JEE Main 2015 (Offline) | Quadratic Equation and Inequalities Question 108 | Mathematics | JEE Main - ExamSIDE.com

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1

JEE Main 2015 (Offline)

MCQ (Single Correct Answer)

+4

-1

Let $$\alpha $$ and $$\beta $$ be the roots of equation $${x^2} - 6x - 2 = 0$$. If $${a_n} = {\alpha ^n} - {\beta ^n},$$ for $$n \ge 1,$$ then the value of $${{{a_{10}} - 2{a_8}} \over {2{a_9}}}$$ is equal to :

A

$$3$$

B

$$ - 3$$

C

$$6$$

D

$$ - 6$$

2

JEE Main 2014 (Offline)

MCQ (Single Correct Answer)

+4

-1

If $$a \in R$$ and the equation $$ - 3{\left( {x - \left[ x \right]} \right)^2} + 2\left( {x - \left[ x \right]} \right) + {a^2} = 0$$ (where [$$x$$] denotes the greater integer $$ \le x$$) has no integral solution, then all possible values of a lie in the interval :

A

$$\left( { - 2, - 1} \right)$$

B

$$\left( { - \infty , - 2} \right) \cup \left( {2,\infty } \right)$$

C

$$\left( { - 1,0} \right) \cup \left( {0,1} \right)$$

D

$$\left( {1,2} \right)$$

3

JEE Main 2014 (Offline)

MCQ (Single Correct Answer)

+4

-1

Let $$\alpha $$ and $$\beta $$ be the roots of equation $$p{x^2} + qx + r = 0,$$ $$p \ne 0.$$ If $$p,\,q,\,r$$ in A.P. and $${1 \over \alpha } + {1 \over \beta } = 4,$$ then the value of $$\left| {\alpha - \beta } \right|$$ is :

A

$${{\sqrt {34} } \over 9}$$

B

$${{2\sqrt 13 } \over 9}$$

C

$${{\sqrt {61} } \over 9}$$

D

$${{2\sqrt 17 } \over 9}$$

4

JEE Main 2013 (Offline)

MCQ (Single Correct Answer)

+4

-1

The number of values of $$k$$, for which the system of equations : $$$\matrix{ {\left( {k + 1} \right)x + 8y = 4k} \cr {kx + \left( {k + 3} \right)y = 3k - 1} \cr } $$$
has no solution, is

A

infinite

B

1

C

2

D

3

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