MCQOPTIONS
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MCQOPTIONS
This section includes 69 Mcqs, each offering curated multiple-choice questions to sharpen your Microwave Engineering knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
For a transmission line, L=1.8mh/m C=0.01pF/m, then the phase constant of the line when operated at a frequency of 1 GHz is: |
| A. | 4.2426 |
| B. | 2.2 |
| C. | 0.3 |
| D. | 1 |
| Answer» B. 2.2 | |
| 2. |
In a certain microwave transmission line, the characteristic impedance was found to be 210 10°Ω and propagation constant 0.2 78°.What is the impedance Z of the line, if the frequency of operation is 1 GHz? |
| A. | 0.035+j41.97 |
| B. | 0.35+j4.97 |
| C. | 35.6+j4.28 |
| D. | 9.254+j4.6 |
| Answer» B. 0.35+j4.97 | |
| 3. |
A microwave generator at 1.2 GHz supplies power to a microwave transmission line having the parameters R=0.8Ω/m, G=O.8millisiemen/m, L=0.01µH/m and C=0.4PF/m. Propagation constant of the transmission line is: |
| A. | 0.0654 +j0.48 |
| B. | 0.064+j4.8 |
| C. | 6.4+j4.8 |
| D. | none of the mentioned |
| Answer» B. 0.064+j4.8 | |
| 4. |
Expression for phase constant β is: |
| A. | √LC |
| B. | ω √LC |
| C. | 1/ (ω √LC) |
| D. | None of the mentioned |
| Answer» C. 1/ (ω √LC) | |
| 5. |
If the admittance and the impedance of a transmission line are 100 Ω and 50 Ω of a respectively, then value of phase constant β is: |
| A. | 0 |
| B. | 20 |
| C. | 132 |
| D. | 50 |
| Answer» B. 20 | |
| 6. |
If a transmission line with inductive reactance of 41.97 Ω and capacitive reactance of 1132.5Ω is operated at 1 GHz , then its phase constant is: |
| A. | 0.0305 |
| B. | 0.3 |
| C. | 30.3 |
| D. | 0.6 |
| Answer» B. 0.3 | |
| 7. |
If propagation constant is 12:60°, then the value of phase constant and attenuation constant is: |
| A. | α=6, β=10.39 |
| B. | α=61, β=78 |
| C. | α=12, β=20.6 |
| D. | none of the mentioned |
| Answer» B. α=61, β=78 | |
| 8. |
The value of ‘α’ for a lossless line is: |
| A. | 0 |
| B. | 1 |
| C. | Infinity |
| D. | Data insufficient |
| Answer» B. 1 | |
| 9. |
If A and B are two points having coordinates (3, 40) and (5, -2) respectively and P is a point such that PA = PB and area of triangle ΔPAB = 10 sq units, then the coordinates of P are: |
| A. | (2, 7) or (4, 13) |
| B. | (7, 4) or (13, 2) |
| C. | None of these |
| D. | (7, 2) or (1, 0) |
| Answer» E. | |
| 10. |
If the lines x + 2y + 1 = 0, 8x + 12y + k = 0, 3x - 2y + 5 = 0 are concurrent, then the value of k is: |
| A. | 11 |
| B. | 5 |
| C. | 9 |
| D. | 7 |
| Answer» D. 7 | |
| 11. |
A bus is travelling at a constant speed of 48 Km/hr. What is the distance travelled by bus from 1:20 pm to 3:40 pm? |
| A. | 326 Km |
| B. | 112 Km |
| C. | 340 Km |
| D. | 144 Km |
| Answer» C. 340 Km | |
| 12. |
Consider the following statements:1) For an equation of a line, x cos θ + y sin θ = p, in normal form, the length of the perpendicular from the point (α, β) to the line is |α cos θ + β sin θ + p|.2) The length of the perpendicular from the point (α, β) to the line \(\frac{x}{a} + \frac{y}{b} = 1\) is \(\left| {\frac{{a\alpha + b\beta - ab}}{{\sqrt {{a^2} + {b^2}} }}} \right|\)Which of the above statements is/are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» E. | |
| 13. |
If θ is the angle between Two lines whose slopes are m1 & m2, then Tan θ = ________ |
| A. | m1 - m2 |
| B. | m1 + m2 |
| C. | (m1 - m2) / (1 + m1 m2) |
| D. | (m1 - m2) / (1 - m1 m2) |
| Answer» D. (m1 - m2) / (1 - m1 m2) | |
| 14. |
If the lines x + (a - 1)y + 1 = 0 and 2x + a2y - 1 = 0 are prepedicular, then the condition satisfied by a is |
| A. | |a| = 2 |
| B. | 0 < a < 1 |
| C. | -1 < a < 0 |
| D. | a = -1 |
| Answer» E. | |
| 15. |
If the foot of the perpendicular drawn from the point (0, k) to the line 3x - 4y - 5 = 0 is (3, 1), then what is the value of k? |
| A. | 3 |
| B. | 4 |
| C. | 5 |
| D. | 6 |
| Answer» D. 6 | |
| 16. |
Line x + y = 4 |
| A. | Never passes through (0,0) |
| B. | Always passes through (0,0) |
| C. | Meets Y axis at y = 0 |
| D. | Always passes through (0) |
| Answer» B. Always passes through (0,0) | |
| 17. |
If A, B and C are in AP, then the straight line Ax + 2By + C = 0 will always pass through a fixed point. The fixed point is |
| A. | (0, 0) |
| B. | (-1, 1) |
| C. | (1, -2) |
| D. | (1, -1) |
| Answer» E. | |
| 18. |
Equation of the line perpendicular to x - 2y = 1 and passing through (1, 1) is: |
| A. | x + 2y = 3 |
| B. | x + y = 2 |
| C. | y = 2x + 3 |
| D. | y = -2x + 3 |
| Answer» E. | |
| 19. |
(a, 2b) is the mid-point of the line segment joining the points (10, -6) and (k, 4). If a – 2b = 7, then what is the value of k? |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | 5 |
| Answer» B. 3 | |
| 20. |
Lines x = ay + b, z = cy + dand x = a'y + b', z = c'y + d'are perpendicular, if |
| A. | aa' + cc' + 1 = 0 |
| B. | aa' + cc' - 1 = 0 |
| C. | ac + a'c' -1 = 0 |
| D. | ac + a'c' + 1 = 0 |
| Answer» B. aa' + cc' - 1 = 0 | |
| 21. |
An equilateral triangle has one vertex at (0, 0) and another at (3, √3). What are the coordinates of the third vertex? |
| A. | (0, 2 √3) only |
| B. | (3, -√3) only |
| C. | (0, 2√3) or (3, -√3) |
| D. | Neither (0, 2, √3) nor (3, - √3) |
| Answer» D. Neither (0, 2, √3) nor (3, - √3) | |
| 22. |
If 3x - 4y - 5 = 0 and 3x - 4y + 15 = 0 are the equations of a pair of opposite sides of a square, then what is the area of the square? |
| A. | 4 square units |
| B. | 9 square units |
| C. | 16 square units |
| D. | 25 square units |
| Answer» D. 25 square units | |
| 23. |
If the line \(\frac{{x - 2}}{3} = \frac{{y + 1}}{2} = \frac{{z - 1}}{{ - 1}}\) intersects the plane 2x + 3y – z + 13 = 0 at a point P and the plane 3x + y + 4z = 16 at a point Q, then PQ is equal to: |
| A. | 14 |
| B. | \(\sqrt {14}\) |
| C. | \(2\sqrt 7\) |
| D. | \(2\sqrt {14}\) |
| Answer» E. | |
| 24. |
If (– 4, 5) is one vertex and 7x – y + 8 = 0 is one diagonal of a square, then the equation of the other diagonal is |
| A. | x + 7y = 21 |
| B. | x + 7y = 31 |
| C. | x + 7y = 28 |
| D. | x + 7y = 35 |
| Answer» C. x + 7y = 28 | |
| 25. |
An equilateral triangle has one vertex at (-1, -1) and another vertex at \(\left( { - \sqrt 3 ,\;\sqrt 3 } \right).\) The third vertex may lie on |
| A. | \(\left( -\sqrt{2},~\sqrt{2} \right)\) |
| B. | \(\left( \sqrt{2},~-\sqrt{2} \right)\) |
| C. | (1, 1) |
| D. | (1, -1) |
| Answer» D. (1, -1) | |
| 26. |
If the image of the point (-4, 2) by a line mirror is (4, -2), then what is the equation of the line mirror? |
| A. | y = x |
| B. | y = 2x |
| C. | 4y = x |
| D. | y = 4x |
| Answer» C. 4y = x | |
| 27. |
A line passes through (2, 2) and is perpendicular to the line 3x + y = 3. Its y-intercept is |
| A. | 3/4 |
| B. | 4/3 |
| C. | 1/3 |
| D. | 3 |
| Answer» C. 1/3 | |
| 28. |
If a line is perpendicular to the line 5x – y = 0 and forms a triangle of area 5 square units with co-ordinate axes, then its equation is |
| A. | \({\rm{x}} + 5{\rm{y}} \pm 5\sqrt 2 = 0\) |
| B. | \({\rm{x}} - 5{\rm{y}} \pm 5\sqrt 2 = 0\) |
| C. | \(5{\rm{x}} + {\rm{y}} \pm 5\sqrt 2 = 0\) |
| D. | \(5{\rm{x}} - {\rm{y}} \pm 5\sqrt 2 = 0\) |
| Answer» B. \({\rm{x}} - 5{\rm{y}} \pm 5\sqrt 2 = 0\) | |
| 29. |
If (2, 1), (–1, –2), (3, 3) are the midpoints of the sides BC, CA, AB of a triangle ABC, then equation of the line BC is |
| A. | 5x + 4y + 6 = 0 |
| B. | 5x - 4y - 6 = 0 |
| C. | 5x + 4y - 6 = 0 |
| D. | 5x - 4y + 6 = 0 |
| Answer» C. 5x + 4y - 6 = 0 | |
| 30. |
Consider the following statements:Statement I: If the line segment joining the points P (m, n) and Q(r, s) subtends an angle α at the origin, then \(\cos \alpha = \frac{{ms - nr}}{{\sqrt {\left( {{m^2} + {n^2}} \right)({r^2} + {s^2}} }}\)Statement II: In any triangle ABC, it true that a2 = b2 + c2 – 2bc cos A.Which one of the following is correct in respect of the above two statements? |
| A. | Both Statement I and statement II are true and Statement II is the correct explanation of statement I |
| B. | Both Statement I and Statement II are true, but Statement II is not the correct explanation of Statement I |
| C. | Statement I is true, but Statement II is false |
| D. | Statement I is false, but Statement II is true |
| Answer» E. | |
| 31. |
In which ratio does the line y - x + 2 = 0 divide the line joining the points (3, -1) and (8, 9)? |
| A. | 1 ∶ 2 |
| B. | 2 ∶ 1 |
| C. | 2 ∶ 3 |
| D. | 3 ∶ 4 |
| Answer» D. 3 ∶ 4 | |
| 32. |
A straight line passes through the point (1, 1, 1) makes an angle 60° with the positive direction of z-axis, and the cosine of the angles made by it with the positive directions of the y-axis and the x-axis are in the ratio √3 : 1. What is the acute angle between the two possible positions of the line? |
| A. | 90° |
| B. | 60° |
| C. | 45° |
| D. | 30° |
| Answer» C. 45° | |
| 33. |
If 2x2 + 7xy + 3y2 + 8x + 14y + λ = 0 represents a pair of straight lines, the value of λ is |
| A. | 2 |
| B. | 4 |
| C. | 6 |
| D. | 8 |
| Answer» E. | |
| 34. |
For which value of k, there is no solution to the equations - x - y = 5kx - 4y = 1 |
| A. | 4 |
| B. | 2 |
| C. | 5 |
| D. | Zero |
| Answer» B. 2 | |
| 35. |
A point P moves on the line 2x – 3y + 4 = 0. If Q(1, 4) and R(3, -2) are fixed points, then the locus of the centroid of ΔPQR is a line: |
| A. | With slope 3/2 |
| B. | Parallel to x-axis |
| C. | With slope 2/3 |
| D. | Parallel to y-axis |
| Answer» D. Parallel to y-axis | |
| 36. |
If the straight line, 2x – 3y + 17 = 0 is perpendicular to the line passing through the points (7, 17) and (15, β), then β equals |
| A. | 35/3 |
| B. | -5 |
| C. | \(- \frac{{35}}{3}\) |
| D. | 5 |
| Answer» E. | |
| 37. |
If the equation3x2 + 7xy + 2y2 + 5x + 5y + k = 0represents a pair of straight lines, then the value of k is |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» C. 3 | |
| 38. |
Find the midpoint of the segment joining the points (4, -2) and (-8,6). |
| A. | (6, 4) |
| B. | (-6, -4) |
| C. | (2, 2) |
| D. | (-2, 2) |
| Answer» E. | |
| 39. |
Consider the following statements:1) The length p of the perpendicular form the origin to the line ax + by = c satisfies the origin to the relation \({{\rm{p}}^2} = \frac{{{{\rm{c}}^2}}}{{{{\rm{a}}^2} + {{\rm{b}}^2}}}\)2) The length p the perpendicular from the origin to the line \(\frac{{\rm{x}}}{{\rm{a}}} + \frac{{\rm{y}}}{{\rm{b}}} = 1\) satisfies the relation \(\frac{1}{{{{\rm{p}}^2}}} = \frac{1}{{{{\rm{a}}^2}}} + \frac{1}{{{{\rm{b}}^2}}}\)3) The length p of the perpendicular from the origin to the line y = mx + c satisfies the relation \(\frac{1}{{{{\rm{p}}^2}}} = \frac{{1 + {{\rm{m}}^2} + {{\rm{c}}^2}}}{{{{\rm{c}}^2}}}\)Which of the above is/are correct? |
| A. | 1, 2 and 3 |
| B. | 1 only |
| C. | 1 and 2 only |
| D. | 2 only |
| Answer» D. 2 only | |
| 40. |
If the point (a, a) lies between the lines |x + y| = 2, then which one of the following is correct? |
| A. | |a| < 2 |
| B. | |a| < √2 |
| C. | |a| < 1 |
| D. | \(\left| {\rm{a}} \right| < \frac{1}{{\sqrt 2 }}\) |
| Answer» D. \(\left| {\rm{a}} \right| < \frac{1}{{\sqrt 2 }}\) | |
| 41. |
Consider the following statements: The distance between:1) The distance between the lines y = mx + c1 and y = mx + c2 is \(\frac{{\left| {{c_1} - {c_2}} \right|}}{{\sqrt {1{\rm{\;}} - {\rm{\;}}{m^2}} }}\)2) The distance between the lines ax + by + c1 = 0 and ax + by + c2 = 0 is \(\frac{{\left| {{c_1} - {c_2}} \right|}}{{\sqrt {{a^2} + {b^2}} }}\)3) The distance between the line x = c1 and x = c2 is |c1 – c2|Which of the above statements are correct? |
| A. | 1 and 2 only |
| B. | 2 and 3 only |
| C. | 1 and 3 only |
| D. | 1, 2 and 3 |
| Answer» C. 1 and 3 only | |
| 42. |
If the lines x = ay + b, z = cy + d andx = a'z + b', y = c'z + d' are perpendicular, then: |
| A. | ab'+ bc'+1 = 0 |
| B. | cc' + a + a' = 0 |
| C. | bb' + cc' + 1 = 0 |
| D. | aa'+ c + c' = 0 |
| Answer» E. | |
| 43. |
Find the distance between the points (3, 2) and (6, 4). |
| A. | √85 |
| B. | √79 |
| C. | 5√3 |
| D. | 3√5 |
| Answer» E. | |
| 44. |
A straight line intersects x and y axes at P and Q respectively. If (3, 5) is the middle point of PQ, then what is the area of the triangle OPQ? |
| A. | 12 square units |
| B. | 15 square units |
| C. | 20 square units |
| D. | 30 square units |
| Answer» E. | |
| 45. |
If the lines 3y + 4x = 1, y = x + 5 and 5y +bx = 3 are concurrent, then what is the value of b? |
| A. | 1/2 |
| B. | 1 |
| C. | 3 |
| D. | 6 |
| Answer» D. 6 | |
| 46. |
If the points (-2, -5), (2, -2) and (8, a) are collinear, then the value of a is: |
| A. | \(-\frac 5 2\) |
| B. | \(\frac 5 2\) |
| C. | \(\frac 3 2\) |
| D. | \(\frac 1 2\) |
| Answer» C. \(\frac 3 2\) | |
| 47. |
(0, 0, 0), (a, 0, 0), (0, b, 0) and (0, 0, c) are four distinct points. What are the coordinates of the point which is equidistant from the four points? |
| A. | \(\left( {\frac{{{\rm{a}} + {\rm{b}} + {\rm{c}}}}{3},\frac{{{\rm{a}} + {\rm{b}} + {\rm{c}}}}{3},\frac{{{\rm{a}} + {\rm{b}} + {\rm{c}}}}{3}} \right)\) |
| B. | (a, b, c) |
| C. | \(\left( {\frac{{\rm{a}}}{2},\frac{{\rm{b}}}{2},\frac{{\rm{c}}}{2}} \right){\rm{\;}}\) |
| D. | \(\left( {\frac{{\rm{a}}}{3},\frac{{\rm{b}}}{3},\frac{{\rm{c}}}{3}} \right)\) |
| Answer» D. \(\left( {\frac{{\rm{a}}}{3},\frac{{\rm{b}}}{3},\frac{{\rm{c}}}{3}} \right)\) | |
| 48. |
Find the angle between two straight lines 2 × + 4y - 20 = 0 and 3 × + 5y - 30 = 0. |
| A. | θ = tan - 1(1/13) |
| B. | θ = tan - 1(13/3) |
| C. | θ = tan - 1(11/40) |
| D. | θ = tan - 1(1/40) |
| Answer» B. θ = tan - 1(13/3) | |
| 49. |
A line through (4, 2) meets the coordinate axes at P and Q. Then the locus of the circumference of ΔOPQ is |
| A. | \(\dfrac{1}{x}+\dfrac{1}{y}=2\) |
| B. | \(\dfrac{2}{x}+\dfrac{1}{y}=1\) |
| C. | \(\dfrac{1}{x}+\dfrac{2}{y}=1\) |
| D. | \(\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{2}\) |
| Answer» C. \(\dfrac{1}{x}+\dfrac{2}{y}=1\) | |
| 50. |
Coordinates of the points O, P, Q and R are respectively (0, 0, 0), (4, 6, 2m), (2, 0, 2n) and (2, 3, 6). Let L, M, N and K points on the side OR, OP, PQ and QR respectively such that LMNK is a parallelogram whose two adjacent sides LK and LM are each of length √2, what are the values of m and n respectively? |
| A. | 6, 2 |
| B. | 1, 3 |
| C. | 3, 1 |
| D. | None of the above |
| Answer» D. None of the above | |