A 2-digit number is such that product of its digits is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.

3

(a)

If the price of a book is reduced by Rs.5, a person can buy 5 more books for Rs.300. Find the original list price of a book.

3

(a)

If a and b are roots o the equation 2x²+7x+5=0 then write a quadratic equation whose roots are 2a+3 and 2b+3

3

(a)

Find the positive value of k, for which the equations x²+kx+64=0 and x²-8x+k=0 will both have real roots.

3

(a)

In the following equations determine the set of values of p for which the given equation has real roots: px²+4x+1=0

3

(a)

Find that non-zero value of k, for which the quadratic equation \(kx^2+1-2(k-1)x+x^2=0\) has equal roots. Hence find the roots of the equation.

3

(a)

Solve for x: \(x^2+5x-(a^2+a-6)=0\)

3

(a)

The age of father is equal to the square of the age of his son. The sum of the age of father and five times the age of the son is 66years. Find their ages.

3

(a)

Find the roots of the following quadratic equation (if they exist) by the method of completing square \(5x^{2} - 6x-2 = 0\) .

3

(a)

Find the roots of the quadratic equation \(x+ {1\over x} = {41\over 20} ; x \neq 0 .\)

3

(a)

Find the roots of the quadratic equation \({x - 1 \over {x - 2}} + {x - 3 \over {x - 4}} = {10\over 3} ; x \neq 2 , 4.\)

3

(a)

Find the nature of the roots of the quadratic equation\(\sqrt{3} x^{2} - 2 \sqrt {2}\ x - 2\ \sqrt {3} = 0.\) If the real roots exist, find them.

3

(a)

Which of the following are quadratic equations?
\((i)x+\frac { 3 }{ x } =x^{ 2 }\)
\((ii)2x^{ 2 }-5x-x^{ 2 }-2x+3\)
\((iii)x^{ 2 }-\frac { 1 }{ x^{ 2 } } =5\)
\((iv)x^{ 2 }-3x-\sqrt { x } +4=0\)
\((v)\sqrt { 2 } x^{ 2 }+7x+5\sqrt { 2 } =0\)

3

(a)

Raja and Raju together have 26 marbles. Both of them lost 3 marbles each and the product of the number of marbles they now have is 91.We want to find out how many marbles they had with them to start with?  Represent the above problem mathematically in terms of a quadratic equation?

3

(a)

Divide 29 into two parts.so that the sum of the squares of the parts is 425.

3

(a)