Test: Linear Equations- 2 - CAT MCQ

Let number of animals be A

Let number of  birds be B.

So first condition we get A=B+11

=>   (11+B)4+2B=X

=>    4B+2(B+11)=4X/5

on solving we get B=11 A=22

Hence (C) is the correct answer.

Let the initial amount be x,

Amount given to his wife =(40/100)x=2x/5

Balance = (x-(2x/5)) = 3x/5

Amount given to his wife = (20/100)*(3x/5) = 3x/25

Balance = 3x/5-3x/25 = 12x/25

Amountt spent on miscellaneous items = (1/2)*(12x/25) = 6x/25 which is equal to 12000

Hence,

=>      6x/25 = 12000

=>      x = 50000

Hence (C) is the correcr answer.

Let the cost of 1 pencil, 1 pen and 1 eraser are respectively x, y, z. Then according to the given condition

=>  1x + 2y + 4z = 22

=>  5x + 4y + 2z = 32

On adding these two equations we get

=>   6x + 6y + 6z = 54 

=>  3x + 3y + 3z = 27

Hence (C) is the correct answer.

Let weight of arun,akash,amir and aswanth be a,b,c and d respectively.

a+b=132.......(1)

b+c=130.......(2)

c+d=102.......(3)

b+d=116.......(4)

Evaluating 3 and 4 we get

2b=144

b=72

From (4) we have d=116-72=44.

Therefore weight of aswanth is 44 kg.

Let price of Lemon and Apple is L and A respectively

As given,

=>     L+A=12 .....(1)

=>     L+T=4 .......(2)

=>      A=8+L

=>      or L-A=-8 ......(3)

=>      A=8+T .......(4) 
=>      Simply adding eq. 1 and 3

We get..
=>       2L=4

=>       So, L=2

Hence (D) is correct answer

 Let the no. of questions correctly be x &  no. of questions correctly be y
So, no. of questions left unattempted be (50-x-y)
  x - y/3 - (50 - x - y) / 6 = 32
 6x - 2y - 50 + x + y = 192
 7x - y = 242
 y = 7x - 242
If ( x =35 ) y=3
If ( x = 36 ) y=10
So, min. Value of y is 3
The no. of wrongly answered questions cannot be less than 3.

There are two equations to be formed 40m + 50f = 1000.

250m + 300f + 40 x 15m + 50 x 10f = A.

850m + 800f = A.

m and f are the number of males and females. A is the amount paid by the employer.

Then the possible value of f = 8,9,10,11,12.

Iif f= 8,  M =15.

If f = 9,10,11 then m will not be an integer while f =12 then m will be 10.

By putting f = 8 and m=15 , A = 18800.

when f =12 and m= 10 then A = 18100.

Hence, the number of males is 10.

The data is not linear. So check (2).
Let the equation be y = a + bx + cx² .
Putting the values of x and y, we get the following result.
=> 4 = a + b + c,  ....(i)

=> 8 = a + 2b + 4c, and  ...(ii)

=> 14 = a + 3b + 9c. ....(iii)
Solving these, we get a = 2, b = 1 and c = 1.
So the equation is y = 2 + x + x² .

- Given ( x > 2 ) and ( y > -1 ).

- Option B: ( xy > -2 )

- If ( x > 2 ), then ( x ) is positive.
- If ( y > -1 ), then ( y ) is greater than (-1).
- The product ( xy ) is greater than the product of ( 2 times -1 = -2 ).
- Therefore, ( xy > -2 ) is always true.

- Other options are not necessarily true under all circumstances.