SNAP 2023 Question Paper

Centroid = $$(\frac{x_{1}+x_{2}+x_{3}}{3} , \frac{y_{1}+y_{2}+y_{3}}{3})$$

(3, 2) = $$(\frac{x+4-1}{3} , \frac{1+6+y}{3})$$

$$\frac{x+3}{3}$$ = 3 and $$\frac{7+y}{3}$$ = 2

x+3 = 9 and 7+y = 6

x = 6 and y = -1

x+y = 6-1 = 5

So the answer is option C.

We know that in an equilateral triangle, centroid, orthocentre, circumcentre, and incentre are all the same point. Let’s assume O is this point for triangle ABC.
So, AD is perpendicular to BC and bisects it as well. Also, O divides AD in the ratio 2:1.
=> $$AD^2 = AC^2 - DC^2 = 36-9 = 27$$.
So, $$AD=3\sqrt{3}$$
Since, O divides AD in the ratio 2:1, AO will be $$2\sqrt{3}$$ which is the radius of the circle.
Thus, D is the correct answer.

The given table is:

The total number of viewers on Monday = 396

The total number of viewers on Friday = 646

Difference = 250

The number of viewers in Friday is 250/396 * 100 = 63.13% greater than Monday, which is approximately 63%.

Given ,
There are 80 students.
40% of them passed, hence 32 students passed.

20 of the students who passed are girls so the rest 12 are boys.
The ratio = 20 : 12 = 5 : 3

The required pairs of letters are:
ACAD --- ABCD
ACADE --- ABCDE
DE
Hence, There are 3 pairs of letters.

Let F be the age of father and S be the age of he son.
Given, F = 3S  --> eq (1)
and (F - 6) = 5(S - 6)
F - 6 = 5S - 30
Substituting (1) in the equation
3S - 6 = 5S - 30
=> S = 12
thus, F = 3S = 36
the age of the father at the time of birth of his son = 36 - 12 = 24 years

$$\log _{91} (a+1) + \frac{1}{\log _{b+1}(91)} = 1$$ can be written as
$$\log _{91} (a+1) + \log _{91}(b+1) = 1$$
==> (a+1)(b+1) = 91
==> (a,b) can be (90,0), (12,6), (6,12) or (0,90) (Since a+1, b+1 > 0).
==> But a and b cannot be 0 as the base of the logarithm cannot be 1.
==> a+b = 18

Given (1/a)+(1/b)=3/40
(1/b)+(1/c)=3/80
(1/c)+(1/a)=1/16
(1/a)-(1/c)=3/80
Adding both the above equations we get
(2/a)=1/10
a=20 days
Substituting in above equation we get b=40 days
c=80 days
Three combinedly can do the total work in x days
(1/20)+(1/40)+(1/80)=1/x
x=80/7 days

Let amount of alcohol in A = x
Thus, total volume of solution A = x + 3x = 4x
Amount of alcohol in B = 4k
Thus, total volume of solution B = 4k + 5k = 9k
Since, volume of both solutions is equal 4x = 9k (1)
Ratio of alcohol in the final solution = (x + 4k)/(4x + 9k)
On substituting (1) we get ratio of alcohol in the final solution = 25 : 72
Thus, ratio of alcohol and water in the final solution = 25 : 47

Let the weights be 5x and 6x. 5x - 10 : 6x = 2: 3 = > 12x = 15x - 30
So, x = 10. Babu’s weight = 6x = 60 kgs.