Question : If $2a+3b=14$ and $2a-3b=10$, then find the value of ' $ab$ '.

Option 1: 5

Option 2: 3

Option 3: 4

Option 4: 2

Question : Comprehension:

Read the following passage and answer the questions that follow.

Indian mathematician Nikhil Srivastava, working at the University of California in Berkeley, is among the winners of the Prestigious 2021 Michael and Sheila Held Prize, announced last week by the US National Academy of Sciences (NAS). Adam W. Marcus, EPFL (Swiss Federal Institute of Technology, Lausanne), and Daniel Alan Spielman, Yale University, are the other two winners.

"Marcus, Spielman, and Srivastava solved longstanding questions on the Kadison-Singer problem and on Ramanujan graphs, and in the process, they uncovered a deep new connection between linear algebra, the geometry of polynomials, and graph theory that has inspired the next generation of theoretical computer scientists," the NAS said in a statement.

An Indian national, Nikhil was born in New Delhi in November 1983 and has attended educational institutions across the world—Syria, the UK, Saudi Arabia, and the US—as his father was an Indian Foreign Services officer, who has served as the Indian ambassador to Uganda and Denmark. At present, Nikhil is an associate professor of mathematics at UC Berkeley. The Michael and Sheila Held Prize is presented annually to honour outstanding, innovative, creative, and influential research in the area of combinatorial mathematics.

Question:
In what way have the prize winners helped future theoretical computer scientists?

Option 1: They have found connections between algebra, geometry and computer science.

Option 2: They solved new problems in graph theory used in theoretical computer science.

Option 3: The new connection they have discovered has inspired future theoretical computer scientists.

Option 4: They have done innovative research on Ramanujan graphs and geometry of polynomials.

Question : Select the most appropriate word which means the same as the group of words given.

Two lengths of rope, bamboo or wood with rungs used for climbing up and down walls, sides of ships etc.

Option 1: staircase

Option 2: steps

Option 3: bridge

Option 4: ladder

Question : Comprehension:
In the following passage, some words have been deleted. Fill in the blanks with the help of the alternatives given. Select the most appropriate option for each number.

All state universities and colleges in Uttar Pradesh, one of the (1)________ in India, will now (2)______ a "save water" ritual named 'Jal Bharo' in place of 'lamp lighting' to inaugurate their annual convocations. The governor of the state, who is also chancellor of state universities, instructed that every university and college in the state should install rainwater harvesting plants on its campus. 'Jal Bharo' signifies (3)_______ the vision of 'Jal Shakti'. This ceremony symbolises the (4)________ importance of water conservation, whereas the lamp lighting ceremony symbolised removing darkness through education and spreading the light of learning. It is really a (5)________ initiative. Every educational institute in India should ensure to save and recharge groundwater by installing rainwater harvesting plants. These kinds of initiatives provide awareness of using and saving water, the elixir of life.

Question:
Select the most appropriate option to fill in blank no. 5.

Option 1: laudable

Option 2: louder

Option 3: labelled

Option 4: lower

Question : Directions: In the question, a part of the sentence is in bold. Below are given alternatives to the bold part at (1), (2), and (3) that may improve the sentence. Choose the correct alternative. In case no improvement is needed, your answer is (4).

Kunal looked very manliness in his police uniform.

(1) menliness

(2) man-like

(3) manly

(4) No Improvement

Option 1: (1)

Option 2: (2)

Option 3: (3)

Option 4: (4)