A sector of a circle with radius 8 cm has a central angle of 45°. What is the area of the corresponding segment?

If the lateral surface area of a cylinder is 320 cm² and height is 10 cm, what is the radius?

Solve system: y = 3x - 2 and y = x + 4

If the perimeter of a regular hexagon is 72 cm, what is the side length?

Two chords, PQ and RS, are equal in length and are at a distance of 12 cm from the center of a circle. If the radius is 20 cm, what is the length of PQ?

A right circular cone has radius 8 cm and height 20 cm. A sphere is inscribed in the cone such that it touches the base and the lateral surface. Find the radius of the inscribed sphere.

A vertical tower of height H stands on the ground. From point A on the ground, the angle of elevation to the top is 45°. From point B, located 15 meters away from A (directly along the line extending from the base), the angle of elevation is 30°. What is the height of the tower?

A circular disc is divided into 6 equal sectors. If the area of one sector is 66cm², what is the radius of the disc ?

If two circles are touching externally how many common tangents do they have?

Express 0.363636... as a fraction.

Simplify: √72 - √18 + √50

Which is the correct spelling for a word meaning "countless"?

What does the passage suggest by calling art an “epistemic act”?

Read the following passage and answer the questions based on the passage:

In the passage, the phrase “commodification of art” most nearly means: Read the following passage and answer the questions based on the passage:

As per the passage, what role can art play under politically restrictive conditions? Read the following passage and answer the questions based on the passage:

Which option best explains the “dialectical” character of art mentioned in the passage? Read the following passage and answer the questions based on the passage:

What is the closest meaning of the word “banality” as used in the passage? Read the following passage and answer the questions based on the passage:

Choose the most suitable option to replace the highlighted part of the sentence: He dislikes to speak in public.

Choose the correct one-word substitution for: “Someone who challenges or resists the established system or authority.”

. Convert the sentence provided below from its passive voice structure to an active voice structure: The applicants were being interviewed by the panel members.

Rearrange the following sentences to form a coherent paragraph: 1. One effective approach is to broaden energy options by moving from fossil fuels to renewables such as solar, wind, and geothermal power. 2. To limit the harshest impacts of climate change, the world must sharply cut dependence on carbon-heavy energy systems. 3. This transition not only reduces greenhouse gases but also improves air quality and opens fresh economic pathways. 4. In addition, policies that increase efficiency in buildings and transport can further reduce overall energy demand.

Change the following from active to passive: Did the manager approve the revised budget plan?

Select the most appropriate antonym of the given word: Somniferous

In the following question, select the related word from the given alternatives. Mercury: Thermometer:: Fuel : ?

In the following question, select the related word from the given alternatives Justice: Equity :: Governance : ?

Select the letter-cluster from among the given options that can replace the question mark (?) in the following series. DAG, FCI, ?, JGM, LIO

Select the letter-cluster from among the given options that can replace the question mark (?) in the following series. RST, UVW, XYZ, ?

Select the letter-cluster from among the given options that can replace the question mark (?) in the following series. MNO, OPQ, QRS, ?

Select the letter-cluster from among the given options that can replace the question mark （？） in the following series： PCHJ, PGPV, PKXH, POFT, ?

Select the letter-cluster from among the given options that can replace the question mark (?) in the following series: BDFH, BFJN, BHNT, BJRZ, ?

Complete the series: 28, 42,59,79,102, ?

Each of the letters in the word FAMILY is arranged in alphabetical order. How many letters are there in the English alphabetical series between the letter that is second from the left and the one that is third from the right in the new letter-cluster formed?

Which of the following is/are identical to the address given: Ajay Yadav 16A, Maple Heights, Sector 45, Gurgaon, 122001

1. Ajay Yadav 16A, Maple Heights, Sector 45, Gurgaon, 122001

2. Ajay Yadav 16A, Maple Heights, Sector 45, Gurugram, 122001

3. Ajay Yadav 16A, Maple Heights, Sector 45, Gurgaon, 122002

4. Ajay Yadav 16A, Maple Heights, Sector 45, Gurgaon, 122001

Which of the following is/ are identical to the address given: Neha Singh 10/3, Crystal Park, Faridabad, 121001

1. Neha Singh 10/3, Crystal Park, Faridabad, 121001

2. Neha Singh 10/3, Crystal Park, Faridabad, 121002

3. Neha Singh 10-3, Crystal Park, Faridabad, 121001

4. Neha Singh 10/3, Crystal Park, Faridabad, 121001

Find the group of letters that best completes the analogy based on the given letter transformation pattern. PAPER: QBUFS :: STONE : ?

in the following question, a pair of letters is given, followed by its corresponding product of alphabetical positions (A = 1, B = 2, .... Z = 26). A second pair of letters is given without its product. Identify the correct product for the second pair that maintains the same relationship as the first. HxL: 8x12 :: TxZ: ?

In a row of 60 students, Meena is 25th from the left and Rupa is 20th from the right. How many students are there between them?

In each of the following questions, the second word is formed by rearranging the letters of the first word according to a specific pattern. Identify the same rearrangement rule and apply it to the third word to select the correct answer from the given alternatives. EIGHTY: GIEVTH :: OUTPUT : ?

Which of the following best describes the little magazine movement in Malayalam ?

The Vernacular Press Act of 1878 was enacted to suppress Indian- language newspapers. Who repealed it ?

Arrange the following freedom movement newspapers in chronological order of their founding.

I. Young India

II. Kesari

III. Navajivan

IV. Harijan

Match the cartoonist with the Malayalam newspaper/publication they were primarily associated with

Abu Abraham	Malayala Manorama
O.V. Vijayan	Sanker's Weekly
Yesudasan	Mathrubhumi .
Toms	Kerala Kaumudi

Bal Gangadhar Tilak used journalism as a weapon for the freedom struggle through two newspapers. Identify the correct pair.

Swami Vagbhatananda denounced caste barriers and idol worship and exhorted his followers to abjure such practices. He was the founder of

The first full fledged Malayalam work printed in the language using Malayalam types was

in each of the following questions, the second word is formed by rearranging the letters of the first word according to a specific pattern. Identify the same rearrangement rule and apply it to the third word to choose the correct answer from the given alternatives. NATION: ANTINO :: HUNGRY: ?

M introduces R as the son of the only brother of her mother's husband. How is R related to M?

What comes next in the series: 2, 6, 12, 20, 30, ?

In each of the following questions, a group of three numbers/symbols is given in each option. Identify the group that does NOT follow the same pattern as the others.

In each of the following questions, a group of three numbers/symbols is given in each option. Identify the group that does NOT follow the same pattern as the others.