# Previous GATE Questions

1
Raman is confident of speaking English _______six months as he has been practising regularly_______the last three weeks during, for for, since for, in within, for
1 vote
2
His knowledge of the subject was excellent but his classroom performance was_______. extremely poor good desirable praiseworthy
3
Select the word that fits the analogy: Cook : Cook :: Fly : _______ Flyer Flying Flew Flighter
1 vote
4
The dawn of the $21$st century witnessed the melting glaciers oscillating between giving too much and too little to billions of people who depend on them for fresh water. The UN climate report estimates that without deep cuts to man-made emissions, at ... water to billions of people. Billions of people are responsible foe man-made emissions. Billions of people are affected by melting glaciers.
5
There are multiple routes to reach from node $1$ to node $2$, as shown in the network. The cost of travel on an edge between two nodes is given in rupees. Nodes a', b', c', d', e', and f' are toll booths. The toll price at toll booths marked a' and e' is Rs. $200$, and is ... the other toll booths. Which is the cheapest route from node $1$ to node $2$? $1-a-c-2$ $1-f-b-2$ $1-b-2$ $1-f-e-2$
6
Goods and Services Tax (GST) is an indirect tax introduced in India in $2017$ that is imposed on the supply of goods and services, and it subsumes all indirect taxes except few. It is a destination-based tax imposed on goods and services used, and it is not ... includes all indirect taxes. GST does not have a component specific to UT. GST is imposed at the point of usage of goods and services.
7
If $P = 3$, $R = 27$, $T = 243$, then $Q + S =$ ________ $40$ $80$ $90$ $110$
8
The figure below shows an annular ring with outer and inner as $b$ and $a$, respectively. The annular space has been painted in the form of blue colour circles touching the outer and inner periphery of annular space. If maximum $n$ ... $\pi [(b^{2}-a^{2})+n(b-a)^{2}]$
9
Two straight lines are drawn perpendicular to each other in $X-Y$ plane. If $\alpha$ and $\beta$ are the acute angles the straight lines make with the $\text{X-}$ axis, then $\alpha + \beta$ is_______. $60^{\circ}$ $90^{\circ}$ $120^{\circ}$ $180^{\circ}$
10
The total revenue of a company during $2014-2018$ is shown in the bar graph. If the total expenditure of the company in each year is $500$ million rupees, then the aggregate profit or loss (in percentage) on the total expenditure of the company during $2014-2018$ is ___________. $16.67 \%$ profit $16.67 \%$ loss $20 \%$ profit $20 \%$ loss
11
Consider the functions $e^{-x}$ $x^{2}-\sin x$ $\sqrt{x^{3}+1}$ Which of the above functions is/are increasing everywhere in $[ 0,1]$? Ⅲ only Ⅱ only Ⅱ and Ⅲ only Ⅰ and Ⅲ only
12
For parameters $a$ and $b$, both of which are $\omega(1)$, $T(n) = T(n^{1/a})+1$, and $T(b)=1$. Then $T(n)$ is $\Theta (\log_a \log _b n)$ $\Theta (\log_{ab} n$) $\Theta (\log_{b} \log_{a} \: n$) $\Theta (\log_{2} \log_{2} n$)
13
Consider the following statements. Daisy chaining is used to assign priorities in attending interrupts. When a device raises a vectored interrupt, the CPU does polling to identify the source of interrupt. In polling,the CPU periodically checks the status bits to know if any device needs its ... same time. Which of the above statements is/are TRUE? Ⅰ and Ⅱ only Ⅰ and Ⅳ only Ⅰ and Ⅲ only Ⅲ only
14
Consider the following data path diagram. Consider an instruction: $R0 \leftarrow R1 +R2$. The following steps are used to execute it over the given data path. Assume that PC is incremented appropriately. The subscripts $r$ and $w$ ... of execution of the above steps? $2,1,4,5,3$ $1,2,4,3,5$ $3,5,2,1,4$ $3,5,1,2,4$
15
The preorder traversal of a binary search tree is $15, 10, 12, 11, 20, 18, 16, 19$. Which one of the following is the postorder traversal of the tree? $10,11,12,15,16,18,19,20$ $11,12,10,16,19,18,20,15$ $20,19,18,16,15,12,11,10$ $19,16,18,20,11,12,10,15$
1 vote
16
What is the worst case time complexity of inserting $n^{2}$ elements into an AVL-tree with $n$ elements initially? $\Theta (n^{4})$ $\Theta (n^{2})$ $\Theta (n^{2}\log n)$ $\Theta (n^{3})$
17
Which one of the following regular expressions represents the set of all binary strings with an odd number of $1’$s? $((0+1)^*1(0+1)^*1)^*10^*$ $(0^*10^*10^*)^*0^*1$ $10^*(0^*10^*10^*)^*$ $(0^*10^*10^*)^*10^*$
Consider the following statements. If $L_1 \cup L_2$ is regular, then both $L_1$ and $L_2$ must be regular. The class of regular languages is closed under infinite union. Which of the above statements is/are TRUE? Ⅰ only Ⅱ only Both Ⅰ and Ⅱ Neither Ⅰ nor Ⅱ
Consider the language $L = \{a^{n}\mid n \geq 0\} \cup \{a^{n}b^{n}\mid n \geq 0\}$ and the following statements. $L$ is deterministic context-free. $L$ is context-free but not deterministic context-free. $L$ is not $LL(k)$ for any $k$. Which of the above statements is/are TRUE? Ⅰ only Ⅱ only Ⅰ and Ⅲ only Ⅲ only