Correct Answer: 30

Solution : Given: $p^2-4 p-1=0$
⇒ $p-\frac{1}{p}=4$
Squaring both sides, we get:
$⇒(p-\frac{1}{p})^2=(4)^2$
$⇒ (p^2+\frac{1}{p^2}-2×p×\frac{1}{p})=16$
$⇒ (p^2+\frac{1}{p^2})=16+2$
$⇒ (p^2+\frac{1}{p^2})=18$
Now, $p^2+3 p+\frac{1}{p^2}-\frac{3}{p}$
$=p^2+\frac{1}{p^2}+3 p-\frac{3}{p}$
$=p^2+\frac{1}{p^2}+3(p-\frac{1}{p})$
Putting the values, we get:
$=18+3×4$
$=30$
Hence, the correct answer is 30.

Correct Answer: INR 20,25,000

Solution : The total sum of the teacher's salary and rent = INR 45 lakhs
$\therefore$ (15% + 25%) of school expenditure = 45,00,000
School expenditure = $\frac{100}{40}×4500000$ = 2.5 × 4500,000 = 1,12,50,000
$\therefore$ Savings = 18% of school expenditure = $\frac{18}{100}×11250000$ = 20,25,000
Hence, the correct answer is INR 20,25,000.

Correct Answer: 24

Solution : The given figure can be labelled as shown below –

In the above figure, there are 24 triangles. They are ABJ, AIJ, IJK, BJK, ILF, FLE, LEK, ILK, BCK, CKD, KDE, AHI, HIG, GIF, AIK, BIK, IEF, KFE, IKF, IKE, ABK, AIB, AKF, and BIE.

Hence, the fourth option is correct.

Correct Answer: Tansen

Solution : The correct answer is Tansen.

Sangeet Samrat Mian Tansen composed this raga in the sixteenth century. A monsoon raga known as Miya Ki Malhar is often used to welcome the monsoon and invoke rain, soaking the land. Tansen composed devotional scores for his life; he was born a Hindu.

Correct Answer: Manipur

Solution : The correct option is Manipur.

Lui Ngai Ni is a festival associated with the state of Manipur. It is a major cultural celebration of the Naga tribes in Manipur, and it marks the onset of the seed-sowing season. The festival is characterised by vibrant traditional dances, songs, rituals, and feasting. Communities have to come together, showcase their cultural heritage, and strengthen social bonds.

Correct Answer: The new product will be released by the company next month.

Solution : The correct choice is the first option.

Passive voice is the voice in which the object experiences an action rather than the person who performs the action. Hence, the object in the active sentence becomes the subject in the passive voice.

The structure of the passive voice in the case of the simple future tense is: "Singular object + will + be + past participle form of the verb + 'by' followed by the agent of the action."

Therefore, the sentence in the passive voice is: "The new product will be released by the company next month."

Correct Answer: Consolidated fund of India

Solution : Correct answer is consolidated fund of India 

The pension of the High Court Judges is given from the consolidated of India. But the salaries and allowances of the judges of the high courts are charged on the consolidated fund of states where they are serving.

Salaries & allowances of the Supreme Court judges are both provided from the consolidated fund of India

Correct Answer: 12

Solution :
Let $r{_1}$​ and $r{_2}$​ be the radii of the two circles, and let $d$ be the distance between their centres.
In this case:
$d=r{_1}​+r{_2}$​
Given that the radii are 18 cm and 8 cm, we have:
$d=9+4=13\ \mathrm{cm}$
Now, the direct common tangent is the line segment that joins the points of contact of the two circles. This forms a right-angled triangle with the line segment connecting the centres. The length of the direct common tangent can be found using the Pythagorean theorem.
Let $t$ be the length of the direct common tangent.
Then:
$t^2=d^2−(r{_1}​−r{_2}​)^2$
$⇒t^2=13^2−(9−4)^2$
$⇒t^2=169−5^2$
$⇒t^2=169−25$
$⇒t^2=144$
$\therefore t=12\ \mathrm{cm}$
Hence, the correct answer is 12.

Correct Answer: China

Solution : The correct answer is China.

No feature has been taken from China in the Indian Constitution. The spirit and content of the Indian Constitution are distinct. It did, however, inherit many of the best elements from past international constitutions. India's constitution stands out from that of other nations due to several notable characteristics.

Correct Answer: 2

Solution : Given: $a^{2} + b^{2} + c^{2} = (ab+bc+ca)$
⇒ $a^{2} + b^{2} + c^{2} - (ab+bc+ca)=0$
Since : $a^2+b^2+c^2-ab-bc-ca = \frac{1}{2}[(a-b)^2+(b-c)^2+(c-a)^2]$
So, $a^2+b^2+c^2-ab-bc-ca = \frac{1}{2}[(a-b)^2+(b-c)^2+(c-a)^2]=0$
⇒ $a=b=c $
So, $\frac{a+c}{b} = \frac{a+a}{a} = 2$
Hence, the correct answer is 2.