Question : The simplified value of $\small \left (1-\frac{2xy}{x^{2}+y^{2}}\right )\div\left (\frac{x^{3}-y^{3}}{x-y}-3xy\right)$ is:

Option 1: $\frac{1}{x^{2}-y^{3}}$

Option 2: $\frac{1}{x^{2}+y^{2}}$

Option 3: $\frac{1}{x-y}$

Option 4: $\frac{1}{x+y}$

Question : Directions: In an institution where there are 800 students, students use different modes of transport to go to the institution and return. The given pie diagram represents the required data. Study the diagram carefully and answer the question.

The number of students who travelled by Public bus is:

Option 1: 150

Option 2: 120

Option 3: 130

Option 4: 125

Question : Select the INCORRECTLY spelt word in the given sentence.
To achieve somthing gigantic, you have to grind for a considerable amount of time.

Option 1: somthing

Option 2: considerable

Option 3: gigantic

Option 4: achieve

Question : In which of the following places is the Tak Tok festival celebrated?

Option 1: Assam

Option 2: Nagaland

Option 3: Ladakh

Option 4: Tripura

Question : Directions: By interchanging the given two signs and numbers which of the following equations will be not correct?
+ and ×, 5 and 4
I. 4 + 8 × 5 – 7 ÷ 1 = 37
II. 5 × 3 – 4 + 6 ÷ 2 = – 8

Option 1: Only II

Option 2: Neither I nor II

Option 3: Only I

Option 4: Both I and II

Question : In the figure, $\mathrm{XYZ}$ is a secant and $\mathrm{ZT}$ is a tangent to the circle at $\mathrm{T}$. If $\mathrm{TZ}=12$ $\mathrm{cm}$ and $Y Z=8 \mathrm{~cm}$, then find the length of $XY$.

Option 1: 8 cm

Option 2: 9 cm

Option 3: 6 cm

Option 4: 10 cm

Question : Directions: A + B means A is the father of B;
A * B means A is the sister of B;
A % B means A is the daughter of B;
A \$ B means A is the son of B.
If L % M + N * O \$ P, then how is L related to P?

Option 1: Sister

Option 2: Daughter

Option 3: Mother

Option 4: Mother-in-law

Question : Two persons A and B working separately can sanitise a building in 6 hours and 10 hours, respectively. They work in stretches of one hour alternately. If A begins at 8 a.m., then when will the work be finished?

Option 1: $9\frac{1}{3}$ h

Option 2: $7\frac{1}{3}$ h

Option 3: $6\frac{1}{3}$ h

Option 4: $8\frac{1}{3}$ h

Question : Which one of the following bio reserves of India is not included in the World Network of Biosphere Reserve?

Option 1: Sundarbans

Option 2: Gulf of Mannar

Option 3: Nanda Devi

Option 4: Corbett

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 Sun is the star at the centre of (1) __________ Solar System. It is a nearly perfect ball of hot plasma. The Sun has inspired us since ancient times. It’s central to mythology and religion in (2) ____________ around the world. It keeps our planet warm enough for living things to grow. It gives us light, so we can see. It is by far the most important (3) _________of energy for life on Earth. It is about a hundred times as wide (4)________ the Earth. If there were no sun, many things wouldn’t occur, like photosynthesis or the presence of oxygen, which would have caused no existence of life.

Select the most appropriate option to fill in the blank number 1.

Option 1: huge

Option 2: typical

Option 3: a

Option 4: the