1
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Find the value(s) of k for which the pair of linear equations kx + y = k^2 and x + ky = 1

Find the value(s) of k for which the pair of linear equations kx + y = k^{2} and x + ky = 1 have infinitely many solutions.

2
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For what values of m and n the following system of linear equations

For what values of m and n the following system of linear equations has infinitely many solutions.

3x + 4y = 12

(m + n)x + 2(m – n)y = 5m – 1

3
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In Figure, ABCD is a rectangle. Find the values of x and y

In Figure, ABCD is a rectangle. Find the values of x and y.

4
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The sum of a two-digit number and the number obtained by reversing the digits is 66

The sum of a two-digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there?

5
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The ratio of incomes of two persons is 9:7 and the ratio of their expenditures is 4:3

The ratio of incomes of two persons is 9:7 and the ratio of their expenditures is 4:3. If each of them manages to save Rs. 2000 per month, find their monthly incomes.

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