

Solution : The correct choice is the fourth option.

Monotonous means lacking in variety and interest, being repetitive and dull, which precisely describes the concept of never changing and being boring.

The meanings of other options are as follows:

• Outdated: This term refers to something that is no longer current or fashionable.

• Impractical: This word describes something that is not useful or effective in practice.

• Idealistic: It refers to having high moral or ethical principles.

Therefore, the correct one-word substitute is monotonous.

Correct Answer: Sculptor-Chisel

Solution : Let's check each option –
First option: Scalpel - Surgeon; The scalpel is an essential tool used by surgeons.
Second option: Axe - Woodcutter; An axe is a tool used by woodcutter.
Third option: Sword - Warrior; A sword is used by a warrior.
Fourth option: Sculptor - Chisel; a sculptor is a person who carves figures or forms of clay, stone, metal, wood, etc. 

So, the fourth option does not follow the pattern as followed by the other given pairs.
Hence, the fourth option is correct.