1
GATE CSE 2003
+1
-0.3
$$\mathop {Lim}\limits_{x \to 0} \,{{Si{n^2}x} \over x} = \_\_\_\_.$$
A
$$0$$
B
$$\infty$$
C
$$1$$
D
$$-1$$
2
GATE CSE 2001
+1
-0.3
The value of the integral is $${\rm I} = \int\limits_0^{{\raise0.5ex\hbox{\pi } \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{4}}} {{{\cos }^2}x\,dx}$$
A
$${\pi \over 8} + {1 \over 4}$$
B
$${\pi \over 8} - {1 \over 4}$$
C
$${{ - \pi } \over 8} - {1 \over 4}$$
D
$${{ - \pi } \over 8} + {1 \over 4}$$
3
GATE CSE 1998
+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
4
GATE CSE 1996
+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
$${{f\left( {{x_0} + h} \right) - 2f\left( {{x_0}} \right) + f\left( {{x_0} - h} \right)} \over {{h^2}}}$$
GATE CSE Subjects
Discrete Mathematics
Programming Languages
Theory of Computation
Operating Systems
Digital Logic
Computer Organization
Database Management System
Data Structures
Computer Networks
Algorithms
Compiler Design
Software Engineering
Web Technologies
General Aptitude
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