MCQOPTIONS
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MCQOPTIONS
This section includes 71 Mcqs, each offering curated multiple-choice questions to sharpen your Php knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
Given two complex numbers \({Z_1} = 5 + \left( {5\sqrt 3 } \right)i,\) and \({Z_2} = \frac{2}{{\surd 3}} + 2i\) the argument of \(\frac{{{Z_1}}}{{{Z_2}}}\) in degrees is |
| A. | 0 |
| B. | 30 |
| C. | 60 |
| D. | 90 |
| Answer» B. 30 | |
| 52. |
Let \(S\) be the set of points in the complex plane corresponding to the unit circle.\((\;i.e.,\;S = \left\{ {Z:\left| Z \right| = 1} \right\})\).Consider the function.\(f\left( z \right) = z{z^*},\;\) where\(\;{z^*}\) denotes the complex conjugate of \(z\). The \(f\left( z \right)\) maps \(S\) to which one the following in the complex plane? |
| A. | Unit circle. |
| B. | horizontal axis line segment from origin to \(\left( {1,\;0} \right)\) |
| C. | the point \(\left( {1,\;0} \right)\) |
| D. | the entire horizontal axis. |
| Answer» D. the entire horizontal axis. | |
| 53. |
Let z1 = 4 + 7i and z2 = 7 – 2i, then z1 + z2 will be: |
| A. | 12 + 5i |
| B. | 11 + 6i |
| C. | 11 + 5i |
| D. | 12 + 4i |
| Answer» D. 12 + 4i | |
| 54. |
Let f(Z) = u(x, y) + i(v(x, y)) be an analytical function. If u = 5x + 2xy then v is equal to _________, where c is a constant. |
| A. | x2 + y2 - 5x + c |
| B. | x2 - y2 - 5xy + c |
| C. | x2 + y2 + 5xy + c |
| D. | y2 - x2 + 5y + c |
| Answer» E. | |
| 55. |
An analytic function of a complex variable z = x + i y is expressed as f(z) = u(x,y) + i v(x, y), where \(i = \sqrt { - 1}\). If u(x, y) = 2 x y, then v(x, y) must be |
| A. | x2 + y2 constant |
| B. | x2 – y2 constant |
| C. | -x2 + y2 + constant |
| D. | -x2 – y2 + constant |
| Answer» D. -x2 – y2 + constant | |
| 56. |
For a complex variable Ƶ, if \(f\left( Ƶ \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{ Ƶ}{{\left| Ƶ \right|}}}&{for\;Ƶ \ne 0}\\ {0,}&{for\;Ƶ = 0} \end{array}} \right\}\) then, |
| A. | \(\mathop {\lim }\limits_{Ƶ \to \infty } f(Ƶ) = 1\) |
| B. | f(Ƶ) is discontinuous at origin |
| C. | f(Ƶ) is continuous at origin |
| D. | \(\mathop {\lim }\limits_{Ƶ \to \infty } f(Ƶ) = i\) |
| Answer» C. f(Ƶ) is continuous at origin | |
| 57. |
If two complex numbers are \({z_1} = \left( {5 + 5\sqrt 3i } \right)\) and \({z_2} = \left( {\frac{2}{\sqrt3} + 2i} \right)\) , then radian value of the argument of \(\frac{z_1}{z_2}\) is: |
| A. | \(\frac{\pi}{2}\) |
| B. | \(\frac{\pi}{3}\) |
| C. | \(\frac{\pi}{6}\) |
| D. | 0 |
| Answer» E. | |
| 58. |
If f (z) is an analytic function whose modulus is constant, then f (z) is a |
| A. | Function of z |
| B. | Constant |
| C. | Function whose only imaginary part is constant |
| D. | Function whose only real part is constant |
| Answer» C. Function whose only imaginary part is constant | |
| 59. |
An integral I over a counterclockwise circle C is given by\(I = \mathop \oint \limits_C^\; \frac{{{z^2} - 1}}{{{z^2} + 1}}{e^z}dz.\)If C is defined as |z| = 3, then the value of I is |
| A. | -πi sin (1) |
| B. | -2πi sin (1) |
| C. | -3πi sin (1) |
| D. | -4πi sin (1) |
| Answer» E. | |
| 60. |
A complex function f(z) = u (x, y) + i v (x, y) and its complex conjugate f*(z) = u(x, y) – i v(x, y) are both analytic in the entire complex plane, where z = x + i y and \({\rm{i}} = \sqrt { - 1}\). The function f is then given by |
| A. | f(z) = x + i y |
| B. | f(z) = x2 − y2 + i 2xy |
| C. | f(z) = constant |
| D. | (D) f(z) = x2 + y2 |
| Answer» D. (D) f(z) = x2 + y2 | |
| 61. |
If f(z) is analytic in a simply connected domain D, then for every closed path C and D |
| A. | \(\mathop \oint \limits_C f\left( z \right)dz = 1\) |
| B. | \(\mathop \oint \limits_C f\left( z \right)dz = 0\) |
| C. | \(\mathop \oint \limits_C f\left( z \right)dz \ne 0\) |
| D. | \(\mathop \oint \limits_C f\left( z \right)dz \ne 1\) |
| Answer» C. \(\mathop \oint \limits_C f\left( z \right)dz \ne 0\) | |
| 62. |
Integration of the complex function \(f\left( z \right) = \frac{{{z^2}}}{{{z^2} - 1}}\) in the counterclockwise direction, around |z – 1| = 1, is |
| A. | -πi |
| B. | 0 |
| C. | πi |
| D. | 2πi |
| Answer» D. 2πi | |
| 63. |
If f(z) is analytic in a simply connected domain D, then for every closed path C in D: |
| A. | \(\mathop \smallint \limits_c^{} f\left( z \right)dz = 1\) |
| B. | \(\mathop \smallint \limits_c^{} f\left( z \right)dz = 0\) |
| C. | \(\mathop \smallint \limits_c^{} f\left( z \right)dz \ne 0\) |
| D. | \(\mathop \smallint \limits_c^{} f\left( z \right)dz \ne 1\) |
| Answer» C. \(\mathop \smallint \limits_c^{} f\left( z \right)dz \ne 0\) | |
| 64. |
Let |
| A. | Both 𝑓1(𝑧) and 𝑓2(𝑧) are analytic |
| B. | Only 𝑓1(𝑧) is analytic |
| C. | Only 𝑓2(𝑧) is analytic |
| D. | Both 𝑓1(𝑧) and 𝑓2(𝑧) are not analytic |
| Answer» C. Only 𝑓2(𝑧) is analytic | |
| 65. |
You can define a constant by using the define() function. Once a constant is defined |
| A. | It can never be changed but can be undefined |
| B. | It can never be changed or undefined |
| C. | It can be changed and can be undefined |
| D. | It can be changed but can not be undefined |
| Answer» C. It can be changed and can be undefined | |
| 66. |
Which of the following method sends input to a script via a URL? |
| A. | Post |
| B. | Get |
| C. | None |
| D. | Both |
| Answer» C. None | |
| 67. |
When compared to the compiled program, scripts run |
| A. | Slower |
| B. | Faster |
| C. | All of above |
| D. | The execution speed is similar |
| Answer» B. Faster | |
| 68. |
Which of the following variables is not a predefined variable? |
| A. | $ask |
| B. | $get |
| C. | $post |
| D. | $request |
| Answer» B. $get | |
| 69. |
z |
| A. | 15 |
| B. | 8 |
| C. | 1 |
| Answer» B. 8 | |
| 70. |
4 = 4 + 3 + 1 |
| A. | 8 |
| B. | 8 = 4 + 3 +1 |
| C. | Error |
| Answer» C. Error | |
| 71. |
15 |
| A. | 10 + 5 |
| B. | $z |
| C. | $x + $y |
| Answer» B. $z | |