1
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
If non zero numbers $$a, b, c$$ are in $$H.P.,$$ then the straight line $${x \over a} + {y \over b} + {1 \over c} = 0$$ always passes through a fixed point. That point is :
A
$$(-1,2)$$
B
$$(-1, -2)$$
C
$$(1, -2)$$
D
$$\left( {1, - {1 \over 2}} \right)$$
2
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
The plane $$x+2y-z=4$$ cuts the sphere $${x^2} + {y^2} + {z^2} - x + z - 2 = 0$$ in a circle of radius
A
$$3$$
B
$$1$$
C
$$2$$
D
$${\sqrt 2 }$$
3
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
Let $$f:( - 1,1) \to B$$, be a function defined by
$$f\left( x \right) = {\tan ^{ - 1}}{{2x} \over {1 - {x^2}}}$$,
then $$f$$ is both one-one and onto when B is the interval
A
$$\left( {0,{\pi \over 2}} \right)$$
B
$$\left[ {0,{\pi \over 2}} \right)$$
C
$$\left[ { - {\pi \over 2},{\pi \over 2}} \right]$$
D
$$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$
4
AIEEE 2005
MCQ (Single Correct Answer)
+4
-1
A real valued function f(x) satisfies the functional equation

f(x - y) = f(x)f(y) - f(a - x)f(a + y)

where a is given constant and f(0) = 1, f(2a - x) is equal to
A
- f(x)
B
f(x)
C
f(a) + f(a - x)
D
f(- x)
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