Correct Answer: 2880

Solution : Given:
5, 20, 60, 240, 720, ?

To get the required missing number in the series, multiply the number by 4 and 3 alternatively –
5 × 4 = 20; 20 × 3 = 60; 60 × 4 = 240; 240 × 3 = 720;

Correct Answer: 1887

Solution : The correct option is 1887.

In the year 1887, German physicist Heinrich Hertz made a pivotal discovery related to the photoelectric effect while researching radio waves. In the course of his experiments, Hertz utilised a spark gap consisting of two closely spaced, sharp electrodes capable

Correct Answer: $1$

Solution : Given:
$\operatorname{cosec}\theta-\sin\theta=l$ and $\sec\theta-\cos\theta=m$, $l^2m^2(l^2+m^2+3)$
$=(\operatorname{cosec}\theta-\sin\theta)^2(\sec\theta-\cos\theta)^2[(\operatorname{cosec}\theta-\sin\theta)^2+(\sec\theta-\cos\theta)^2+3]$
$= (\frac{1}{\sin\theta}-\sin\theta)^2(\frac{1}{\cos\theta}-\cos\theta)^2[(\frac{1}{\sin\theta}-\sin\theta)^2+(\frac{1}{\cos\theta}-\cos\theta)^2+3]$
$=(\frac{1-\sin^2\theta}{\sin\theta})^2(\frac{1-\cos^2\theta}{\cos\theta})^2[(\frac{1-\sin^2\theta}{\sin\theta})^2+(\frac{1-\cos^2\theta}{\cos\theta})^2+3]$
$=(\frac{cos^2\theta}{\sin\theta})^2(\frac{\sin^2\theta}{\cos\theta})^2[(\frac{\cos^2\theta}{\sin\theta})^2+(\frac{\sin^2\theta}{\cos\theta})^2+3]$
$=(\frac{\cos^4\theta}{\sin^2\theta})(\frac{\sin^4\theta}{\cos^2\theta})[(\frac{\cos^4\theta}{\sin^2\theta})+(\frac{\sin^4\theta}{\cos^2\theta})+3]$
$= \sin^2\theta \cos^2\theta[\frac{\cos^6\theta+\sin^6\theta+3\sin^2\theta \cos^2\theta}{\sin^2\theta \cos^2\theta}]$
$= \cos^6\theta+\sin^6\theta+3\sin^2\theta \cos^2\theta$
$=(\cos^2\theta)^3+\sin^2\theta)^3+3\sin^2\theta \cos^2\theta$
$=(\cos^2\theta+\sin^2\theta)^3-3\cos^2\theta \sin^2\theta(\cos^2\theta+\sin^2\theta)+3\sin^2\theta \cos^2\theta$
$=1^3-3\cos^2\theta \sin^2\theta(1)+3\sin^2\theta \cos^2\theta$
$=1$
Hence, the correct answer is $1$.

Correct Answer: 45°

Solution : Given: $239x-239y+5=0$
$\therefore$ Slope = $\frac{-239}{-239}$ = 1
So, $\tan\theta= 1=\tan 45°$
$\therefore\theta = 45°$
Hence, the correct answer is 45°.

Correct Answer: 39.7

Solution : Given: The average marks of 100 students were found to be 40.
It was discovered that a score of 53 was misread as 83.
Difference = 83 – 53 = 30
$\therefore$ Final average = 40 – $\frac{30}{100}$ = 39.7
Hence, the correct answer is

Correct Answer: 25% loss

Solution : Given in question, the cost price (CP) of 1000 gm of cashew nut = Rs. 250
So, CP of 50 gm of cashew nut = $\frac{250}{1000}$ × 50 = Rs. 12.5
The selling price (SP) of 50 gm of cashew nut = Rs. 10

Correct Answer: 2

Solution : The correct choice is the second option.

Explanation: The phrase aggressive then should be replaced with aggressive than to convey the intended meaning that some children display a higher level of aggression as compared to others. Than is used for comparison, and then 

Correct Answer: Urja Mitra

Solution : The correct option is Urja Mitra.

The Union Ministry of Power has introduced the Urja Mitra app. This comprehensive platform includes a mobile application, a web portal, and a central hub for state power distribution utilities. It provides real-time updates on the power supply.

Correct Answer: gymnosperms

Solution : The correct answer is gymnosperms.

One of the gymnosperms, the giant redwood tree Sequoia, is one of the tallest tree species. Gymnosperms are a group of seed-producing plants that include conifers like the Sequoia. Renowned for their immense height, these trees exemplify the grandeur

Correct Answer: January

Solution : The correct option is January

Mahatma Gandhi returned from South Africa to India in January 1915 after successfully leading campaigns against racial discrimination. His efforts, marked by nonviolent resistance, contributed to social change and laid the foundation for his later role in India's struggle for