A man running a race course notes that the sum of the distances from two flag posts from him is always $10\,\text{m}$ and the distance between the flag posts is $8\,\text{m}$. The equation of the path traced by the man is:
Previous 10 Questions — JAMIA MILLIA ISLAMIA MCA 2019
Nearest first
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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
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
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
The orthocentre of the triangle formed by $(0,0)$, $(4,0)$ and $(3,4)$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
If the sum of two numbers is 6 times their geometric mean, then the numbers are in the
Topic: JAMIA MILLIA ISLAMIA MCA 2019
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
The remainder when $27^{40}$ is divided by $12$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
The sum of integers from 1 to 100 that are divisible by 2 or 5 is:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
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
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
Next 10 Questions — JAMIA MILLIA ISLAMIA MCA 2019
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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
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
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
Evaluate $\displaystyle \lim_{x\to 0}\frac{\sqrt{1-\cos 2x}}{x}$.
Topic: JAMIA MILLIA ISLAMIA MCA 2019
The mean of $5$ observations is $4.4$ and their variance is $8.24$. If three observations are $1,2,6$, the other two ob…
Topic: JAMIA MILLIA ISLAMIA MCA 2019
Three letters are dictated to three persons and an envelope is addressed to each of them.
The letters are inserted in…
Topic: JAMIA MILLIA ISLAMIA MCA 2019
A tourist visits four cities A, B, C and D in a random order.
What is the probability that he visits A before B?
Topic: JAMIA MILLIA ISLAMIA MCA 2019
The function $f:[0,3] \to [1,29]$ defined by
$f(x) = 2x^3 - 15x^2 + 36x + 1$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
If $f:\mathbb{R}\to\mathbb{R}$ is given by $f(x) = (3 - x^3)^{1/3}$,
then $f(f(f(f(x))))$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
If the matrix $A$ is both symmetric and skew-symmetric, then:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
