Explore topic-wise MCQs in General Aptitude.

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.

101.

If cube root of unity are 1, ω, ω2 then the roots of equation (x - 1)3 + 8 = 0 are

A. -1, -1 + 2ω, -1 - 2ω2
B. -1, -1, -1
C. -1, 1 - 2ω, 1 – 2ω2
D. -1, -1 + 2ω, 1 + 2ω2
Answer» D. -1, -1 + 2ω, 1 + 2ω2
Discussion
102.

For the complex numbers z1 = 2 + 3i and z2 = 4 - 5i, the value of (z1 + z2)2 is

A. 32 - 24i
B. -32 - 24i
C. 32 + 24i
D. -32 + 24i
Answer» B. -32 - 24i
Discussion
103.

A particle P starts from the point z0 = 1 + 2i, where \(\rm i = \sqrt{-1}\). It moves first horizontally away from the origin by 5 units and then vertically away from origin by 3 units to reach a point z1. From z1 the particle moves √2 units in the direction of the vector î + ĵ to reach z2, and then it moves through an angle \(\rm \frac{\pi}{2}\) in an anti-clock-wise direction on a circle with center at origin, to reach a point z3. The point z3 is given by:

A. 6 + 7i
B. -7 + 6i
C. 7 + 6i
D. -6 + 7i
Answer» E.
Discussion
104.

If \({\rm{z}} = {\left( {\frac{{\sqrt 3 }}{2} + \frac{{\rm{i}}}{2}} \right)^{107}} + {\left( {\frac{{\sqrt 3 }}{2} - \frac{{\rm{i}}}{2}} \right)^{107}}\), then what is the imaginary part of z equal to?

A. 0
B. \(\frac{1}{2}\)
C. \(\frac{{\sqrt 3 {\rm{\;\;}}}}{2}\)
D. -1
Answer» B. \(\frac{1}{2}\)
Discussion
105.

If the area of the triangle on the complex plane formed by the points z, z + iz and iz is 50, then |z| is

A. 1
B. 5
C. 10
D. 100
Answer» D. 100
Discussion
106.

Geometrically Re (z2 – i) = 2, where \(i = \sqrt { - 1} \) and Re is the real part, represents

A. Circle
B. Ellipse
C. Rectangular hyperbola
D. Parabola
Answer» D. Parabola
Discussion
107.

If |z| < √3 - 1, then |z2 + 2z cos α| is

A. less than 2
B. √3 + 1
C. √3 - 1
D. None of these T1 T2
Answer» B. √3 + 1
Discussion
108.

(3 + i)/(5 + 5i) is same as

A. (2 - i)/5
B. 3 - i
C. 5 - 5i
D. (2 + i)/5
Answer» B. 3 - i
Discussion
109.

For any complex number Z, the minimum value of IzI + Iz - 1I is:

A. 1
B. 0
C. 1/2
D. 3/2
Answer» B. 0
Discussion
110.

If |z + 4| ≤ 3, then the maximum value of |z + 1| is

A. 0
B. 4
C. 6
D. 10
Answer» D. 10
Discussion
111.

Let z1 and z2 be two complex numbers satisfying |z1| = 9 and |z2 – 3 – 4i|= 4 . Then, the minimum value of |z1 – z2| is

A. 1
B. 2
C. \(\sqrt 2\)
D. 0
Answer» E.
Discussion
112.

In complex numbers, the value of i37 =

A. 37i
B. i
C. -i
D. -37i
Answer» C. -i
Discussion
113.

If \(x + iy = \sqrt {\frac{{a + ib}}{{c + id}}}\), then the value of x2 + y2 is -

A. \(\sqrt {\frac{{{a^2} + {b^2}}}{{{c^2} + {d^2}}}}\)
B. \({\frac{{{a^2} + {b^2}}}{{{c^2} + {d^2}}}}\)
C. ad - bc
D. \(\sqrt {\frac{{a - ib}}{{a + ib}}}\)
Answer» B. \({\frac{{{a^2} + {b^2}}}{{{c^2} + {d^2}}}}\)
Discussion
114.

If \(\mathop {{\rm{lim}}}\limits_{x \to 1} \frac{{{x^2} - ax + b}}{{x - 1}} = 5\), then a + b is equal to:

A. -4
B. 5
C. -7
D. 1
Answer» D. 1
Discussion
115.

If the point z1 = 1 + i where \({\rm{i}} = \sqrt { - 1} \) is the reflection of a point z2 = x + iy in the line iz̅ - iz = 5, then the point z2 is

A. 1 + 4i
B. 4 + i
C. 1 - i
D. -1 - i
Answer» B. 4 + i
Discussion
116.

If z = x + iy then area of the triangle whose vertices are z, iz and z + iz is :

A. \(2|z|^2\)
B. \(\dfrac{1}{2}|z|^2\)
C. \(|z|^2\)
D. \(\dfrac{3}{2}|z|^2\)
Answer» C. \(|z|^2\)
Discussion
117.

If a phasor is multiplied by j then

A. Only its magnitude changes
B. Only its direction changes
C. Both magnitude and direction changes
D. Both magnitude and direction remains unchanged
Answer» C. Both magnitude and direction changes
Discussion
118.

If \(x+iy=\begin{vmatrix}6i & -3i & 1 \\\ 4 & 3i & -1 \\\ 20 & 3 & i \end{vmatrix}\) then what is x - iy equal to?

A. 3 + i
B. 1 + 3i
C. 3i
D. 0
Answer» E.
Discussion
119.

Absolute value of z = x + iy is

A. \(\left| z \right| = \sqrt {\left( {{x^2}{y}} \right)}\)
B. \(\left| z \right| = \sqrt {\left( {{x^2}/{y^2}} \right)}\)
C. \(\left| z \right| = \sqrt {\left( {{x^2} - {y^2}} \right)}\)
D. \(\left| z \right| = \sqrt {\left( {{x^2}+{y^2}} \right)}\)
Answer» E.
Discussion
120.

If \({\rm{Re}}\left( {\frac{{{\rm{z}} - 1}}{{{\rm{z}} + 1}}} \right) = 0,\) where z = x + iy is a complex number, then which one of following is correct?

A. z = 1 + i
B. |z| = 2
C. z = 1 - i
D. |z| = 1
Answer» E.
Discussion
121.

If \({\rm{z}} = {\rm{}} - \frac{{2\left( {1\; + \;2{\rm{i}}} \right)}}{{3\; + \;{\rm{i}}}}\) Where \(i = \sqrt { - 1}\) then the argument θ (-π < θ ≤ π) of z is

A. \(\frac{{3\pi }}{4}\)
B. \(\frac{\pi }{4}\)
C. \(\frac{{5\pi }}{6}\)
D. \(- \frac{{3\pi }}{4}\)
Answer» E.
Discussion
122.

Let \(A = \left\{ {\theta \in \left( { - \frac{\pi }{2},{\rm{\;}}\pi } \right):\frac{{3 + 2i\;sin\theta }}{{1 - 2i\;sin\theta }}{\rm{\;is\;purely\;imaginary}}} \right\}\). Then the sum of elements in A is:

A. \(\frac{{5\pi }}{6}\)
B. π
C. \(\frac{{3\pi }}{4}\)
D. \(\frac{{2\pi }}{3}\)
Answer» E.
Discussion
123.

Evaluate \(\mathop \oint \nolimits_{\rm{c}}^{} \frac{{{\rm{Z}} + 2}}{{\rm{Z}}}{\rm{dz}}\) where c is |Z - 2| = 1

A. π
B. 2πi
C. πt
D. 0
Answer» E.
Discussion
124.

If \(\frac{z-\alpha }{z+\alpha }\) (α ∈ R) is a purely imaginary number and |z| = 2, then a value of α is number and |z| = 2, then a value of α is

A. √2
B. 1/2
C. 1
D. 2
Answer» E.
Discussion
125.

If sin2(x + iy) = A + iB, then value of A is

A. \(\frac{1}{2}(1+cos2x\:cosh\:2y)\)
B. \(\frac{1}{2}(1-cos2x\:cosh\:2y)\)
C. \(\frac{1}{2}(sin2x\:sinh\:2y)\)
D. \(-\frac{1}{2}(sin2x\:sinh\:2y)\)
Answer» C. \(\frac{1}{2}(sin2x\:sinh\:2y)\)
Discussion
126.

If \(\left| {z + \bar {z}\ |= \;} \right|z - \bar z|\), then the locus of z is

A. A pair of straight lines
B. A line
C. A set of four straight lines
D. A circle
Answer» B. A line
Discussion