1
IIT-JEE 2000 Screening
MCQ (Single Correct Answer)
+2
-0.5
Consider the following statements in $$S$$ and $$R$$
$$S:$$ $$\,\,\,$$$ Both $$\sin \,\,x$$ and $$\cos \,\,x$$ are decreasing functions in the interval $$\left( {{\pi \over 2},\pi } \right)$$
$$R:$$$$\,\,\,$$ If a differentiable function decreases in an interval $$(a, b)$$, then its derivative also decreases in $$(a, b)$$.
Which of the following is true ?
A
Both $$S$$ and $$R$$ are wrong
B
Both $$S$$ and $$R$$ are correct, but $$R$$ is not the correct explanation of $$S$$
C
$$S$$ is correct and $$R$$ is the correct explanation for $$S$$
D
$$S$$ is correct and $$R$$ is wrong
2
IIT-JEE 2000 Screening
MCQ (Single Correct Answer)
+2
-0.5
If the normal to the curve $$y = f\left( x \right)$$ and the point $$(3, 4)$$ makes an angle $${{{3\pi } \over 4}}$$ with the positive $$x$$-axis, then $$f'\left( 3 \right) = $$
A
$$-1$$
B
$$ - {3 \over 4}$$
C
$${4 \over 3}$$
D
$$1$$
3
IIT-JEE 2000 Screening
MCQ (Single Correct Answer)
+2
-0.5
The dimension of $$\left( {{1 \over 2}} \right){\varepsilon _0}{E^2}$$
( $${\varepsilon _0}$$ : permittivity of free space, E electric field )
A
MLT-1
B
ML2T-2
C
ML-1T-2
D
ML2T-1
4
IIT-JEE 2000 Screening
MCQ (Single Correct Answer)
+2
-0.5
A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be proportional to
A
v
B
v2
C
v3
D
v4
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