1
IIT-JEE 1998
MCQ (More than One Correct Answer)
+2
-0.5
If $$\,\left| {\matrix{ {6i} & { - 3i} & 1 \cr 4 & {3i} & { - 1} \cr {20} & 3 & i \cr } } \right| = x + iy$$ , then
A
x = 3, y = 2
B
x = 1, y = 3
C
x = 0, y = 3
D
x = 0, y = 0
2
IIT-JEE 1998
MCQ (Single Correct Answer)
+2
-0.5
Let $${A_0}{A_1}{A_2}{A_3}{A_4}{A_5}$$ be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments $${A_0}{A_1},{A_0}{A_2}$$ and $${A_0}{A_4}$$ is
A
$${3 \over 4}$$
B
$$3\sqrt 3 $$
C
$$3$$
D
$${{3\sqrt 3 } \over 2}$$
3
IIT-JEE 1998
MCQ (Single Correct Answer)
+2
-0.5
If $$\int_0^x {f\left( t \right)dt = x + \int_x^1 {t\,\,f\left( t \right)\,\,dt,} } $$ then the value of $$f(1)$$ is
A
$$1/2$$
B
$$0$$
C
$$1$$
D
$$-1/2$$
4
IIT-JEE 1998
Subjective
+8
-0
Suppose $$f(x)$$ is a function satisfying the following conditions
(a) $$f(0)=2,f(1)=1$$,
(b) $$f$$has a minimum value at $$x=5/2$$, and
(c) for all $$x$$, $$$f'\left( x \right) = \matrix{ {2ax} & {2ax - 1} & {2ax + b + 1} \cr b & {b + 1} & { - 1} \cr {2\left( {ax + b} \right)} & {2ax + 2b + 1} & {2ax + b} \cr } $$$
where $$a,b$$ are some constants. Determine the constants $$a, b$$ and the function $$f(x)$$.
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