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Linear Equation with two variables

Q21. The system of equations 3x + 7y = 9 and 10x + ky = 30 has infinite number of solutions when
(a) k = 50/3
(b) k = 55/3
(c) k = 70/3
(d) k = 77/3

Q22. If 3x - 5y = 5 and x/(x+y) = 5/7 then x + y = ?
(a) 5
(b) 7
(c) 11
(d) 13

Q23. On solving 3x + y = 7 and 3y = 2 + 2x we have
(a) x = 23/11, y =8/11
(b) x = 21/11, y =9/11
(c) x = 17/11, y =7/11
(d) x = 13/11, y =5/11

Q24. The system of equations 3x + 2y = 3 and 6x + 4y = 3 has
(a) exactly two solutions
(b) no solutions
(c) a unique solution
(d) infinitely many solutions

Q25. On solving 3x + y = 6 and 5y + x = 10, we get
(a) a = 5/7, y = 9/7
(b) a = 9/7, y = 11/7
(c) a = 10/7, y = 12/7
(d) a = 12/7, y = 13/7

Q26. If 4x + 6y = 32 and 4x - 2y = 4 then 6y = ?
(a) 13
(b) 16
(c) 17
(d) 21

Q27. The solution of 2x + 3y = 2 and 3x + 2y = 2 can be represented by a point in the co-ordinate plane in
(a) 1st quadrant
(b) 2nd quadrant
(c) 3rd quadrant
(d) 4th quadrant

Q28. If α, β are the roots of the equations x2 - px + q = 0 then the value of α2 + β2 is
(a) q - 2p
(b) p - 2q
(c) q2 - 2p
(d) p2 - 2q

Q29. A and B solved a quadratic equation. In solving it, A made a mistake in the constant term and obtained the roots as 6 and 2, while B made a mistake in the co-efficient of x only and obtained the roots -7 and -1. Find the correct roots of the equation.
(a) 1, 5
(b) 2, 5
(c) 1, 7
(d) 2, 9

Q30. The sum of the roots of the equation 3x2 + (p + q + r)x + pqr = 0 is equal to zero. What is the value of (p3 + q3 + r3) = ?
(a) 2pqr
(b) 3pqr
(c) 2pq/r
(d) 3qr/p


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