1
IIT-JEE 2002 Screening
MCQ (Single Correct Answer)
+3
-0.75
The area bounded by the curves $$y = \left| x \right| - 1$$ and $$y = - \left| x \right| + 1$$ is
A
$$1$$
B
$$2$$
C
$$2\sqrt 2$$
D
$$4$$
2
IIT-JEE 2002 Screening
MCQ (Single Correct Answer)
+3
-0.75
Let $$f\left( x \right) = \int\limits_1^x {\sqrt {2 - {t^2}} \,dt.}$$ Then the real roots of the equation
$${x^2} - f'\left( x \right) = 0$$ are
A
$$\pm 1$$
B
$$\pm {1 \over {\sqrt 2 }}$$
C
$$\pm {1 \over 2}$$
D
$$0$$ and $$1$$
3
IIT-JEE 1997
MCQ (Single Correct Answer)
+2
-0.5
If $$g\left( x \right) = \int_0^x {{{\cos }^4}t\,dt,}$$ then $$g\left( {x + \pi } \right)$$ equals
A
$$g\left( x \right) + g\left( \pi \right)$$
B
$$g\left( x \right) - g\left( \pi \right)$$
C
$$g\left( x \right) g\left( \pi \right)$$
D
$${{g\left( x \right)} \over {g\left( \pi \right)}}$$
4
IIT-JEE 1982
MCQ (Single Correct Answer)
+2
-0.5
The area bounded by the curves $$y=f(x)$$, the $$x$$-axis and the ordinates $$x=1$$ and $$x=b$$ is $$(b-1)$$ sin $$(3b+4)$$. Then $$f(x)$$ is
A
$$\left( {x - 1} \right)\cos \left( {3x + 4} \right)$$
B
$$\sin \left( {3x + 4} \right)$$
C
$$\sin \left( {3x + 4} \right) + 3\left( {x - 1} \right)\cos \left( {3x + 4} \right)$$
D
none of these
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