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Which of the following is not a quadratic equation? (A) 2(x – 1) = 4x² – 2x + 1 (B) 2x – x² = x² + 5 (C) (√2x + √3)² + x² = 3x² − 5x (D) (x² + 2x)² = x⁴ + 3 + 4x³

Answer The correct answer is (D) (x2 + 2x)2 = x4 + 3 + 4x3 Solution We know that a quadratic equation is represented by... View Article

Which of the following is a quadratic equation? (A) x² + 2x + 1 = (4 – x)² + 3 (B) -2x² = (5 – x)(2x-(2/5)) (C) (k + 1) x² + (3/2) x = 7, where k = -1 (D) x³ – x² = (x – 1)3

Answer The correct answer is (D) x3 – x2 = (x – 1)3 Solution We know that the standard form of a... View Article

Ankita travels 14 km to her home partly by rickshaw and partly by bus. She takes half an hour if she travels 2 km by rickshaw, and the remaining distance by bus.

Given Distance travelled by Ankita to her home partly by rickshaw and partly by bus= 14km She takes half an hour if she travels 2 km by... View Article

Determine, algebraically, the vertices of the triangle formed by the lines 3x – y = 3 2x – 3y = 2 x + 2y = 8

3x – y = 2 …(1) 2x -3y = 2 …(2) x + 2y = 8 …(3) Let the equations of the line (1), (2) and (3) represent the side... View Article

The cost of 4 pens and 4 pencil boxes is Rs 100. Three times the cost of a pen is Rs 15 more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pen and a pencil box.

Given The cost of 4 pens and 4 pencil boxes = Rs 100 Three times the cost of a pen is Rs 15 more than the cost of a pencil box. Find out We... View Article

Draw the graphs of the equations x = 3, x = 5 and 2x – y – 4 = 0. Also find the area of the quadrilateral formed by the lines and the x-axis.

Solution Given equation of lines x = 3, x = 5 and 2x-y-4 = 0. Table for line 2x – y – 4 = 0 is tabulated below x 0 2... View Article

Determine, graphically, the vertices of the triangle formed by the lines y = x, 3y = x, x + y = 8

Solution Given linear equations are y = x …(i) 3y = x …(ii) and x + y = 8 …(iii) Table for line y = x is tabulated... View Article

Graphically, solve the following pair of equations: 2x + y = 6 2x – y + 2 = 0 Find the ratio of the areas of the two triangles formed by the lines representing these equations with the x-axis and the lines with the y-axis.

Solution Given equations are 2x + y = 6 2x – y + 2 = 0 Table for equation 2x + y – 6 = 0, For x = 0 y = 6 and for y = 0,... View Article

Find the values of x and y in the following rectangle [see Figure].

Solution: By the property of rectangel we know that Lengths are equal, i.e., CD = AB Hence, x + 3y = 13 …(i) Breadth are equal,... View Article

If 2x + y = 23 and 4x – y = 19, find the values of 5y – 2x and y/x – 2.

Given Given pair of linear equations is 2x + y = 23 …(i) 4x – y = 19 …(ii) Find out We have to determine the values of... View Article

Write a pair of linear equations which has the unique solution x = – 1, y =3. How many such pairs can you write?

Solution Condition for the pair of system to have unique solution a1/a2 ≠ b1/b2 Let us assume the equations be, a1x + b1y +... View Article

Two straight paths are represented by the equations x – 3y = 2 and -2x + 6y = 5.Check whether the paths cross each other or not.

Given Given pair of linear equations is x – 3y – 2 = 0 …(i) -2x + 6y – 5 = 0 …(ii) Find out We have to... View Article

Find the value(s) of p and q in the following pair of equations: 2x + 3y = 7 and 2px + py = 28 – qy, if the pair of equations have infinitely many solutions.

Given Given pair of linear equations is 2x + 3y = 7 2px + py = 28 – qy or 2px + (p + q)y – 28 = 0 Find out We have to... View Article

Find the value(s) of p in the following pair of equations: 2x + 3y – 5 = 0 and px – 6y – 8 = 0, if the pair of equations has a unique solution.

Given Given pair of linear equations is 2x + 3y – 5 = 0 px – 6y – 8 = 0 Find out We have to determine the value of p in... View Article

Find the value(s) of p in the following pair of equations: – 3x + 5y = 7 and 2px – 3y = 1, if the lines represented by these equations are intersecting at a unique point.

Given Given pair of linear equations is – 3x + 5y = 7 2px – 3y = 1 Find out We have to determine the value of p in the given... View Article

Find the value(s) of p in the following pair of equations: – x + py = 1 and px – y = 1, if the pair of equations has no solution.

Given Given pair of linear equations is – x + py = 1 …(i) px – y – 1 = 0 …(ii) Find out We have to determine the... View Article

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 = 0 …(ii) Find out We have to... 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... 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 = k …(2) On comparing the equations (1) and... 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, b1= 1, c1 =... View Article

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