Let us assume N be the given number.
According to the question,
Sum of third , fourth and fifth part of a number exceeds half of the number by 34.
N/3 + N/4 + N/5 - 34 = N/2
Solving this equation and get the answer.

Correct Option: B

Let us assume N be the given number.
According to the question,
Sum of third , fourth and fifth part of a number exceeds half of the number by 34.
N/3 + N/4 + N/5 - 34 = N/2
N/3 + N/4 + N/5 - N/2 = 34
(20N + 15N + 12N - 30N)/60 = 34
17N/60 = 34
N = 34 x 60/17
N = 2 x 60
N = 120

Let the number of correct answer be x and number of wrong answer be y.
Then, 4x - y = 200 ..(i)
and x + y = 200 ..(ii)

Correct Option: B

Let the number of correct answer be x and number of wrong answer be y.
Then, 4x - y = 200 ..(i)
and x + y = 200 ..(ii)

On adding Eqs. (i) and (ii), we get
4x - y = 200
x + y = 200
----------------
5x = 400
∴ x = 80

For infinite solution
a₁/a₂ = b₁/₂ = c₁/c₂

Correct Option: C

For infinite solution
a₁/a₂ = b₁/₂ = c₁/c₂
⇒ K/12 = 3/K = (-K + 3)/ -K
⇒ K/12 = 3/K
⇒ K² = 36
∴ K = √36 = 6

Let cost of 1 pencil and 1 clipper be p and c, respectively.
Now, according to the question,
21p + 9c = ₹ 819

Now find the value of 7p + 3c.

Correct Option: C

Let cost of 1 pencil and 1 clipper be p and c, respectively.
Now, according to the question,
21p + 9c = ₹ 819
⇒ 3(7p + 3c) = ₹ 819
₹ 7p + 3c = ₹ 273
Cost of 7 pencil and 3 clippers = ₹ 273

Given, (x/4) + (y/3) = 10/24
⇒ (3x + 4y)/12 = 10/24
∴ 3x + 4y = 5 ...(i)
and (x/2) + y = 1
x + 2y = 2 ...(ii)

Solve equation (i) and (ii) and find the value of x and y.

Correct Option: B

Given, (x/4) + (y/3) = 10/24
⇒ (3x + 4y)/12 = 10/24
∴ 3x + 4y = 5 ...(i)
and (x/2) + y = 1
x + 2y = 2 ...(ii)
On multiplying Eq. (ii) by 2 and subtracting from Eq. (i).
3x + 4y = 5
2x + 4y = 4
- - -
--------------------------
x = 1
On putting the value of x in Eq. (ii), we get
x + 2y = 2
⇒ 1 + 2y = 2
⇒ y = 1/2

∴ x + y = 1 + 1/2 = 3/2