1
JEE Main 2014 (Offline)
+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
$$\left( {1,2} \right)$$
2
JEE Main 2014 (Offline)
+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
$${{2\sqrt 17 } \over 9}$$
3
JEE Main 2013 (Offline)
+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
4
JEE Main 2013 (Offline)
+4
-1
The real number $$k$$ for which the equation, $$2{x^3} + 3x + k = 0$$ has two distinct real roots in $$\left[ {0,\,1} \right]$$
A
lies between 1 and 2
B
lies between 2 and 3
C
lies between $$- 1$$ and 0
D
does not exist.
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