# Recent questions tagged gate2018-ch 1 vote
1
The deacy ratio for a system having complex conjugate poles as $(-\dfrac{1}{10} + j\dfrac{2}{15})$ and $(-\dfrac{1}{10} - j\dfrac{2}{15})$ is $7\times10^{-1}$ $8\times10^{-2}$ $9\times10^{-3}$ $10\times10^{-4}$
1 vote
2
The figure which represents $y = \dfrac{sin x}{x}$ for $x>0$ ($x$ in radians) is
1 vote
3
If $y = e^{-x^2}$ then the value of $\displaystyle\lim_{x \to \infty} \dfrac{1}{x}\dfrac{\mathrm{d}y}{\mathrm{d}x}$ is _________ .
1 vote
4
For the matrix $A = \begin{bmatrix}\cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$ if $\textit{det}$ stands for the determinant and $A^T$ is the transpose of $A$ then the value of $\textit{det}(A^TA)$ is __________ .
5
A set of $4$ parallel lines intersect with another set of $5$ parallel lines. How many parallelograms are formed? $20$ $48$ $60$ $72$
6
In a detailed study of annual crow births in India, it was found that there was relatively no growth during the period $2002$ to $2004$ and a sudden spike from $2004$ to $2005$. In another unrelated study, it was found that the revenue from cracker sales ... birth rate. If cracker sale declines, crow birth will decline. Increased birth rate of crows will cause an increase in the sale of crackers.
7
To pass a test, a candidate needs to answer at least $2$ out of $3$ questions correctly. A total of $6,30,000$ candidates appeared for the test. Question $A$ was correctly answered by $3,30,000$ candidates. Question $B$ was answered correctly by $2,50,000$ candidates. Question ... as the number answering none, how many candidates failed to clear the test? $30,000$ $2,70,000$ $3,90,000$ $4,20,000$
8
An automobile travels from city $A$ to city $B$ and returns to city $A$ by the same route. The speed of the vehicle during the onward and return journeys were constant at $60km/h$ and $90 km/h$, respectively. What is the average speed in $km/h$ for the entire journey? $72\hspace{0.2cm} km/h$ $73\hspace{0.2cm} km/h$ $74\hspace{0.2cm} km/h$ $75 \hspace{0.2cm}km/h$
9
"In spite of being warned repeatedly, he failed to correct his _________ behaviour ." The word that best fills the blank in the above sentence is rational reasonable errant good
10
"When she fell down the ________ , she received many _________ but little help." The words that best fill the blanks in the above sentence are stairs, stares stairs, stairs stares, stairs stares, stares
11
The area of an equilateral triangle is $\sqrt{3}$. What is the perimeter of the triangle$?$ $2$ $4$ $6$ $8$
1 vote
Arrange the following three-dimensional objects in the descending order of their volumes: A cuboid with dimensions $\text{10 cm, 8 cm and 6 cm}$ A cube of side $\text{8 cm}$ A cylinder with base radius $\text{7 cm}$ and height $\text{7 cm}$ A sphere of radius $\text{7 cm}$ $\text{i), ii), iii), iv)}$ $\text{ii), i), iv), iii)}$ $\text{iii), ii), i), iv)}$ $\text{iv), iii), ii), i)}$
For $0\leq{x}\leq{2\pi}$, $\sin x \text{ and } \cos x$ are both decreasing functions in the interval _________ . $\left(0,\dfrac{\pi}{2}\right)$ $\left(\dfrac{\pi}{2},\pi\right)$ $\left(\pi,\dfrac{3\pi}{2}\right)$ $\left(\dfrac{3\pi}{2},2\pi\right)$
If $x^{2}+ x - 1 = 0$ what is the value of $x^4 + \dfrac{1}{x^4}$? $1$ $5$ $7$ $9$