Test Details

Pair of Linear Equations in Two Variables

Jan 21, 2:14 PM

60 minutes

Jan 21, 11:00 PM

30.0 marks

MCQ

15 questions

Upendra Joshi

B.Sc, M.A. Hindi & B.Ed

Class Details

Maths

Maths & Science Class 6 to 10 English Medium & Hindi Medium . Class 11 & 12 maths

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Question Text

Question 1 :
State whether the following pair of linear equations has unique solution, no solution, or infinitely many solutions : $2x + y = 5 ; 3x + 2y = 8$

Question 2 :
For which value of k will the following pair of linear equations have no solution? $3x + y = 1; (2k – 1)x + (k – 1) y = 2k + 1$

Question 3 :
The cost of 2 kg of apples and 1kg of grapes on a day was found to be Rs. 160. After a month, the cost of 4 kg of apples and 2 kg of grapes is Rs. 300. Which of these represent the situation algebraically?

Question 4 :
If the lines are represented by the equation $a_1x + b_1y + c_1 =0$ and $a_2x + b_2y + c_2 =0$, then the lines are coinciding when _____________.

Question 5 :
Solve the following pair of equations by reducing them to a pair of linear equations : $6x + 3y = 6xy ; 2x + 4y = 5xy$.

Question 7 :
Solve the following pair of linear equations: $px + qy = p – q ; qx – py = p + q$

Question 8 :
Find out whether the lines representing a pair of linear equations are consistent or inconsistent: $x + y = 5 , 2x + 2y = 10$

Question 9 :
Solve the following pair of linear equations by the substitution and cross-multiplication methods : $8x + 5y = 9 ; 3x + 2y = 4$

Question 10 :
If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes $\frac{1}{2}$ if we only add 1 to the denominator. What is the fraction?

Question 11 :
State whether the following pair of linear equations has unique solution, no solution, or infinitely many solutions : $x – 3y – 3 = 0 ; 3x – 9y – 2 = 0$

Question 13 :
Every solution of the equation is a _________ on the line representing it.

Question 14 :
Solve the following pair of linear equations by the elimination method and the substitution method : $3x – 5y – 4 = 0 ~and ~9x = 2y + 7$

Question 15 :
Let a pair of linear equations in two variables be $a_{1}x+b_{1}y+c_{1}=0$ and $a_{2}x+b_{2}y+c_{2}=0$. If $\frac{a_1}{a_2}\ne\frac{b_1}{b_2}$, then the pair of linear equations is _______.

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