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
If the equations $${x^2} + 2x + 3 = 0$$ and $$a{x^2} + bx + c = 0,$$ $$a,\,b,\,c\, \in \,R,$$ have a common root, then $$a\,:b\,:c\,$$ is
A
$$1:2:3$$
B
$$3:2:1$$
C
$$1:3:2$$
D
$$3:1:2$$
4
AIEEE 2012
+4
-1
The equation $${e^{\sin x}} - {e^{ - \sin x}} - 4 = 0$$ has:
A
infinite number of real roots
B
no real roots
C
exactly one real root
D
exactly four real roots
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