1
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+4
-1
A variable plane at a distance of the one unit from the origin cuts the coordinates axes at $$A,$$ $$B$$ and $$C.$$ If the centroid $$D$$ $$(x, y, z)$$ of triangle $$ABC$$ satisfies the relation $${1 \over {{x^2}}} + {1 \over {{y^2}}} + {1 \over {{z^2}}} = k,$$ then the value $$k$$ is
A
$$3$$
B
$$1$$
C
$${1 \over 3}$$
D
$$9$$
2
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+2
-0.5
A six faced fair dice is thrown until $$1$$ comes, then the probability that $$1$$ comes in even no. of trials is
A
$$5/11$$
B
$$5/6$$
C
$$6/11$$
D
$$1/6$$
3
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+2
-0.5
The differential equation $${{dy} \over {dx}} = {{\sqrt {1 - {y^2}} } \over y}$$ determines a family of circles with
A
variable radii and a fixed centre at $$(0,1)$$
B
variable radii and a fixed centre at $$(0,-1)$$
C
fixed radius $$1$$ and variable centres along the $$x$$-axis.
D
fixed radius $$1$$ and variable centrs along the $$y$$-axis.
4
IIT-JEE 2005 Screening
MCQ (Single Correct Answer)
+2
-0.5
The solution of primitive integral equation $$\left( {{x^2} + {y^2}} \right)dy = xy$$
$$dx$$ is $$y=y(x),$$ If $$y(1)=1$$ and $$\left( {{x_0}} \right) = e$$, then $${{x_0}}$$ is equal to
A
$$\sqrt {2\left( {{e^2} - 1} \right)} $$
B
$$\sqrt {2\left( {{e^2} + 1} \right)} $$
C
$$\sqrt 3 \,e$$
D
$$\sqrt {{{2\left( {{e^2} + 1} \right)} \over 2}} $$
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