1
GATE CSE 2001
MCQ (Single Correct Answer)
+1
-0.3
The value of the integral is $${\rm I} = \int\limits_0^{{\raise0.5ex\hbox{\scriptstyle \pi } \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 4}}} {{{\cos }^2}x\,dx}$$
A
$${\pi \over 8} + {1 \over 4}$$
B
$${\pi \over 8} - {1 \over 4}$$
C
$${{ - \pi } \over 8} - {1 \over 4}$$
D
$${{ - \pi } \over 8} + {1 \over 4}$$
2
GATE CSE 1998
MCQ (Single Correct Answer)
+1
-0.3
Consider the function $$y = \left| x \right|$$ in the interval $$\left[ { - 1,1} \right]$$. In this interval, the function is
A
continuous and differentiable
B
continuous but not differentiable
C
differentiable but not continuous
D
neither continuous nor differentiable
3
GATE CSE 1996
MCQ (Single Correct Answer)
+1
-0.3
The formula used to compute an approximation for the second derivative of a function $$f$$ at a point $${x_0}$$ is
A
$${{f\left( {{x_0} + h} \right) + f\left( {{x_0} - h} \right)} \over 2}$$
B
$${{f\left( {{x_0} + h} \right) - f\left( {{x_0} - h} \right)} \over 2h}$$
C
$${{f\left( {{x_0} + h} \right) + 2f\left( {{x_0}} \right) + f\left( {{x_0} - h} \right)} \over {{h^2}}}$$
D
$${{f\left( {{x_0} + h} \right) - 2f\left( {{x_0}} \right) + f\left( {{x_0} - h} \right)} \over {{h^2}}}$$
4
GATE CSE 1995
MCQ (Single Correct Answer)
+1
-0.3
If at every point of a certain curve, the slope of the tangent equals $${{ - 2x} \over y}$$ the curve is
A
A straight line
B
A parabola
C
A circle
D
An ellipse
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