1
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
If $$2a+3b+6c=0,$$ $$\left( {a,b,c \in R} \right)$$ then the quadratic equation $$a{x^2} + bx + c = 0$$ has
A
at least one root in $$\left[ {0,1} \right]$$
B
at least one root in $$\left[ {2,3} \right]$$
C
at least one root in $$\left[ {4,5} \right]$$
D
none of these
2
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$a>0$$ and discriminant of $$\,a{x^2} + 2bx + c$$ is $$-ve$$, then
$$\left| {\matrix{ a & b & {ax + b} \cr b & c & {bx + c} \cr {ax + b} & {bx + c} & 0 \cr } } \right|$$ is equal to
A
$$+ve$$
B
$$\left( {ac - {b^2}} \right)\left( {a{x^2} + 2bx + c} \right)$$
C
$$-ve$$
D
$$0$$
3
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
Change Language
$$\int\limits_0^{10\pi } {\left| {\sin x} \right|dx} $$ is
A
$$20$$
B
$$8$$
C
$$10$$
D
$$18$$
4
AIEEE 2002
MCQ (Single Correct Answer)
+4
-1
Change Language
$${I_n} = \int\limits_0^{\pi /4} {{{\tan }^n}x\,dx} $$ then $$\,\mathop {\lim }\limits_{n \to \infty } \,n\left[ {{I_n} + {I_{n + 2}}} \right]$$ equals
A
$${1 \over 2}$$
B
$$1$$
C
$$\infty $$
D
zero
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