List of top Civil Engineering Questions on Numerical Methods asked in AP PGECET

Secant formula is applicable for

Secant formula is applicable for

The coefficient of \(\dfrac{1}{z}\) in the Laurent's series expansion of the function \[ f(z)=\frac{1}{z^2(1-z)} \] about \(z=0\), is ____.

The value of the integral \[ \oint_{|z|=2}\frac{\cos\left(\dfrac{z}{2}\right)}{z^3}\,dz \] is ____.

Suppose the probability that an individual suffers an adverse reaction from a particular drug is known to be \(0.001\). The probability that out of \(2000\) individuals, exactly three will suffer an adverse reaction is ____.

If \(X\) is a normal random variable with mean \(\mu=100\) and variance \(\sigma^2=25\), then \[ P(90<X<120) \] is same as ____.

The values of \(x\) and \(f(x)\) of a curve are as follows: \[ \begin{array}{|c|c|c|c|c|c|} \hline x & 2 & 2.5 & 3 & 3.5 & 4 \hline f(x) & 3 & 6 & 8 & 10 & 12 \hline \end{array} \] By Simpson's one-third rule, the area under the curve \(f(x)\) is ____.

The integral \[ \int_{0}^{\pi/2}\frac{\sin x}{x^p}\,dx \] converges if ____.

Suppose \(C\) is the closed curve defined as the circle \(x^2+y^2=1\) with \(C\) oriented anti-clockwise. The value of the line integral \[ \oint_C (x\,dy-y\,dx) \] is equal to ____.

If \(y=A(x)\cdot e^{-x^2\) is a solution of the differential equation} \[ \frac{dy}{dx}+2xy=2e^{-x^2} \] with \(y(0)=-3\), then the value of \(A(1)\) is ____.

If \(F(s)\) is the Laplace transform of the function \[ f(t)=e^{-3t}(2\cos5t-3\sin5t), \] then \(F(0)=\_\_\_\_.\)

If the matrix \[ A=\begin{pmatrix} -8 & 5 2 & 4 \end{pmatrix} \] satisfies the equation \(x^2+4x-k=0\), then the value of \(k\) is ____.