Aspire Faculty ID #14046 · Topic: JAMIA MILLIA ISLAMIA MCA 2019 · Just now
JAMIA MILLIA ISLAMIA MCA 2019

Evaluate $\displaystyle \lim_{x\to 0}\frac{\sqrt{1-\cos 2x}}{x}$.

Solution

$1-\cos 2x=2\sin^2 x \Rightarrow \dfrac{\sqrt{1-\cos 2x}}{x}=\sqrt{2},\dfrac{|\sin x|}{x}$. As $x\to0^+$, this $\to\sqrt{2}$; as $x\to0^-$, it $\to -\sqrt{2}$. Thus two-sided limit does not exist; the right-hand limit is $\sqrt{2}$.
← Previous Next →

Previous 10 Questions — JAMIA MILLIA ISLAMIA MCA 2019

Nearest first
1
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
 2
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
 3
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
 4
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
 5
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
 6
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
 7
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
 8
The orthocentre of the triangle formed by $(0,0)$, $(4,0)$ and $(3,4)$ is:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 9
If the sum of two numbers is 6 times their geometric mean, then the numbers are in the
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 10
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

Next 10 Questions — JAMIA MILLIA ISLAMIA MCA 2019

Ascending by ID
1
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
 2
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
 3
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
 4
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
 5
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
 6
If the matrix $A$ is both symmetric and skew-symmetric, then:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 7
If $A = \begin{bmatrix} 3 & -9 \\ -12 & 6 \end{bmatrix}$, then $\operatorname{adj}(3A + 12A^2)$ is equal to:
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 8
If $a,b,c$ are in A.P., then the value of determinant $\begin{vmatrix} x+2 & x+3 & x+2a \\ x+3 & x+4 & x+2b \\ x+4 & …
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 9
If a determinant of order $3\times3$ is formed using numbers $1$ or $-1$, then the minimum value of the determinant i…
Topic: JAMIA MILLIA ISLAMIA MCA 2019
 10
Consider two functions $f(x)$ and $g(x)$ such that $f(x) = |x| + [x]$ and $g(x) = |x|[x]$, where $[x]$ denotes the …
Topic: JAMIA MILLIA ISLAMIA MCA 2019
Ask Your Question or Put Your Review.

loading...