It's a Question of your Career!

Correct Answer: 52

Solution : $x^4+\frac{1}{x^4}=194$
Adding 2 on both sides,
⇒ $x^4+\frac{1}{x^4}+2=194+2$
⇒ $(x^2+\frac{1}{x^2})^2=196$
Taking square root on both sides,
⇒ $x^2+\frac{1}{x^2}=14$
Adding 2 on both sides,
⇒ $x^2+\frac{1}{x^2}+2=14+2$
⇒ $(x+\frac{1}{x})^2=16$
Taking square root on both sides,
⇒ $x+\frac{1}{x}=4$
⇒ $(x+\frac{1}{x})^3=4^3$
⇒ $x^3+\frac{1}{x^3}+3(x+\frac{1}{x})=64$
⇒ $x^3+\frac{1}{x^3}+3×4=64$
⇒ $x^3+\frac{1}{x^3}=64-12 = 52$

Correct Answer: A

Solution : As per the given information, the family tree will be as follows –

Here, the quadrilateral represents the male, and the circular figure represents the female in the figure.

So, from the above family tree, A is the grandmother of E. Hence, the first option

Correct Answer: 40 days

Solution : Time taken by A alone to complete the work = 60 days
Time taken by B alone to complete the work
= 33.33% less than 60 days
= $(1-\frac{1}{3})×60$
= $\frac{2}{3}×60$ = 40 days
Hence, the correct answer is 40 days.

Correct Answer: 94265

Solution : Given:

ANCIENT is coded as 2516859 and NATURE is coded as 529048

The code of letters in the given word ANCIENT is A → 2; N → 5; C → 1; I → 6; E → 8; N→ 5; T → 9

The code of

Correct Answer: $\sqrt{10}$

Solution : $a=\frac{1}{a-\sqrt{6}}(x>0)$
$⇒a^2-a\sqrt 6-1=0$
$⇒a^2-1=a\sqrt 6$
Multiplying both sides by $\frac{1}{a}$, we get,
$⇒a-\frac{1}{a}=\sqrt 6$
Squaring both sides, we get,
$⇒(a-\frac{1}{a})^2=(\sqrt 6)^2$
$⇒a^2+\frac{1}{a^2}-2=6$
Adding 4 to both sides, we get,
$⇒a^2+\frac{1}{a^2}+2=6+4$
$⇒(a+\frac{1}{a})^2=10$
$\therefore a+\frac{1}{a}=\sqrt{10}$
Hence, the correct answer is $\sqrt{10}$.

Correct Answer: $6+\sqrt{161}$

Solution :
Let PQ be a common chord. O and O' are the centres of the two circles such that
OP = 15 cm, O'P = 10 cm, and PQ = 16 cm
OO' perpendicularly bisects PQ at L. 
So, PL = $\frac{1}{2}$ × PQ = $\frac{16}{2}$

Correct Answer: Odisha

Solution : The correct answer is Odisha.

The state of Odisha in India hosted the 2023 Men's Hockey World Cup. The two locations for the games were Birsa Munda International Hockey Stadium in Rourkela and Kalinga Stadium in Bhubaneswar. At the opening ceremony, Chief Minister Naveen

Correct Answer: India

Solution : The correct answer is India.

India hosted the 1982 Asian Games in Delhi from November 19 to December 4. India secured the 5th rank with a total of 57 medals, comprising 13 gold, 19 silver, and 25 bronze medals. India also hosted the Asian

Correct Answer:  –990

Solution : Given:
$x=5$, $y=6$ and $z=-11$
Here $x+y+z= 5 + 6 -11 = 0$
So, $x^{3}+y^{3}+z^{3} = 3xyz = 3\times 5\times 6 \times (-11) = -990$
Hence, the correct answer is $-990$.

Correct Answer: < 6,000 m²/s

Solution : The correct answer is < 6,000 m²/s.

When the ventilation coefficient reaches 6,000 m²/s, the possibility of air pollution increases. The ventilation coefficient measures the capacity of the atmosphere to diffuse and dilute pollutants. It is computed