Aspire Faculty ID #14035 · Topic: JAMIA MILLIA ISLAMIA MCA 2019 · Just now
JAMIA MILLIA ISLAMIA MCA 2019

The remainder when $27^{40}$ is divided by $12$ is:

Solution

We use modulo properties: $27 \equiv 3 \pmod{12}$ $\Rightarrow 27^{40} \equiv 3^{40} \pmod{12}$ Now, $3^1 \equiv 3$, $3^2 \equiv 9$, $3^3 \equiv 3$, $3^4 \equiv 9$, pattern repeats every 2 powers. So, for even power $40$, remainder = $9$.
← Previous Next →

Previous 10 Questions — JAMIA MILLIA ISLAMIA MCA 2019

Nearest first
1
The sum of integers from 1 to 100 that are divisible by 2 or 5 is:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 2
If $x + y + z = 5$ and $xy + yz + zx = 3$, then the least and greatest values of $x$ are:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 3
If $\omega$ is a cube root of unity and $(1 + \omega)^7 = A + B\omega$, then $A + B$ equals:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 4
The number of complex numbers $Z$ such that $|Z - 1| = |Z + 1| = |Z - i|$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 5
The value of $\tan\left(\frac{\pi}{8}\right)$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 6
The product of two binary numbers $00001101_2$ and $00001111_2$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 7
$\cot x - \cot 2x + \cot 3x - \cot 3x \cdot \cot 2x \cdot \cot x$ equals:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 8
The value of $\tan^{-1}(\tan 13)$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 9
If A, B and C are three sets such that $A \cap B = A \cap C$ and $A \cup B = A \cup C$, then:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 10
Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of $A \times B$ havi…
Topic: JAMIA MILLIA ISLAMIA MCA 2019

Next 10 Questions — JAMIA MILLIA ISLAMIA MCA 2019

Ascending by ID
1
The sum of the series $1 + \dfrac{1}{4 \cdot 2!} + \dfrac{1}{16 \cdot 4!} + \dfrac{1}{64 \cdot 6!} + \cdots$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 2
If the sum of two numbers is 6 times their geometric mean, then the numbers are in the
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 3
The orthocentre of the triangle formed by $(0,0)$, $(4,0)$ and $(3,4)$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 4
A ray of light passing through the point $(1,2)$ reflects on the $X$–axis at point $A$, and the reflected ray passes …
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 5
From a point on the circle $x^2 + y^2 = a^2$, tangents are drawn to the circle $x^2 + y^2 = b^2$. The chord of contac…
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 6
If the chord of contact of tangents from a point $P$ to the parabola $y^2 = 4 a x$ touches the parabola $x^2 = 4 b y$…
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 7
A man running a race course notes that the sum of the distances from two flag posts from him is always $10\,\text{m}$…
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 8
The vertices of a parallelogram $ABCD$ are $A(3,-1,2)$, $B(1,2,-4)$ and $C(-1,1,2)$. The fourth vertex $D$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 9
If all words (with or without meaning) formed using letters of “JAMIA” are arranged in dictionary order, what is the 50…
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 10
Evaluate $\displaystyle \lim_{x\to 0}\left\lfloor \frac{\sin x}{x}\right\rfloor$, where $[;]$ denotes the greatest-inte…
Topic: JAMIA MILLIA ISLAMIA MCA 2019
Ask Your Question or Put Your Review.

loading...