1
GATE CSE 2023
+2
-0.67

Consider two functions of time (t),

$$f(t)=0.01\,t^2$$

$$g(t)=4\,t$$

where $$0 < t < \infty$$.

Now consider the following two statements :

(i) For some $$t > 0,g(t) > f(t)$$.

(ii) There exists a $$T$$, such that $$f(t) > g(t)$$ for all $$t > T$$.

Which one of the following options is TRUE?

A
only (i) is correct
B
only (ii) is correct
C
both (i) and (ii) are correct
D
neither (i) nor (ii) is correct
2
GATE CSE 2023
+2
-0.67

$$f(x)$$ and $$g(y)$$ are functions of x and y, respectively, and $$f(x)=g(y)$$ for all real values of x and y. Which one of the following options is necessarily TRUE for al x and y?

A
$$f(x)=0$$ and $$g(y)=0$$
B
$$f(x)=g(y)=$$ constant
C
$$f(x)\ne$$ constant and $$g(y)\ne$$ constant
D
$$f(x)+g(y)=f(x)-g(y)$$
3
GATE CSE 2021 Set 2
+2
-0.67
The number of student in three classes is in the ratio 3 : 13 : 6. If 18 students are added to each class, the ratio changes to 15 : 35 : 21.

The total number of students in all the three classes in the beginning was :
A
88
B
110
C
66
D
22
4
GATE CSE 2021 Set 2
+2
-0.67 The number of units of a product sold in three different years and the respective net profits are presented in the figure above. The cost/unit in year 3 was Rs. 1, which was half the cost/unit in year 2. The cost/unit in year 3 was one-third of the cost/unit in year 1. Taxes were paid on the selling price at 10%, 13% and 15% respectively for the three years. Net profit is calculated as the difference between the selling price and the sum of cost and taxes paid in that year.

The ratio of the selling price in Year 2 to the selling price in Year 3 is _______
A
3 : 4
B
1 : 2
C
1 : 1
D
4 : 3
GATE CSE Subjects
Theory of Computation
Operating Systems
Algorithms
Digital Logic
Database Management System
Data Structures
Computer Networks
Software Engineering
Compiler Design
Web Technologies
General Aptitude
Discrete Mathematics
Programming Languages
Computer Organization
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