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CBSE Questions for Class 12 Commerce Applied Mathematics Linear Equations Quiz 2 - MCQExams.com

The cost of 4 pens and 4 pencil boxes is Rs 100. Three times the cost of a pen is Rs 15 more than the cost of a pencil box. The cost of a pen and a pencil box respectively are 
  • Rs 15 and Rs 8
  • Rs 10 and Rs 15
  • Rs 12 and Rs 10
  • Rs 16 and Rs 12
Solve the following pair of simultaneous equations:
2x+3y=12;5x3y=9
  • x=1;y=0
  • x=3;y=2
  • x=7;y=3
  • x=2;y=5
The ages of Hari and Harry are in the ratio 5:7. If four years from now, the ratio of their ages will be 3:4, then the present age of
  • Hari is 20 years and Harry is 28 years.
  • Hari is 28 years and Harry is 20 years.
  • Hari is 25 years and Harry is 35 years.
  • Hari is 35 years and Harry is 25 years.
Determine the vertices of the triangle formed by the lines
y=x,3y=x and x+y=8.

  • (0,0),(0,4),(6,2)
  • (0,0),(4,4),(0,2)
  • (0,0),(7,7),(5,2)
  • (0,0),(4,4),(6,2)
Solve the following pairs of equations:
xa+yb=a+b; xa2+yb2=2; a,b0
  • x=2a2,y=2b2
  • x=a3,y=2b2
  • x=a3,y=3b2
  • x=a2,y=b2
If  2x+y=23  and  4xy=19, find the values of  5y2x 
  • 31
  • 22
  • 65
  • 10
Use the method of substitution to solve the equations
x+2y=4 and 4x+5y=2
  • 163 and 23
  • 163 and 23
  • 8 and 6
  • 163 and 23
The father's age is six times his son's age. Four years hence, the age of the father will be four times his son's age. The present ages, in years, of the son and the father respectively are
  • 4 and 24
  • 5 and 30
  • 6 and 36
  • 3 and 24
If x=a,y=b is the solution of the equations xy=2 and x+y=4, then the values of a and b are, respectively:
  • 3 and 5
  • 5 and 3
  • 3 and 1
  • 1 and 3
The values of x and y satisfying the two equations 32x+33y=31, 33x+32y=34 respectively will be
  • 1,2
  • 2,1
  • 0,0
  • 2,3
If p+q=k, pq=n and k>n, then q is ________ .
  • positive
  • negative
  • 0
  • none of the above
Solution of the equations x+34+2y+93=3 and 2x12y+34=412 is
  • x=5,y=3
  • x=5,y=3
  • x=5,y=3
  • x=5,y=3
The solution of
37x+41y=70
41x+37y=86 is
  • x=3,y=1
  • x=3,y=1
  • x=3,y=1
  • x=1,y=3
The solution of
217x+131y=913
131x+217y=827  is
  • x=2,y=3
  • x=3,y=2
  • x=2,y=2
  • x=3,y=3
The solution of
x+2y=32
2x+y=32  is
  • x=3,y=1
  • x=12,y=12
  • x=12,y=0
  • x=0,y=12
If 22xy=32 and 2x+y=16 then x2+y2 is equal to
  • 9
  • 10
  • 11
  • 13
Suresh is half his father's Age. After 20 years, his father's age will be one and a half times the Suresh's age. What is his father's age now?
  • 40
  • 20
  • 26
  • 30
3xy=27 and 3x+y=243, then x is equal to
  • 0
  • 4
  • 2
  • 6
If 6 kg of sugar and 5 kg of tea together cost Rs. 209 and 4 kg of sugar and 3 kg of tea together cost Rs. 131, then the cost of 1 kg sugar and 1 kg tea are respectively
  • Rs. 11 and Rs. 25
  • Rs. 12 and Rs. 20
  • Rs. 14 and Rs. 20
  • Rs. 14 and Rs. 25
Solve the systems of equations:

x24+y+13=2; x+17+y32=12
  • (6,2)
  • (2,2)
  • (2,3)
  • (3,4)
Choose the correct matching(s) for solving questions of the system of linear equation in two variables

Methods
Uses/Disadvantages
(a)
Graphical
(i)  Use: When the coefficients of the variables and the solutions are integers.
Disadvantage: If the solutions are not integers, they are hard to plot and read on the graph.
(b)
Substitution
(ii) Use: When variables with coefficients that are the same or additive inverse of each other ( for example, 2x and 2x) are present.
Disadvantage: If fractions are involved, you may have much computation.
(c)
Elimination
(iii) Use: When one of the variables is isolated (alone) on one side of the equation
Disadvantage: You may have lots of computations involving signed numbers.

  • (a)(i)
  • (b)(iii)
  • (c)(ii)
  • (b)(i)
Solve the following simultaneous equations. 
2x+y=5,3xy=5
  • x=2, y=1
  • x=2, y=1
  • x=2, y=1
  • x=2, y=1
Solve the following simultaneous equations by substitution method.
2x+3y=4;x5y=11
  • x=1,y=2
  • x=1,y=2
  • x=1,y=2
  • x=1,y=2
If (x+y,1)  =  (3,yx), then x  =          , y  =         
  • 2, 1
  • -1, -2
  • 1, 2
  • 2, -1
Solve :
3x2y=1
2x+y=3
  • 1,1
  • 3,3
  • 4,4
  • None of thse
Sum of two numbers isIf the larger number is divided by the smaller, the quotient is 7 and the remainder isFind the numbers. 
  • 75,14
  • 90,14
  • 75,18
  • 85,12
A man starts his job with a certain monthly salary and a fixed increment every year. If his salary will be Rs. 11000  after 2  years and Rs. 14000 after 4 years of his service. What is his starting salary and what is the annual increment?
  • Starting salary is Rs. 7500 and increment is Rs. 2500
  • Starting salary is Rs.5000 and increment is Rs. 1800
  • Starting salary is Rs. 8000 and increment is Rs. 1500
  • Starting salary is Rs. 7000 and increment is Rs. 1300
Solve the following simultaneous equations: 
4m+3n=18;3m2n=5
  • m=3,n=2
  • m=3,n=2
  • m=3,n=2
  • m=3,n=2
Find the values of the x+y and xy from the examples given below without solving for x and y

5x3y=14;3x5y=2
  • 2, 6
  • 2, 6
  • 6, 2
  • 6, 2
Find the values of the x+y and xy from the examples given below without solving for x and y

5x+7y=17;7x+5y=19
  • 3, 1
  • 3, 1
  • 1, 3
  • 1, 3
0:0:1


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