1
IIT-JEE 2000 Screening
MCQ (Single Correct Answer)
+3
-0.75
If $$f\left( x \right) = \left\{ {\matrix{ {{e^{\cos x}}\sin x,} & {for\,\,\left| x \right| \le 2} \cr {2,} & {otherwise,} \cr } } \right.$$ then $$\int\limits_{ - 2}^3 {f\left( x \right)dx = } $$
A
$$0$$
B
$$1$$
C
$$2$$
D
$$3$$
2
IIT-JEE 2000 Screening
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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
MCQ (Single Correct Answer)
+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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