Question : The radius of two circles is 3 cm and 4 cm. The distance between the centres of the circles is 10 cm. What is the ratio of the length of the direct common tangent to the length of the transverse common tangent?

Option 1: $\sqrt{51}:\sqrt{68}$

Option 2: $\sqrt{33}:\sqrt{17}$

Option 3: $\sqrt{66}:\sqrt{51}$

Option 4: $\sqrt{28}:\sqrt{17}$

Question : A shopkeeper marks up his wares by 60% and offers a 10% discount. What will be the selling price (in Rs.) if the cost price is Rs. 7500?

Option 1: 11800

Option 2: 12800

Option 3: 13800

Option 4: 10800

Question : Comprehension:
In the following passage some words have been deleted. Read the passage carefully and select the most appropriate option to fill in each blank.

The civil service is an integral part of the government and plays a crucial role in implementing policies and programmes that benefit the public. The (1)_____ of civil services is to ensure that the government is able to provide services to citizens in a timely and effective manner. Civil servants are responsible for a wide range of tasks, including (2)_______ the implementation of policies and programmes, managing budgets, and providing advice to government officials. In order to perform their duties effectively, civil servants must have a deep understanding of government processes, as well as strong (3)______ and analytical skills. They must also be able to communicate effectively with a wide range of stakeholders, including government officials, citizens, and other organisations. To become a civil servant, individuals typically need to pass a rigorous exam and undergo extensive training. Once they are appointed, civil servants are expected to abide by a code of conduct that emphasises impartiality, integrity, and (4)________ in carrying out their duties. Despite the challenges and demands of civil service work, it can be a highly rewarding career path, providing opportunities to make a positive impact on society and improve the lives of citizens. Whether working in a local, state, or federal government agency, civil servants play a vital role in (5)_________ democratic values and promoting the public good.
Select the most appropriate option to fill in the blank no. 3.

Option 1: technical

Option 2: problem-solving

Option 3: interpersonal

Option 4: accounting

Question : Directions: In the following question, select the related number from the given alternatives.
12.5 : 6.25 :: 7 : ?

Option 1: 3.5

Option 2: 3.25

Option 3: 6.5

Option 4: 12

Question : During the first year, the strength of a school increased by 12%, in the second year it decreased by 12%, and in the third year it increased by 10%. At the end of the third year, its strength was nearly 10842. What was the strength at the beginning of the first year?

Option 1: 8000

Option 2: 10000

Option 3: 6500

Option 4: 12000

Question : Which of the following is added to the national income to obtain the personal income of the households?

Option 1: Net interest payments

Option 2: Transfer payments from the government and firms

Option 3: Undistributed profits

Option 4: Corporate tax

Question : A man travels 450 km to his home, partly by train and partly by car. It takes 8 hours and 40 minutes if he travels 240 km by train and rests by car. It takes 20 minutes more if he travels 180 km by train and the rest by car. The speed of the car in km/h is:

Option 1: 45

Option 2: 50

Option 3: 60

Option 4: 48

Question : Select the most appropriate option to improve the underlined segment in the given sentence. If there is no need to improve it, select 'No improvement'.

You will participate in the marathon, won't you?

Option 1: didn't you

Option 2: isn't it

Option 3: will you

Option 4: No improvement

Question : Comprehension:
Read the passage and answer the questions given after it.

The savanna landscape is typified by tall grass and short trees. It is rather misleading to call the savanna 'tropical grassland' because trees are always present with the luxuriant tall grass. The terms 'parkland' or 'bush-veld' perhaps describe the landscape better.

Trees grow best towards the equatorial humid latitudes or along river banks but decrease in height and density away from the equator. They occur in clumps or as scattered individuals. The trees are deciduous, shedding their leaves in the cool, dry season to prevent excessive loss of water through transpiration, e.g. acacias. Others have broad trunks, with water-storing devices to survive through the prolonged drought such as baobabs and bottle trees. Trees are mostly hard, gnarled and thorny and may exude gum-like gum arable. Many trees are umbrella-shaped, exposing only a narrow edge to the strong winds.

Palms which cannot withstand the drought are confined to the wettest areas or along rivers. Vegetative luxuriance reaches its peak in the rainy season when trees renew their foliage and flower. In true savanna lands, the grass is tall and coarse, growing 6 to 12 feet high. The elephant grass may attain a height of even 15 feet! The grass tends to grow in compact tufts and has long roots which reach down in search of water. It appears greenish and well-nourished in the rainy season but turns yellow and dies down in the dry season that follows. The grass lies dormant throughout the long, rainless period and springs up again in the next rainy season.

In between the tall grass are scattered short trees and low bushes. As the rainfall diminishes towards the deserts the savanna merges into thorny scrub. In Australia, this scrubland is particularly well represented by a number of species: mallee, mulga, spinifex grass and other bushes.

The savanna, particularly in Africa, is the home of wild animals. It is known as the "big game country' and thousands of animals are trapped or killed each year by people from all over the world. Some of the animals are tracked down for their skins, horns, tusks, bones or hair, others are captured alive and sent out of Africa as zoo animals, laboratory specimens or pets. There is such a wealth of animal life in Africa that many of the animal films that we see at the cinema are actually taken in the savanna. There are, in fact, two main groups of animals in the savanna, the grass-eating herbivorous animals and the fleshing-eating carnivorous animals. The herbivorous animals are often very alert and move swiftly from place to place in search of green pastures.

They are endowed with great speed to run away from the savage flesh-eaters that are always after them. The leaf and grass-eating animals include the zebra, antelope, giraffe, deer, gazelle, elephant and okapi.

Many are well camouflaged species and their presence amongst the tall greenish-brown grass cannot be easily detected. The giraffe with such a long neck can locate its enemies a great distance away, while the elephant is so huge and strong that few animals will venture to come near it. It is well equipped with tusks and a trunk for defence.

Carnivorous animals like the lion, tiger, leopard, hyena, panther, jaguar, jackal, lynx and puma have powerful jaws and teeth for attacking other animals. Their natural colourings of light yellowish-brown, often with stripes like the tiger or spots like the leopard, match perfectly with the tawny background of the savanna. They often hide themselves in shady spots up in the branches or amidst the tall bushes, and many wild animals, as well as hunters themselves, are caught unawares in this manner.

Question:
What kind of a passage is it?

Option 1: Analytical

Option 2: Informative

Option 3: Narrative

Option 4: Literary

Question : The mean of marks secured by 50 students in Division A of class X is 61, 25 students in Division B is 57 and that of 50 students in Division C is 55. What will be the mean marks of the students of the three divisions of Class X?

Option 1: 57.1

Option 2: 56.4

Option 3: 59.2

Option 4: 57.8