1
GATE CSE 2014 Set 1
Numerical
+2
-0
The function $$f(x) =$$ $$x$$ $$sinx$$ satisfies the following equation:
$$f$$"$$\left( x \right) + f\left( x \right) + t\,\cos \,x\,\, = \,\,0$$. The value of $$t$$ is ______ .
Your input ____
2
GATE CSE 2014 Set 1
MCQ (Single Correct Answer)
+2
-0.6
A function $$f(x)$$ is continuous in the interval $$\left[ {0,2} \right]$$. It is known that $$f(0)$$ $$=$$ $$f(2)$$ $$= -1$$ and $$f(1)$$ $$ = 1$$. Which one of the following statements must be true?
A
There exists $$a$$ $$y$$ in the interval $$(0, 1)$$ such that $$f(y) = $$ $$f(y+1)$$
B
For every $$y$$ in the interval $$(0, 1)$$, $$f(y)$$ $$=$$ $$f(2 - y)$$
C
The maximum value of the function in the interval $$(0,2)$$ is $$1$$
D
There exists $$a$$ $$y$$ in the interval $$(0,1)$$ such that $$f(y)$$ $$=-$$$$f(2-y)$$
3
GATE CSE 2011
MCQ (Single Correct Answer)
+2
-0.6
Given $$i = \sqrt { - 1} ,$$ what will be the evaluation of the definite integral $$\int\limits_0^{\pi /2} {{{\cos x +i \sin x} \over {\cos x - i\,\sin x}}dx?} $$
A
$$0$$
B
$$2$$
C
$$-1$$
D
$$i$$
4
GATE CSE 2009
MCQ (Single Correct Answer)
+2
-0.6
$$\int\limits_0^{\pi /4} {\left( {1 - \tan x} \right)/\left( {1 + \tan x} \right)dx} $$ $$\,\,\,\,\,\,$$ evaluates to
A
$$0$$
B
$$1$$
C
In $$2$$
D
$${1 \over 2}$$ in $$2$$
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