6x + 1 > 7 - 4x
⇒ x > 3/5
∴ 3/5 < x ≤ 2

Correct Option: A

6x + 1 > 7 - 4x
⇒ x > 3/5
∴ 3/5 < x ≤ 2

Let the number be x and y.
Then, according to the question,
x + y = 15 ...(1)
x - y = 3 ...(ii)

Correct Option: E

Let the number be x and y.
Then, according to the question,
x + y = 15 ...(1)
x - y = 3 ...(ii)
on adding Eqs. (i) and (ii), we get
2x = 18
⇒ x = 9
On putting the value of in Eq. (i), we get
y = 6
∴ Product = xy = 54

Let hens = H, goats = G
According to the question,
H + G = 90 ...(i)
2H + 4G = 248 ...(ii)
Multiplying Eq. (i) by 2 and subtracting from Eq. (ii)

Correct Option: C

Let hens = H, goats = G
According to the question,
H + G = 90 ...(i)
2H + 4G = 248 ...(ii)
On multiplying Eq. (i) by 2 and subtracting from Eq. (ii) , we get
2H + 2G = 180
2H + 4G = 248
-------------------
-2G = -68
∴ G = 34

Given equation are 6x + 3y = 7xy
⇒ (6/y) + (3/x) = 7 .....(i)

And 3x + 9y = 11xy
⇒ (3/y) + (9/x) = 11 .....(ii)

Multiplying Eq. (ii) by 2 and subtracting from Eq. (i)

Correct Option: A

Given equation are 6x + 3y = 7xy
⇒ (6/y) + (3/x) = 7 .....(i)

And 3x + 9y = 11xy
⇒ (3/y) + (9/x) = 11 .....(ii)

On multiplying Eq. (ii) by 2 and subtracting from Eq. (i), we get
(6/y) + (3/x) = 7
(6/y) + (18/x) = 22
-------------------------
- 15/x = - 15
∴ x = 1

On putting this value in Eq. (i), we get
(6/y) + 3 = 7
∴ 6/y = 4
∴ y = 6/4 = 3/2

Given, 3^{x + y} = 81
⇒ 3^{x + y} = 3⁴
⇒ x + y = 4 ...(i)
and 81^{x - y} = 3 or (3⁴)^{x - y} = 3
⇒ x - y = 1/4

Correct Option: B

Given, 3^{x + y} = 81
⇒ 3^{x + y} = 3⁴
⇒ x + y = 4 ...(i)
and 81^{x - y} = 3 or (3⁴)^{x - y} = 3
⇒ x - y = 1/4
On solving the Eqs. (i) and (ii), we get
2x = 17/4 ⇒ x = 17/8