Junior Clerk (BS-11) Labour & Human Resource Dept. 2019

If 3 is a solution of equation, then it should satisfy that equation,

3x²+(k−1)x+9=0

3(3²)+(k−1)3 +9=0

27+3k−3+9=0

3k=−33

∴k=−11

Boys : girls = 8 : 5 (let the boys = 8x, girl = 5x)
Total strength = 286
8x + 5x = 286
13x = 286
    x = 22
Boys = 176 and girls = 110
22 more girls get admitted then number of girls become
(5x + 22) = 110 + 22 = 132
Now, new ratio of boys and girls = 176 : 132 = 4 : 3

Let the Number of Rabbits in the Zoo be : R

Let the Number of Pigeons in the Zoo be : P

Given : The Total Number of Heads : 200

We know that : Each Rabbit and Pigeon have One Head

⇒ R + P = 200 ———– [1]

Given : The Total Number of Legs are : 580

We know that : Each Rabbit has 4 Legs and Each Pigeon has 2 Legs

⇒ (4 × R) + (2 × P) = 580

⇒ 2R + P = 290 ———– [2]

Subtracting Equation [1] from Equation [2], We get :

⇒ (2R + P) – (R + P) = 290 – 200

⇒ 2R – R = 90

⇒ R = 90

Substituting R = 90 in Equation [1], We get :

⇒ 90 + P = 200

⇒ P = 200 – 90 ⇒ P = 110

⇒ The Number of Pigeons in the Zoo are : 110