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Test of consistency and solution of simultaneous linear equations in two or three variables using matrices Mock Test for JEE

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Part of Matrices and Determinants in JEE Main Mathematics.

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Q1MathsUnit 3: Matrices and Determinants
If 2a=b,2 a=b, the pair of equations ax+a x+ by=2a2−3b2,x+2y=2a−6bb y=2 a^{2}-3 b^{2}, x+2 y=2 a-6 b possess
Q2MathsUnit 3: Matrices and Determinants
The addition of two numbers is −72.-72 . If one number is thrice the another number. Find the greater number
Q3MathsUnit 3: Matrices and Determinants
Solve the following equations by substitution method. x=2y−1;y=2x−7\boldsymbol{x}=\mathbf{2} \boldsymbol{y}-\mathbf{1} ; \boldsymbol{y}=\mathbf{2} \boldsymbol{x}-\mathbf{7}
Q4MathsUnit 3: Matrices and Determinants
Dashrath and Naresh are friends ,Naresh is 2 years younger than Dashrath.If the sum of their age is 56 years, find their present age.
Q5MathsUnit 3: Matrices and Determinants
The ratio of income of two persons is 9: 7 and the ratio of their expenditure is 4:3.4: 3 . If each of them manages to save Rs. 2000 per month, find their monthly income.
Q6MathsUnit 3: Matrices and Determinants
Solve the following pair of linear (simultaneous) equations by the method of elimination: 8x+5y=98 x+5 y=9 3x+2y=4\mathbf{3} \boldsymbol{x}+\mathbf{2} \boldsymbol{y}=\mathbf{4}
Q7MathsUnit 3: Matrices and Determinants
Solve the following pair of equations: ax−by=0\frac{a}{x}-\frac{b}{y}=0 ab2x+a2by=a2+b2\frac{a b^{2}}{x}+\frac{a^{2} b}{y}=a^{2}+b^{2}
Q8MathsUnit 3: Matrices and Determinants
The number of values of k for which the system of linear equations, (2k+(2 k+ 1) x+5ky=k+2x+5 k y=k+2 and kx+(k+k x+(k+ 2) y=2y=2 has no solution, is:
Q9MathsUnit 3: Matrices and Determinants
A two-digit number is 3 more than six times the sum of its digits. If 18 is added to the number obtained by interchanged by interchanging the digits, we get the original number. Find the number
Q10MathsUnit 3: Matrices and Determinants
The total salary drawn by 3 watchmen, A, B and C is Rs. 1720. They spend 70\%, 60%60 \% and 50%50 \% respectively from their salaries. If the balance with them are into Ratio 1:2:3,1: 2: 3, what is the salary of each?
Q11MathsUnit 3: Matrices and Determinants
Solve for xx and yy by using method of substitution: 0.2x+0.3y=1.3;0.4x+0.5y=2.3\mathbf{0 . 2 x + 0 . 3 y}=\mathbf{1 . 3 ; 0 . 4 x + 0 . 5 y}=\mathbf{2 . 3}
Q12MathsUnit 3: Matrices and Determinants
AA earns 800Rs.800 R s . more than B.B . They both save together 3,200Rs.3,200 R s . which is one-fourth of A′\boldsymbol{A}^{\prime} s salary plus one-sixth of B′B^{\prime} s salary. Find out their total monthly expenditure.
Q13MathsUnit 3: Matrices and Determinants
Solve for x,y\boldsymbol{x}, \boldsymbol{y} (a+2b)x+(2a−b)y=2,(a−(a+2 b) x+(2 a-b) y=2,(a- 2b) x+(2a+b)y=3x+(2 a+b) y=3

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