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Find the value(s) of p in the following pair of equations: 3x – y – 5 = 0 and 6x – 2y – p = 0, if the lines represented by these equations are parallel.

Given Given pair of linear equations is 3x – y – 5 = 0 …(i) 6x – 2y – p... View Article

For which values of a and b, will the following pair of linear equations have infinitely many solutions? x + 2y = 1 (a – b)x + (a + b)y = a + b – 2

Given x + 2y = 1 (a – b)x + (a + b)y = a + b – 2 Find out We have to find for which values of a and b the... View Article

For which value(s) of k will the pair of equations kx + 3y = k – 3 12x + ky = k have no solution?

Solution The given pair of linear equations is kx + 3y = k – 3 …(1) 12x + ky =... View Article

For which value(s) of λ , do the pair of linear equations λx + y = λ2 and x + λy = 1 have (i) no solution? (ii) infinitely many solutions? (iii) a unique solution?

Solution: The given pair of linear equations is λx + y = λ2 and x + λy = 1 a1 = λ,... View Article

Are the following pair of linear equations consistent? Justify your answer. (i) -3x- 4y = 12 4y + 3x = 12 (ii) (3/5)x – y = ½ (1/5)x – 3y= 1/6 (iii) 2ax + by = a ax + 2by – 2a = 0; a, b ≠ 0 (iv) x + 3y = 11 2 (2x + 6y) = 22

Solution: We know that Conditions for pair of linear equations to be consistent are: a1/a2 ≠ b1/b2. [unique solution] a1/a2 = b1/b2 = c1/c2 [coincident or... View Article

Do the following equations represent a pair of coincident lines? Justify your answer. (i) 3x + 1/7y = 3 7x + 3y = 7 (ii) -2x – 3y = 1 6y + 4x = – 2 (iii) x/2 + y + 2/5 = 0 4x + 8y + 5/16 = 0

Solution We know that the condition for coincident lines, a1/a2 = b1/b2 = c1/c2; (i) 3x + 1/7y = 3 7x +... View Article

Do the following pair of linear equations have no solution? Justify your answer. (i) 2x + 4y = 3 12y + 6x = 6 (ii) x = 2y y = 2x (iii) 3x + y – 3 = 0 2x + 2/3y = 2

Solution We know that the condition for no solution is a1/a2 = b1/b2 ≠ c1/c2 (parallel lines) (i) 2x + 4y = 3 12y + 6x =... View Article

The pair of equations x = a and y = b graphically represents lines which are (A) parallel (B) intersecting at (b, a) (C) coincident (D) intersecting at (a, b)

Answer A correct answer is an option (D) intersecting at (a, b) Solution Graphically in every condition, we know that... View Article

The pair of equations y = 0 and y = -7 has (A) one solution (B) two solutions (C) infinitely many solutions (D) no solution

Answer The correct answer is an option (D) no solution Solution The given pair of equations are y = 0... View Article

If a pair of linear equations is consistent, then the lines will be (A) parallel (B) always coincident (C) intersecting or coincident (D) always intersecting

Answer The correct answer is an option (C) intersecting or coincident Solution Condition for a pair of linear equations to... View Article

The pair of equations x + 2y + 5 = 0 and -3x – 6y + 1 = 0 have (A) a unique solution (B) exactly two solutions (C) infinitely many solutions (D) no solution

Answer The correct answer is an option (D)No solution Solution The given equations are: x + 2y + 5 = 0 –3x –... View Article

Graphically, the pair of equations 6x – 3y + 10 = 0 2x – y + 9 = 0 represents two lines which are (A) Intersecting at exactly one point. (B) Intersecting at exactly two points. (C) Coincident (D) parallel.

Answer The correct answer is option (D) Parallel Solution The given equations are, 6x-3y+10 = 0 On dividing by 3,... View Article

Given that √2 is a zero of the cubic polynomial 6x³ + √2 x² – 10x – 4√2 , find its other two zeroes.

Given √2 is a zero of the cubic polynomial 6x3 + √2 x2 – 10x – 4√2 Find out We have to determine the other two... View Article

Given that the zeroes of the cubic polynomial x³ – 6x² + 3x + 10 are of the form a, a + b, a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.

Given a, a+b, a+2b are roots of given polynomial x³-6x²+3x+10 Find out We have to determine the values of a and... View Article

For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation. (i) (-8/3), 4/3 (ii) 21/8, 5/16 (iii) -2√3, -9 (iv) (-3/(2√5)), -½

Solution: (i) (–8/3), 4/3 Sum of the zeroes = – 8/3 Product of the zeroes = 4/3 We know that,... View Article

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