MCQOPTIONS
Saved Bookmarks
MCQOPTIONS
This section includes 126 Mcqs, each offering curated multiple-choice questions to sharpen your General Aptitude knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
Which one of the following is the common factor of (4743 + 4343) and (4747 + 4347) ? |
| A. | (47 - 43) |
| B. | (47 + 43) |
| C. | (4743 + 4343) |
| D. | None of these |
| Answer» C. (4743 + 4343) | |
| 52. |
What will be remainder when 17200 is divided by 18 ? |
| A. | 17 |
| B. | 16 |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 53. |
Which of the following numbers will completely divide (4915 - 1) ? |
| A. | 8 |
| B. | 14 |
| C. | 46 |
| D. | 50 |
| Answer» B. 14 | |
| 54. |
(xn - an) is completely divisible by (x - a), when |
| A. | n is any natural number |
| B. | n is an even natural number |
| C. | n is and odd natural number |
| D. | n is prime |
| Answer» B. n is an even natural number | |
| 55. |
If n is a natural number, then (6n2 + 6n) is always divisible by: |
| A. | 6 only |
| B. | 6 and 12 both |
| C. | 12 only |
| D. | by 18 only |
| Answer» C. 12 only | |
| 56. |
On dividing 2272 as well as 875 by 3-digit number N, we get the same remainder. The sum of the digits of N is: |
| A. | 10 |
| B. | 11 |
| C. | 12 |
| D. | 13 |
| Answer» B. 11 | |
| 57. |
Let ‘z’ be a complex number such that |z| + z = 3 + i at (where \(i = \sqrt {-1} \)). Then |z| is equal to: |
| A. | \(\frac{{\sqrt {34} }}{3}\) |
| B. | \(\frac{5}{3}\) |
| C. | \(\frac{{\sqrt {41} }}{4}\) |
| D. | \(\frac{5}{4}\) |
| Answer» C. \(\frac{{\sqrt {41} }}{4}\) | |
| 58. |
Let α and β be real numbers and z be a complex number. If z2 + αz + β = 0 has two distinct non-real roots with Re(z) = 1, then it is necessary that. |
| A. | β ϵ (-1, 0) |
| B. | β| = 1 |
| C. | β ϵ (1, ∞) |
| D. | β ϵ (0, 1) |
| Answer» D. β ϵ (0, 1) | |
| 59. |
If 1, ω, ω2 are the cube roots of unity, then the value of (1 + ω) (1 + ω2) (1 + ω4) (1 + ω8) is |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 60. |
If \({\rm{z}} = {\rm{x}} + {\rm{iy}} = {\left( {\frac{1}{{\sqrt 2 }} - \frac{{\rm{i}}}{{\sqrt 2 }}} \right)^{ - 25}}\), where \({\rm{i}} = \sqrt { - 1} \), then what is the fundamental amplitude of \(\frac{{{\rm{z}} - \sqrt 2 }}{{{\rm{z}} - {\rm{i}}\sqrt 2 }}?\) |
| A. | π |
| B. | \(\frac{{\rm{\pi }}}{2}\) |
| C. | \(\frac{{\rm{\pi }}}{3}\) |
| D. | \(\frac{{\rm{\pi }}}{4}\) |
| Answer» B. \(\frac{{\rm{\pi }}}{2}\) | |
| 61. |
If α and β are different complex numbers with |α | = 1, then what is \(\left| {\frac{{\alpha - \beta }}{{1 - \alpha \bar \beta }}} \right|\) equal to? |
| A. | |β| |
| B. | 2 |
| C. | 1 |
| D. | 0 |
| Answer» D. 0 | |
| 62. |
If α, β, γ are the cube roots of any number p(p < 0), then for any three numbers x, y, z; \(\rm \frac {x\alpha + y\beta + z\gamma}{x\beta + y\gamma + z\alpha}\) is equal to: |
| A. | \(\frac {1}{2} \left( -1 + i\sqrt 3 \right)\) |
| B. | \(\frac {1}{2} \left( 1 + i\sqrt 3 \right)\) |
| C. | \(\frac {1}{2} \left( 1 - i\sqrt 3 \right)\) |
| D. | None of these |
| Answer» E. | |
| 63. |
If x = cos θ + i sin θ, then the value of \({x^n} + \frac{1}{{{x^n}}}\) is: |
| A. | 2 cos θ |
| B. | con nθ |
| C. | 2 cos nθ |
| D. | 2 sin nθ |
| Answer» D. 2 sin nθ | |
| 64. |
If 1, ω, ω2 are the cube roots of unity, then (1 + ω) (1 + ω2) (1 + ω3) (1 + ω + ω2) is equal to |
| A. | -2 |
| B. | -1 |
| C. | 0 |
| D. | 2 |
| Answer» D. 2 | |
| 65. |
Let \({\left( { - 2 - \frac{1}{3}i} \right)^3} = \frac{{x + iy}}{{27}}\left( {i = \sqrt { - 1} } \right)\), where x and y are real numbers, then y – x equals: |
| A. | 91 |
| B. | -85 |
| C. | 85 |
| D. | -91 |
| Answer» B. -85 | |
| 66. |
If iz3 + z2 - z + i = 0, then the value of |z| is: |
| A. | 1 |
| B. | -1 |
| C. | 2 |
| D. | 3 |
| Answer» B. -1 | |
| 67. |
Let \(z = {\left( {\frac{{\sqrt 3 }}{2} + \frac{i}{2}} \right)^5} + {\left( {\frac{{\sqrt 3 }}{2} - \frac{i}{2}} \right)^5}\). If R(z) and I(z) respectively denote the real and imaginary parts of z, then: |
| A. | I(z) = 0 |
| B. | R(z) > 0 and I(z) > 0 |
| C. | R(z) < 0 and I(z) > 0 |
| D. | R(z) = -3 |
| Answer» B. R(z) > 0 and I(z) > 0 | |
| 68. |
Find the multiplicative inverse of 4 - 3i ? |
| A. | \(\frac{4}{25} - i \frac{3}{25}\) |
| B. | \(\frac{3}{25} - i \frac{4}{25}\) |
| C. | \(\frac{3}{25} + i \frac{4}{25}\) |
| D. | \(\frac{4}{25} + i \frac{3}{25}\) |
| Answer» E. | |
| 69. |
If ω is cube root of unity, then (3 + ω + 3ω2)6 is equal to |
| A. | 32 |
| B. | 64 |
| C. | 128 |
| D. | 16 |
| Answer» C. 128 | |
| 70. |
If \(z = \frac{{\sqrt 3 }}{2} + \frac{i}{2}\left( {i = \sqrt { - 1} } \right)\), then (1 + iz + z5 + iz8)9 is equal to: |
| A. | 0 |
| B. | 1 |
| C. | (-1 + 2i)9 |
| D. | -1 |
| Answer» E. | |
| 71. |
If |z - 2| ≤ 5, then the maximum value of |z + 4| is |
| A. | 7 |
| B. | 9 |
| C. | 11 |
| D. | 13 |
| Answer» D. 13 | |
| 72. |
For any two complex numbers Z1 and Z2, which of the following results is true? |
| A. | |Z1 - Z2| < |Z1| - |Z2| |
| B. | |Z1 - Z2| < ||Z1| - |Z2|| |
| C. | |Z1 + Z2| < ||Z1| - |Z2|| |
| D. | |Z1 + Z2|2 + |Z1 - Z2|2 = 2(|Z1|2 + |Z2|2) |
| Answer» E. | |
| 73. |
Let z1 and z2 be any two non-zero complex numbers such that 3|z1| = 4|z2|. If \(z = \frac{{3{z_1}}}{{2{z_2}}} + \frac{{2{z_2}}}{{3{z_1}}}\) then: |
| A. | Re(z) = 0 |
| B. | \(\left| {\rm{z}} \right| = \sqrt {\frac{5}{2}}\) |
| C. | \(\left| {\rm{z}} \right| = \frac{1}{2}\sqrt {\frac{{17}}{2}}\) |
| D. | Im(z) = 0 |
| Answer» B. \(\left| {\rm{z}} \right| = \sqrt {\frac{5}{2}}\) | |
| 74. |
If \(\left| {\begin{array}{*{20}{c}} {6i}&{ - 3i}&1\\ 4&{3i}&{ - 1}\\ {20}&3&i \end{array}} \right| = x + iy\), then the values of x and y are: |
| A. | x = 0, y = 0 |
| B. | x = 0, y = 1 |
| C. | x = 0, y = -1 |
| D. | x = 1, y = -1 |
| Answer» B. x = 0, y = 1 | |
| 75. |
Consider the following in respect of a complex number z:1. \(\rm {\overline{\left(z^{-1}\right)}}=(\bar{z})^{-1}\)2. zz-1 = |z|2Which of the above is/are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» B. 2 only | |
| 76. |
Nature of the triangle formed by the points representing the complex numbers 3 + 4i, 8 - 6i and 13 + 9i is: |
| A. | equilateral triangle |
| B. | right angled triangle |
| C. | acute-angled triangle |
| D. | obtuse-angled triangle |
| Answer» C. acute-angled triangle | |
| 77. |
Let z be a complex number satisfying z2 + z + 1 = 0. If n is not a multiple of 3, then the value of zn + z2n = _______ |
| A. | 2 |
| B. | -2 |
| C. | 0 |
| D. | -1 |
| Answer» E. | |
| 78. |
If z is a complex number, then (z̅)-1 (z̅) is equal to: |
| A. | 1 |
| B. | -1 |
| C. | 0 |
| D. | None of these |
| Answer» B. -1 | |
| 79. |
\(\left| {\frac{{{\rm{z}} - 4}}{{{\rm{z}} - 8}}} \right| = 1\) and \(\left| {\frac{{\rm{z}}}{{{\rm{z}} - 2}}} \right| = \frac{3}{2}\)What is |z| equal to? |
| A. | 6 |
| B. | 12 |
| C. | 18 |
| D. | 36 |
| Answer» B. 12 | |
| 80. |
\(\left| {\frac{{{\rm{z}} - 4}}{{{\rm{z}} - 8}}} \right| = 1\) and \(\left| {\frac{{\rm{z}}}{{{\rm{z}} - 2}}} \right| = \frac{3}{2}\)What is \(\left| {\frac{{{\rm{z}} - 6}}{{{\rm{z}} + 6}}} \right|\) equal to? |
| A. | 3 |
| B. | 2 |
| C. | 1 |
| D. | 0 |
| Answer» E. | |
| 81. |
Find the real and imaginary part of the complex number \(z=\frac{1-i}{i}\) |
| A. | 1 ,1 |
| B. | -1 ,1 |
| C. | 1 , -1 |
| D. | -1 , -1 |
| Answer» E. | |
| 82. |
If x = 1 + i, then what is the value of x6 + x4 + x2 + 1? |
| A. | 6i - 3 |
| B. | -6i + 3 |
| C. | -6i - 3 |
| D. | 6i + 3 |
| Answer» D. 6i + 3 | |
| 83. |
If ω is a complex cube root of unit, then 1 + ω + ω2 + ... + ω100 is equal to |
| A. | 0 |
| B. | 1 + ω |
| C. | 1 - ω |
| D. | ω |
| Answer» C. 1 - ω | |
| 84. |
Consider the following statements:1. z1 z2 z3 is purely imaginary.2. z1z2 + z2z3 + z3z1 is purely real.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» D. Neither 1 nor 2 | |
| 85. |
If z = eiθ, then the value of \(\frac{{{z^2} - 1}}{{{z^2} + 1}}\) is: |
| A. | i tan θ |
| B. | tan θ |
| C. | i cot θ |
| D. | i sec2 θ |
| Answer» B. tan θ | |
| 86. |
If a = cos α + i sin α, b = cos β + i sin β, c = cos γ + i sin γ and \(\frac {b}{c} + \frac {c}{a} + \frac {a}{b} = 1\) then [cos (β - γ) + cos (γ - α) + cos (α - β)] is equal to: |
| A. | 3 / 2 |
| B. | -3 / 2 |
| C. | 0 |
| D. | 1 |
| Answer» E. | |
| 87. |
If two complex numbers are equal |
| A. | Only their magnitude will be equal |
| B. | Only their angles will be equal |
| C. | Their in phase and quadrature components will be separately equal |
| D. | Only their angles will not be equal |
| Answer» D. Only their angles will not be equal | |
| 88. |
If z1 and z2 are complex numbers with |z1| = |z2|, then which of the following is/are correct?1. z1 = z22. Real part of z1 = Real part of z23. Imaginary part of z1 = Imaginary part of z2Select the correct answer using the code given below: |
| A. | 1 only |
| B. | 2 only |
| C. | 3 only |
| D. | None |
| Answer» E. | |
| 89. |
If Z = 1 + i, where i = √-1, then what is the modulus of \(\rm z+\frac{2}{z}?\) |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» C. 3 | |
| 90. |
If \({\left( {\frac{{1 + i}}{{1 - i}}} \right)^x} = 1\), then |
| A. | x = 2n + 1, where n is any positive integer |
| B. | x = 2n, where is n is any positive integer |
| C. | x = 4n + 1, where n is any positive integer |
| D. | x = 4n, where is n is any positive integer |
| Answer» E. | |
| 91. |
If ω is a cube root of unity, then the value of (1 - ω + ω2) (1 + ω - ω2) is |
| A. | 1 |
| B. | -1 |
| C. | 4 |
| D. | -4 |
| Answer» D. -4 | |
| 92. |
Consider the following statements in respect of an arbitrary complex number Z:1. The difference of Z and its conjugate is an imaginary number.2. The sum of Z and its conjugate is a real number.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» D. Neither 1 nor 2 | |
| 93. |
Let z0 be a root of the quadratic equation, x2 + x + 1 = 0. If \(z = 3 + 6iz_0^{81} - 3iz_0^{93}\), then arg z is equal to: |
| A. | π/4 |
| B. | π/6 |
| C. | π/3 |
| D. | 0 |
| Answer» B. π/6 | |
| 94. |
Let z ∈ C with Im(z) = 10 and it satisfies \(\frac{{2z - n}}{{2z + n}} = 2i - 1\) for some natural number n. Then: |
| A. | n = 20 and Re(z) = -10 |
| B. | n = 40 and Re(z) = 10 |
| C. | n = 40 and Re(z) = -10 |
| D. | n = 20 and Re(z) = 10 |
| Answer» D. n = 20 and Re(z) = 10 | |
| 95. |
If α and β are different complex numbers with |β| = 1, then \(\left| {\frac{{\beta - \alpha }}{{1 - \bar \alpha \,\,\beta }}} \right|\) is equal to |
| A. | 0 |
| B. | 1/2 |
| C. | 1 |
| D. | 2 |
| Answer» D. 2 | |
| 96. |
If \(\left| {z - \frac{4}{z}} \right| = 2\), then the maximum value of |z| is equal to |
| A. | \(1 + \sqrt 3 \) |
| B. | \(1 + \sqrt 5\) |
| C. | \(1 - \sqrt 5\) |
| D. | \(\sqrt 5 - 1\) |
| Answer» C. \(1 - \sqrt 5\) | |
| 97. |
If A + iB = tan (x + iy), then the value of tan 2x is as |
| A. | \(\frac{2A}{1+A^2 + B^2}\) |
| B. | \(\frac{2A}{1-A^2+B^2}\) |
| C. | \(\frac{2A}{1-A^2-B^2}\) |
| D. | None of these |
| Answer» D. None of these | |
| 98. |
If A = {x ϵ Z : x3 – 1 = 0} and B = {x ϵ Z: x2 + x + 1= 0}, where Z is set of complex numbers, then what is A ∩ B equal to? |
| A. | Null set |
| B. | \(\left\{ {\frac{{ - 12 + \sqrt 3 i}}{2},\frac{{ - 1 - \sqrt 3 i}}{2}} \right\}\) |
| C. | \(\left\{ {\frac{{ - 1 + \sqrt 3 i}}{4},\frac{{ - 1 - \sqrt 3 i}}{4}} \right\}\) |
| D. | \(\left\{ {\frac{{-1 + \sqrt 3 i}}{2},\frac{{-1 - \sqrt 3 i}}{2}} \right\}\) |
| Answer» E. | |
| 99. |
Let Z be the set of integers. If \({\rm{A}} = \left\{ {{\rm{x}} \in {\rm{Z}}:{2^{\left( {{\rm{x}} + 2} \right)\left( {{{\rm{x}}^2} - 5{\rm{x}} + 6} \right)}} = 1} \right\}{\rm{\;}}\) and B = {x ∈ Z : - 3 < 2x – 1 < 9} then the number of subsets of the set A × B, is |
| A. | 212 |
| B. | 218 |
| C. | 215 |
| D. | 210 |
| Answer» D. 210 | |
| 100. |
If rectangular form of complex number is shown as \(z = \frac{5}{2} + \frac{{5\sqrt 3 }}{2}i\) then its polar form is represented as – |
| A. | \(5\left( {\cos \left( {\frac{{2\pi }}{3}} \right) - isin\left( {\frac{{2\pi }}{3}} \right)} \right)\) |
| B. | \(5\left( {\cos \left( {\frac{\pi }{3}} \right) - isin\left( {\frac{\pi }{3}} \right)} \right)\) |
| C. | \(5\left( {\cos \left( {\frac{{2\pi }}{3}} \right) + isin\left( {\frac{{2\pi }}{3}} \right)} \right)\) |
| D. | \(5\left( {\cos \left( {\frac{\pi }{3}} \right) + isin\left( {\frac{\pi }{3}} \right)} \right)\) |
| Answer» E. | |