CBSE Questions for Class 12 Commerce Applied Mathematics Linear Equations Quiz 6 - MCQExams.com

Solve the following pair of equations:
$$\sqrt{2}x+3y=\sqrt{3}; \, \, \sqrt{3}x+3y=\sqrt{2}$$
  • $$x=-1, \, y=\displaystyle \frac{\sqrt{3}+\sqrt{2}}{3}$$
  • $$x=1, \, y=\displaystyle \frac{\sqrt{5}-\sqrt{2}}{3}$$
  • $$x=1, \, y=\displaystyle \frac{\sqrt{7}-\sqrt{13}}{3}$$
  • $$x=1, \, y=\displaystyle \frac{\sqrt{10}-\sqrt{5}}{3}$$
The area of a rectangle gets reduced by $$9$$ sq. units, if its length is reduced by $$5$$ units and the breadth, is increased by $$3$$ units. If we increase the length by $$3$$ units and breadth by $$2$$ units, the area is increased by $$67$$ sq. units. Find the length and breadth of the rectangle. 
  • length $$ = 12$$, breadth $$=6$$
  • length $$ = 20$$, breadth $$=15$$
  • length $$ = 17$$, breadth $$=9$$
  • length $$ = 21$$, breadth $$=8$$
A man gets Rs. 100 per day if he works, but he is  fined by Rs. 10 per day if he is absent. In the whole month of April he received Rs. 1900 only. How many days did he work ? 
  • 20 days
  • 22 days
  • 29 days
  • 23 days
From the following figure, we can say: 
$$0.9x+0.5y=6; \, \, 0.7x+0.7y=5.6$$
  • $$x=5, \, y=3$$
  • $$x=4, \, y=3$$
  • $$x=1, \, y=3$$
  • $$x=2, \, y=3$$
Solve the following pair of equations:
$$6x+5y=7x+3y+1=2x+12y-2$$
  • $$x=3, \, y=2$$
  • $$x=1, \, y=0$$
  • $$x=5, \, y=3$$
  • $$x=7, \, y=1$$
Solve the following simultaneous equations:
$$8x+13y-29= 0$$, $$12x-7y-17= 0$$
  • $$x=3;\, y=2$$
  • $$x=0;\, y=5$$
  • $$x=2;\, y=1$$
  • $$x=-1;\, y=3$$
Solve the following simultaneous equations:
$$217x+131y= 913$$
$$131x+217y= 827$$
  • $$x=7, y=3$$
  • $$x=2, y=1$$
  • $$x=3, y=2$$
  • $$x=1, y=5$$
Solve the following simultaneous equation :
$$ax\, +\, by\, =\, 5$$ and $$\, bx\, +\, ay\, =\, 3,$$ where $$a$$ and $$b$$ are constants.
  •  $$\displaystyle x\, =\, \frac{5a\, -\, 3b}{a^2\, +\, b^2}, \quad\, y\, =\, \frac{3a\, -\, 5b}{a^2\, +\, b^2}$$
  •  $$\displaystyle x\, =\, \frac{5a\, -\, 3b}{a^2\, -\, b^2}, \quad\, y\, =\, \frac{3a\, -\, 5b}{a^2\, -\, b^2}$$
  •  $$\displaystyle x\, =\, \frac{3a\, -\, 5b}{a^2\, -\, b^2}, \quad\, y\, =\, \frac{5a\, -\, 5b}{a^2\, -\, b^2}$$
  •  $$\displaystyle x\, =\, \frac{3a\, -\, 5b}{a^2\, +\, b^2}, \quad\, y\, =\, \frac{5a\, -\, 5b}{a^2\, +\, b^2}$$
The given lines are 
$$2x\, +\, y\, =\, 6;\quad\, x\, +\, 2y\, =\, 6;\quad\, 7x\, -\, 4y\, =\, 6$$
  • Concurrent 
  • Coincident
  • Parallel 
  • None of these
Solve the following simultaneous equations :
$$3x-5y+1= 0$$, $$2x-y+3= 0$$
  • $$x= 2;\, y= -1$$
  • $$x= 7;\, y= -9$$
  • $$x= -1;\, y= -4$$
  • $$x= -2;\, y= -1$$
Solve the following simultaneous equations:
$$3x+2y= 14$$, $$-x+4y= 7$$
  • $$x= 0;\, y= -4$$
  • $$x= 3;\, y= 2.5$$
  • $$x= 3.5;\, y= -2$$
  • $$x= 4.5;\, y= 3$$
Solvw the following pair of linear equations:
 $$2x\, +\, 5y\, =\, 13$$ and $$4x\, -\, 9y\, =7$$
  • $$(1,4)$$
  • $$(2,-3)$$
  • $$(-2,3)$$
  • $$(4,1)$$
If $$12x\, +\, 13y\, =\, 29\, and\, 13x\, +\, 12y\, =\, 21,$$ find $$x\, +\, y$$.
  • $$2$$
  • $$7$$
  • $$4$$
  • $$11$$
In the following figure, $$ABCD$$ is a parallelogram. Find the values of $$x$$.

182362_4225d828fbb943ef83aa27b79c417d06.png
  • $$3$$
  • $$5$$
  • $$7$$
  • $$9$$
Solve the following simultaneous equations:
$$12x+15y+18= 0$$, $$18x-7y+86= 0$$
  • $$x=-4;\, y=2$$
  • $$x=1;\, y=0$$
  • $$x=-3;\, y=5$$
  • $$x=4;\, y=1$$
Solve the following pairs of linear (simultaneous) equation by the method of elimination: $$x + 8y = 19$$, $$2x + 11y = 28$$
  • $$x=3$$ and $$y =2$$
  • $$x=1$$ and $$y =4$$
  • $$x=3$$ and $$y =5$$
  • $$x=4$$ and $$y =7$$
Solve the following pairs of linear (simultaneous) equation by the method of elimination :$$2x + 3y = 8$$, $$2x = 2 + 3y$$
  • $$x=2$$, $$y=\dfrac{3}{2}$$
  • $$x=3$$, $$y=5$$
  • $$x=\dfrac{5}{2}$$, $$y=1$$
  • $$x=\dfrac{3}{2}$$, $$y=4$$
Solve the following pairs of linear (simultaneous) equation by the method of elimination:
$$x + y = 7$$, $$5x + 12y = 7$$
  • $$x =13$$ and $$y=5$$
  • $$x=11$$ and $$y=-4$$
  • $$x=7 $$ and $$y =-2$$
  • $$x=5$$ and $$y =7$$
If $$1$$ is added to each of the two certain numbers, their ratio is $$1:2$$; and if $$5$$ is subtracted from each of the two numbers, their ratio becomes $$5:11$$. Find the numbers. 
  • $$35$$ and $$70$$
  • $$35$$ and $$71$$
  • $$35$$ and $$72$$
  • $$35$$ and $$73$$
Solve the following pair of equations :
$$\displaystyle \frac{3}{5}\, x\, -\, \displaystyle \frac{2}{3}\, y\, +\, 1\, =\, 0$$
$$\displaystyle \frac{1}{3}\, y\, +\, \displaystyle \frac{2}{5}\, x\, =\, 4$$
  • $$x\, =\, 2\, ;\, y\, =\, 6$$
  • $$x\, =\, 5\, ;\, y\, =\, 6$$
  • $$x\, =\, 1\, ;\, y\, =\, 6$$
  • $$x\, =\, 7\, ;\, y\, =\, 6$$
Solve the following pairs of linear (simultaneous) equation by the method of elimination:$$2x + 7y = 39$$, $$3x + 5y = 31$$
  • $$x = 0, y = 7$$
  • $$x = 6, y = 2$$
  • $$x = -1, y = 3$$
  • $$x = 2, y = 5$$
Solve the following pairs of linear (simultaneous) equation by the method of elimination: $$8x + 5y = 9$$, $$3x + 2y = 4$$
  • $$x=1$$ and $$y =7$$
  • $$x=-3$$ and $$y =4$$
  • $$x=-2$$ and $$y =5$$
  • $$x=0$$ and $$y =1$$
Solve the following pairs of linear (simultaneous) equation by the method of elimination:$$0.2x + 0.1y = 25$$, $$2(x - 2) - 1.6y = 116$$
  • $$x= 100$$, $$y= 50$$
  • $$x= 80$$, $$y= 30$$
  • $$x= -78$$, $$y= 35$$
  • $$x= -65$$, $$y= -75$$
Solve the following pairs of linear (simultaneous) equation by the method of elimination:$$6x = 7y +7$$, $$7y - x = 8$$
  • $$x =3$$, $$y = \displaystyle \frac{11}{7}$$
  • $$x=7$$, $$y= \displaystyle \frac{2}{3}$$
  • $$x =\displaystyle \frac{1}{3}$$ , $$y =5$$
  • $$x= \displaystyle \frac{2}{5}$$ , $$y=4$$
Solve the following pairs of linear (simultaneous) equation by the method of elimination:$$y =\, 4x\, -\, 7$$, $$16x\, -\, 5y\, =\, 25$$
  • $$x\, =\, \displaystyle \frac{7}{5},\, y\, =\, 10$$
  • $$x\, =\, \displaystyle \frac{5}{2},\, y\, =\, 3$$
  • $$x\, =\, \displaystyle \frac{1}{2},\, y\, =\, 4$$
  • $$x\, =\, \displaystyle \frac{9}{2},\, y\, =\, 8$$
Solve the following pairs of linear (simultaneous) equation by the method of elimination : $$2x - 3y= 7$$, $$5x + y  =9$$
  • $$x=2$$ and $$y =-1$$
  • $$x=4$$ and $$y =0$$
  • $$x=-3$$ and $$y =-5$$
  • $$x=-7$$ and $$y =6$$
Solve the following pair of equations:
$$3x\, -\, y\, =\, 23$$
$$\displaystyle \frac{x}{3}\, +\, \displaystyle \frac{y}{4}\, =\, 4$$
  • $$x\, =-\, 4\, ;\, y\, =\, 1$$
  • $$x\, =-\, 1\, ;\, y\, =\, 7$$
  • $$x\, =\, 9\, ;\, y\, =\, 4$$
  • $$x\, =\, 7\, ;\, y\, =\, 13$$
Solve the following pair of equations:
$$13 + 2y = 9x$$, $$3y = 7x$$
  • $$x=6$$; $$y =-7$$
  • $$x=5$$ ; $$ =13$$
  • $$x=-7$$; $$y =1$$
  • $$x=3$$; $$y =7$$
Solve the following pair of equations :
$$x\, -\, y\, =\, 0.9$$
$$\displaystyle \frac{11}{2\, (x\, +\, y)}\, =\, 1$$
  • $$x\, =\, 1.2\, ;\, y\, =\, 2.3$$
  • $$x\, =\, 7.2\, ;\, y\, =\, 2.3$$
  • $$x\, =\, 3.2\, ;\, y\, =\, 2.3$$
  • $$x\, =\, 4.2\, ;\, y\, =\, 2.3$$
Solve the following pair of equations :
$$7x + 6y = 71$$
$$5x - 8y = -23$$
  • $$x = 2; y = 7$$
  • $$x = 5; y = 6$$
  • $$x = 4; y = 9$$
  • $$x = 1; y = 8$$
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 12 Commerce Applied Mathematics Quiz Questions and Answers