91Ó°ÊÓ

Find the sum and the product of the roots of the equation \(\sqrt{3} \mathrm{x}^{2}+27 \mathrm{x}+5 \sqrt{3}=0\). (1) \(-9 \sqrt{3}, 5\) (2) \(9 \sqrt{3}, 5\) (3) \(6 \sqrt{3},-5\) (4) \(6 \sqrt{3}, 5\)

If one of the roots of a quadratic equation having rational coefficients is \(\sqrt{7}-4\), then the quadratic equation is (1) \(x^{2}-2 \sqrt{7} x-9=0 .\) (2) \(\mathrm{x}^{2}-8 \mathrm{x}+9=0\). (3) \(\mathrm{x}^{2}+8 \mathrm{x}+9=0 .\) (4) \(\mathrm{x}^{2}-2 \sqrt{7} \mathrm{x}+9=0 .\)

Find the sum and the product of the roots of the quadratic equation \(-x^{2}-\frac{25}{3} x+25=0\) (1) \(\frac{25}{3}, 25\) (2) \(\frac{-25}{3}, 25\) (3) \(\frac{25}{3},-25\) (4) \(\frac{-25}{3},-25\)

If \(\alpha\) and \(\beta\) are the zeroes of the quadratic polynomial \(a x^{2}+b x+c\) such that \(x\) does not lie between \(\alpha\) and \(\beta\), then (1) \(a>0\) and \(a x^{2}+b x+c<0\) (2) \(a x^{2}+b x+c \leq 0\) and \(a<0\) (3) \(\mathrm{a}>0\) and \(\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c}>0\) (4) both (2) and (3).

The quadratic equation having rational coefficients and one of the roots as \(4+\sqrt{15}\) is (1) \(\mathrm{x}^{2}-8 \mathrm{x}+1=0\). (2) \(\mathrm{x}^{2}+\mathrm{x}-8=0 .\) (3) \(\mathrm{x}^{2}-\mathrm{x}+8=0\). (4) \(\mathrm{x}^{2}+8 \mathrm{x}+8=0\).

If the sum of the squares of three consecutive odd natural numbers is 155, then their product will be equal to (1) 99 (2) 105 (3) 693 (4) 315

If \(3.2^{2 x+1}-5.2^{x+2}+16=0\) and \(x\) is an integer, find the value of \(x\). (1) 1 (2) 2 (3) 3 (4) 4

If \((x+1)(x+3)(x+5)(x+7)=5760\), find the real values of \(x\) (1) \(5,-13\) (2) \(-5,13\) (3) \(-5,-13\) (4) 5,13

A man bought 50 dozen fruits consisting of apples and bananas. An apple is cheaper than a banana. The number of dozens of apples he bought is equal to the cost per dozen of bananas in rupees and vice versa. If he had spent a total amount of \(\mathrm{Rs} 1050\), find the number of dozens of apples and bananas he bought respectively. (1) 12 and 38 (2) 14 and 36 (3) 15 and 35 (4) 18 and 32

Find the product of the roots of \(\mathrm{x}^{2}+8 \mathrm{x}-16=0\). (1) 8 (2) \(-8\) (3) 16 (4) \(-16\)