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Question : If $x^2-11x+1=0$, what is the value of $x^8-14159x^4+11$?

Option 1: 9

Option 2: 10

Option 3: 12

Option 4: 11

Team Careers360 25th Jan, 2024

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,

16 Views

Question : Directions: In the following question, some parts of the sentence may have some errors. Find out which part of the sentence has an error and select the appropriate option. If the sentence is free from error, select "No error".

UNICEF (1) / is (2) / an international organisation. (3) / No error (4)

Option 1: (1)

Option 2: (2)

Option 3: (3)

Option 4: (4)

Team Careers360 25th Jan, 2024

Correct Answer: (1)


Solution : The error lies in the first part of the sentence.

Definite article the should be used before UNICEF because it is a collection of states or nations. UNICEF stands for United Nations International Children's Emergency Fund.

Therefore, the correct sentence is: "The UNICEF is

49 Views

Question : Which Kushana ruler was famous in history as a great patron of Buddhism and organised the fourth Buddhist Council?

Option 1: Vasudeva

Option 2: Vima Kadphises

Option 3: Kanishka

Option 4: Huvishka

Team Careers360 25th Jan, 2024

Correct Answer: Kanishka


Solution : The correct option is Kanishka.

Kanishka, the Kushan ruler, was a great patron of Buddhism and the organiser of the Fourth Buddhist Council. During his reign, in the first century CE, Kashmir hosted the Fourth Buddhist Council. The propagation and preservation of Buddhist teachings were

46 Views

Question : Which script was used in Ashoka's inscriptions?

Option 1: Brahmi

Option 2: Devanagari

Option 3: Gurmukhi

Option 4: Sanskrit

Team Careers360 24th Jan, 2024

Correct Answer: Brahmi


Solution : The correct answer is Brahmi.

There are three types of Ashokan inscriptions: major rock edicts, minor rock edicts, and pillar edicts. There were different scripts (Brahmi and Kharosthi) and different languages (Prakriti, Greek, and Aramaic). Brahmi was the most widely used script. According to some

14 Views

Question : If $\frac{\cos \theta}{(1+\sin \theta)}+\frac{\cos \theta}{(1-\sin \theta)}=4$ and $\theta$ is acute, then the value of $\theta$ is:

Option 1: $60^{\circ}$

Option 2: $15^{\circ}$

Option 3: $45^{\circ}$

Option 4: $30^{\circ}$

Team Careers360 25th Jan, 2024

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

38 Views

Question : Ramnad V. Raghavan is associated with which of the following musical instruments?

Option 1: Mridangam

Option 2: Flute

Option 3: Sitar

Option 4: Sarod

Team Careers360 25th Jan, 2024

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.

14 Views

Question : Which of the following statement is correct?

Option 1: Water is a cyclic resource

Option 2: Water has only one state

Option 3: Water is a non-renewable resource

Option 4: Water is a biotic resource

Team Careers360 24th Jan, 2024

Correct Answer: Water is a cyclic resource


Solution : The correct answer is Water is a cyclic resource.

Water is a cyclic resource. This statement reflects the fact that water undergoes a natural cycle known as the water cycle or hydrological cycle. In this cycle, water moves between the

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