Correct Answer: 10

Solution : Given:
$x^2-11x+1=0$
Divide both sides by $x$, we get
$x-11+\frac{1}{x}=0$
⇒ $x+\frac{1}{x}=11$
Squaring both sides we get
⇒ $x^2+\frac{1}{x^2}+2×x×\frac{1}{x}=11^2$
⇒ $x^2+\frac{1}{x^2}=121-2$
⇒ $x^2+\frac{1}{x^2}=119$
Again squaring both sides we get,
⇒ $x^4+\frac{1}{x^4}+2×x^2×\frac{1}{x^2}=119^2$
⇒ $x^4+\frac{1}{x^4}=14161-2$
⇒ $x^4+\frac{1}{x^4}-14159=0$
Multiplying with $x^4$ we get
⇒ $x^8-14159x^4+1=0$
$\therefore x^8-14159x^4+11=10$
Hence,

Correct Answer: All conclusions I, II and III follow

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

Let's analyse the conclusions –
Conclusion (I): Some cars are vans – From the Venn diagram, we can see that the two circles representing cars and

Correct Answer: $60^{\circ}$

Solution : $\frac{\cos \theta}{(1+\sin \theta)}+\frac{\cos \theta}{(1-\sin \theta)}=4$
Multiplying the two fractions by $(1+\sin \theta)(1-\sin \theta)=\cos^2 \theta$.
$⇒ \cos \theta (1-\sin \theta) + \cos \theta (1+\sin \theta) = 4 \cos^2 \theta$
$⇒ 2 \cos \theta = 4 \cos^2 \theta$
$⇒ 1 = 2 \cos \theta$
$⇒ \cos \theta

Correct Answer: Mridangam

Solution : The correct answer is the Mridangam.

Ramnad V. Raghavan was indeed associated with the musical instrument "Mridangam". He was a renowned Indian percussionist and mridangam player. The mridangam is a traditional double-headed drum that is widely used in the Carnatic music of South India.

Correct Answer: Sister

Solution : Following the instructions of the question, the family tree will be –

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

So, the woman is the sister of Gaurav. Hence, the fourth option is correct.

Correct Answer: effect

Solution : The correct choice is the third option.

Effect refers to a change that something has brought about. It is a noun that is used to indicate the result of a change. Thus, effect is the correct choice, as the sentence requires a noun.

The

Correct Answer: 66.66%

Solution : Raw materials in 2015 = 330
Raw materials in 2019 = 550
Percentage increase
$=\frac{\text{Raw materials in 2019 – Raw materials in 2015}}{\text{Raw materials in 2015}}\times100$
$=\frac{550-330}{330}\times100$
$=\frac{220}{330}\times100=66.66\%$
Hence, the correct answer is 66.66%.

Correct Answer: INR 6,250

Solution : Let's denote the initial rate of interest as $r$, and the principal amount as $P$ [Given]. The time is given as 4 years.
The interest earned at the initial rate $r$ is $I=\frac{P×r×T}{100}$​, where T is the time in years.
The interest earned at

Correct Answer: 3 : 2

Solution :
By using the rule of alligation, we get the required ratio = (85 – 82) : (82 – 80) = 3 : 2
Hence, the correct answer is 3 : 2.

Correct Answer: 5 km

Solution : Firstly, we will draw the diagram as per the given instructions –

Here, AB = 3 km and BC = 4 km
AC is the distance between the starting and the finishing point.
By applying the Pythagoras theorem –
⇒ (AC)² = (AB)