1
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+2
-0.6
If for non-zero $$x,$$ $$af\left( x \right) + bf\left( {{1 \over x}} \right) = {1 \over x} - 25$$
where $$a \ne b$$ then $$\int\limits_1^2 {f\left( x \right)dx} \,$$ is
A
$${1 \over {{a^2} - {b^2}}}\left[ {a\left( {\ln \,2 - 25} \right) + {{47b} \over 2}} \right]$$
B
$${1 \over {{a^2} - {b^2}}}\left[ {a\left( {2\ln \,2 - 25} \right) - {{47b} \over 2}} \right]$$
C
$${1 \over {{a^2} - {b^2}}}\left[ {a\left( {2\ln \,2 - 25} \right) + {{47b} \over 2}} \right]$$
D
$${1 \over {{a^2} - {b^2}}}\left[ {a\left( {\ln \,2 - 25} \right) - {{47b} \over 2}} \right]$$
2
GATE CSE 2015 Set 2
MCQ (Single Correct Answer)
+2
-0.6
Let $$\,\,f\left( x \right) = {x^{ - \left( {1/3} \right)}}\,\,$$ and $${\rm A}$$ denote the area of the region bounded by $$f(x)$$ and the $$X-$$axis, when $$x$$ varies from $$-1$$ to $$1.$$ Which of the following statements is/are TRUE?
$${\rm I}.$$ $$f$$ is continuous in $$\left[ { - 1,1} \right]$$
$${\rm I}{\rm I}.$$ $$f$$ is not bounded in $$\left[ { - 1,1} \right]$$
$${\rm I}{\rm I}{\rm I}.$$ $${\rm A}$$ is nonzero and finite
A
$${\rm I}$$$${\rm I}$$ only
B
$${\rm I}$$$${\rm I}$$$${\rm I}$$ only
C
$${\rm I}$$$${\rm I}$$ and $${\rm I}$$$${\rm I}$$$${\rm I}$$ only
D
$${\rm I}$$, $${\rm I}$$$${\rm I}$$, and $${\rm I}$$$${\rm I}$$$${\rm I}$$
3
GATE CSE 2015 Set 1
Numerical
+2
-0
$$\,\int\limits_{1/\pi }^{2/\pi } {{{\cos \left( {1/x} \right)} \over {{x^2}}}dx = }$$ __________.
4
GATE CSE 2014 Set 3
MCQ (Single Correct Answer)
+2
-0.6
The value of the integral given below is $$\int_0^\pi {{x^2}\,\cos \,x\,dx}$$\$
A
$$- 2\pi$$
B
$$\pi$$
C
$$-\pi$$
D
$$2\pi$$
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