1
JEE Main 2013 (Offline)
MCQ (Single Correct Answer)
+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.
2
JEE Main 2013 (Offline)
MCQ (Single Correct Answer)
+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
$$3:1:2$$
3
AIEEE 2012
MCQ (Single Correct Answer)
+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
4
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
If $$\alpha $$ and $$\beta $$ are the roots of the equation $${x^2} - x + 1 = 0,$$ then $${\alpha ^{2009}} + {\beta ^{2009}} = $$
A
$$\, - 1$$
B
$$\, 1$$
C
$$\, 2$$
D
$$\, - 2$$
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