1
IIT-JEE 2000 Screening
+2
-0.5
Let $$g\left( x \right) = \int\limits_0^x {f\left( t \right)dt,}$$ where f is such that
$${1 \over 2} \le f\left( t \right) \le 1,$$ for $$t \in \left[ {0,1} \right]$$ and $$\,0 \le f\left( t \right) \le {1 \over 2},$$ for $$t \in \left[ {1,2} \right]$$.
Then $$g(2)$$ satisfies the inequality
A
$$- {3 \over 2} \le g\left( 2 \right) < {1 \over 2}$$
B
$$0 \le g\left( 2 \right) < 2$$
C
$${3 \over 2} < g\left( 2 \right) \le {5 \over 2}$$
D
$$2 < g\left( 2 \right) < 4$$
2
IIT-JEE 2000 Screening
+3
-0.75
The value of the integral $$\int\limits_{{e^{ - 1}}}^{{e^2}} {\left| {{{{{\log }_e}x} \over x}} \right|dx}$$ is :
A
$$3/2$$
B
$$5/2$$
C
$$3$$
D
$$5$$
3
IIT-JEE 2000 Screening
+2
-0.5
If $${x^2} + {y^2} = 1,$$ then
A
$$yy'' - 2{\left( {y'} \right)^2} + 1 = 0$$
B
$$yy'' + {\left( {y'} \right)^2} + 1 = 0$$
C
$$yy'' + {\left( {y'} \right)^2} - 1 = 0$$
D
$$yy'' + 2{\left( {y'} \right)^2} + 1 = 0$$
4
IIT-JEE 2000 Screening
+4
-1
If the vectors $$\overrightarrow a ,\overrightarrow b$$ and $$\overrightarrow c$$ form the sides $$BC,$$ $$CA$$ and $$AB$$ respectively of a triangle $$ABC,$$ then
A
$$\overrightarrow a .\overrightarrow b + \overrightarrow b .\overrightarrow c + \overrightarrow c .\overrightarrow a = 0$$
B
$$\overrightarrow a \times \overrightarrow b = \overrightarrow b \times \overrightarrow c = \overrightarrow c \times \overrightarrow a$$
C
$$\overrightarrow a .\overrightarrow b = \overrightarrow b .\overrightarrow c = \overrightarrow c .\overrightarrow a$$
D
$$\overrightarrow a \times \overrightarrow b + \overrightarrow b \times \overrightarrow c + \overrightarrow c \times \overrightarrow a = \overrightarrow 0$$
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