1
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
$$3:1:2$$
2
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
3
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
$$\, - 2$$
4
AIEEE 2009
MCQ (Single Correct Answer)
+4
-1
If the roots of the equation $$b{x^2} + cx + a = 0$$ imaginary, then for all real values of $$x$$, the expression $$3{b^2}{x^2} + 6bcx + 2{c^2}$$ is :
A
less than $$4ab$$
B
greater than $$-4ab$$
C
less than $$-4ab$$
D
greater than $$4ab$$
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