TISSNET 2023

The first row has 279 buses, and the second row has 277 buses, the third row has 275 buses...and so on

This forms a decreasing A.P with a common difference of 2

The first term of A.P, a = 279, common difference = -2 and last term $$a_n$$ = 5

We know, in an AP $$a_n=a+\left(n-1\right)d$$

=> 5 = 279 + (n-1)*(-2)

=> (n-1)*2 = 274

=> n-1 = 137

Therefore, n = 138

A total of 138 rows are there in the bus station.

The answer is option A.

The points A(2, 3), B(4, k) and C(6, -3) are collinear means they lie on a single line.

Let the equation of line be y = mx + c (General form of a linear equation with slope m )

This line will pass through all three points A, B and C.

By substituting values of coordinates of A, B and C in the given line we get

3 = 2m + c      ------ (1)

-3 = 6m + c     ------ (2)

Subtracting (2) from (1), we get

=> 6 = -4m

m = -1.5

Substituting m = -1.5, we get

3 = -3 + c

c = 6

Equation of line is y = -1.5x + 6

Point B(4,k) passes through the line.

=> k = -1.5*4 + 6

=> k = 0 

The answer is option A.

The volume of the new cube is equal to the sum of volumes of the three cubes i.e., volume of the new cube = 1+216+512 = 729 $$cm^3$$

The volume of cube of side a is given by $$a^3$$

=> $$a^3$$ = 729

=> a = 9

Therefore, the side of new cube is 9 cm.

Length of diagonal of cube = $$\sqrt{3}a$$

Length of diagonal of new cube = $$9\sqrt{3}$$ cm

The answer is option A.

Let Statement P: A is 200 metres from B, B is 100 metres from C, and statement Q: A is 300 metres from C.

In the question, it is given either statement P or statement Q is true.

All of the following statements are compatible with the given statement.

1. If P is true, Q is not true.

2. If Q is true, P is not true.

3. Neither P nor Q are true.

4. If P is not true, Q may be true or false.

5. If Q is not true, Q may be true or false.

Option B, i.e. statements (i) and (iv) represents the condition given in statement 1.

Option C, i.e. statements (iii) and (ii) represents the condition given in statement 4.

Option D, i.e. statements (ii) and (iii) represents the condition given in statement 2.

Option A is not in line with any of the given statements.

Therefore, the answer is option A.

The path of Gopal will look like as shown in figure.

Gopal started from A and went 90 meters to reach B(in the east direction).

Later, he went 20 meters from B to C by turning right(in the south direction).

Later, he went 30 meters from C to D by turning right(in the west direction).

D is the location of Shilu's uncle's house.

=> He went from D to F 100 meters(in the north direction).

Gopal met Shilu at point F.

Therefore, from starting point distance between A and F = $$\sqrt{\left(60\right)^2+\left(80\right)^2}$$

=> $$\sqrt{3600+6400}$$ = 100 meters.

The answer is option D.

It is given that faculty to student ratio = 1:9

Let the number of faculty be 100a, so students will be 900a

=> Two-thirds of students are female = $$\ \dfrac{2}{3}\times900$$a = 600a

=> Therefore, male students = 300a

Also, one-quarter of the faculty is female = $$\ \dfrac{1}{4}\times100$$a = 25a

Therefore, male faculty = 75a

The ratio of female students and faculty out of the total students and faculty = $$\dfrac{\left(600a+25a\right)\ }{1000a}$$

=> ratio = $$\ \dfrac{5}{8}$$

The answer is option D.

It is given that solution 1 contains 12% acid in 600 litres, and solution 2 contains 30% acid in x litres

=> Acid in solution 1 = $$\ \frac{12}{100}\times600$$ = 72 litres

=> Acid in solution 2 = $$\ \frac{30}{100}\times$$ x = 0.3x litres

In the final mixture, acid quantity = (72+0.3x)litres

It is given that the acid content in the resulting mixture will be more than 15% but less than 18%

The equation of acid content will be = 15% of (600+x) < 72+0.3x < 18% of (600+x)   { Final mixture will have a volume of 600+x litres}

=> 90+0.15x < 72+0.3x < 108 + 0.18x

So solving both sides

=> 18 < 0.15x  and 0.12x < 36

Therefore, x lies in 120 < x < 300

Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a close body.

When we reshape a solid into another solid, the quantity of material is the same, so the volume of the solid remains unchanged.

Therefore, if we change the shape of an object from a sphere to a cylinder, the volume of the cylinder will remain unchanged.

The answer is option D.

In order for a year to qualify as a leap year, it must be divisible by 4. If it is a centurial year, it must also be divisible by 400.

Since 1900 is a century year so it must be divisible by 400, but it is not divisible by 400. 

Therefore, Ashok is lying that he was born on 29 February 1900 as it is not a leap year.

The answer is option B.