If $\omega$ is a complex cube root of unity, then the value of $\dfrac{p + q\omega + r\omega^2}{r + p\omega + q\omega^2} + \dfrac{p + q\omega + r\omega^2}{q + r\omega + p\omega^2}$ $(p,q,r \in R)$ is equal to
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A real value of $x$ will satisfy the equation $\left(\dfrac{3 - 4ix}{3 + 4ix}\right)=\alpha - i\beta; (\alpha,\beta \te…
Topic: AMU MCA 2019
The standard deviation of a variable $x$ is $10$. Then the standard deviation of $50 + 5x$ is
Topic: AMU MCA 2019
The probability that in a year of the $22^{\text{nd}}$ century chosen at random, there will be $53$ Sundays, is
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Two persons $A$ and $B$ take turns in throwing a pair of dice. The first person to throw $9$ from both dice will be awa…
Topic: AMU MCA 2019
A five digits number is formed by writing the digits $1,2,3,4,5$ in a random order without repetitions. Then the probab…
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If $A, B, C, D$ are the points $(2,3,-1), (3,5,-3), (1,2,3), (3,5,7)$ respectively, then the angle between $AB$ and $CD…
Topic: AMU MCA 2019
If the point $(a, a)$ falls between the lines $|x + y| = 4$, then
Topic: AMU MCA 2019
The equation of the plane through the intersection of the planes $x + y + z = 1$ and $2x + 3y - z + 4 = 0$ and parallel…
Topic: AMU MCA 2019
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If $P, Q, R, S$ are represented by the complex numbers $4+i, 1+6i, -4+3i, -1-2i$ respectively, then $PQRS$ is a
Topic: AMU MCA 2019
If $n$ is a positive integer, then $(1+i)^n + (1-i)^n$ is equal to
Topic: AMU MCA 2019
The number of ways in which $9$ persons can be divided into three equal groups is
Topic: AMU MCA 2019
A dictionary is printed consisting of $7$ letters words only that can be made with letters of word $CRICKET$. If the wo…
Topic: AMU MCA 2019
If the sum of the coefficient in the expansion of $(x + y)^n$ is $1024$, then the value of the greatest coefficient in …
Topic: AMU MCA 2019
An investigator interviewed $100$ students to determine the performance of three drinks milk, coffee and tea. The inves…
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Let $Y={1,2,3,4,5},; A={1,2},; B={3,4,5}$ and $\phi$ denotes null set. If $(A \times B)$ denotes cartesian product of t…
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Let $A={2,3,4,5,\ldots,16,17,18}$. Let $\approx$ be the equivalence relation on $A \times A$ cartesian product of $A$ a…
Topic: AMU MCA 2019
If $a, b$ be two fixed positive integers such that $f(a + x)= b + \left[b^3 + 1 - 3b^2 f(x) + 3b{f(x) - (f(x))^3}\right…
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The domain of the function $f(x)=\log_{3+x}(x^2 - 1)$ is
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