Rafi told Mary, βI am thinking of watching a film this weekend.β The following reports the above statement in indirect speech: Rafi told Mary that he __________ of watching a film that weekend.
1
thought
2
is thinking
3
am thinking
4
was thinking
Official Solution
Correct Option: (4)
Step 1: Identify the tense in direct speech. The original statement is: βI am thinking of watching a film this weekend.β Here, the verb tense is present continuous (βam thinkingβ). Step 2: Apply the rule of tense change in indirect speech. When reporting speech, if the reporting verb (e.g., βtoldβ) is in past tense, the tense of the reported statement generally shifts back: - Present continuous Past continuous. Step 3: Apply the change. βI am thinkingβ βhe was thinkingβ. Also, βthis weekendβ βthat weekendβ. Step 4: Construct the indirect sentence. Thus, the correct indirect speech is: Final Answer:
02
PYQ 2023
medium
general-aptitudeID: gate-es-
How many triangles are present in the given figure?
1
12
2
16
3
20
4
24
Official Solution
Correct Option: (4)
Step 1: Observe the figure. The figure is a large quadrilateral (a slanted parallelogram-like shape) divided by several lines: - Two vertical slanting lines divide it into three main sections. - Two diagonal slanting lines across each section further subdivide the shape. Step 2: Count small triangles. Each smaller region formed by the internal lines can be broken into triangles. Carefully counting the simplest (smallest) triangles across all regions gives 12 small triangles. Step 3: Count larger triangles. By combining two or more small triangles, larger triangles are also formed: - Triangles formed by combining two adjacent small ones = 8. - Triangles formed by combining three or more adjacent ones = 4. Step 4: Total count. Adding them together: Final Answer:
03
PYQ 2023
medium
general-aptitudeID: gate-es-
Students of all the departments of a college who have successfully completed the registration process are eligible to vote in the upcoming college elections. However, by the time the due date for registration was over, it was found that surprisingly none of the students from the Department of Human Sciences had completed the registration process. Based only on the information provided above, which one of the following sets of statement(s) can be logically inferred with certainty? (i) All those students who would not be eligible to vote in the college elections would certainly belong to the Department of Human Sciences. (ii) None of the students from departments other than Human Sciences failed to complete the registration process within the due time. (iii) All the eligible voters would certainly be students who are not from the Department of Human Sciences.
1
(i) and (ii)
2
(i) and (iii)
3
only (i)
4
only (iii)
Official Solution
Correct Option: (4)
Step 1: Recall the given fact. It is stated that none of the students from the Department of Human Sciences completed the registration process. This means: - All Human Sciences students are ineligible to vote. - Eligible voters must come only from other departments. Step 2: Examine statement (i). (i) says: βAll those students who would not be eligible to vote in the college elections would certainly belong to Human Sciences.β This is not true, because some students from other departments might also have failed to register, but we donβt have data about that. Hence (i) cannot be inferred with certainty. Step 3: Examine statement (ii). (ii) says: βNone of the students from departments other than Human Sciences failed to complete the registration process.β We are not told this. Some students in other departments might have failed too. No certainty here. Step 4: Examine statement (iii). (iii) says: βAll the eligible voters would certainly be students who are not from Human Sciences.β This is true, since Human Sciences students completed no registrations, making them all ineligible. Thus only non-Human Sciences students could be voters. Final Answer:
04
PYQ 2023
medium
general-aptitudeID: gate-es-
Which one of the following options represents the given graph?
1
2
3
4
Official Solution
Correct Option: (2)
Step 1: Analyze graph behavior near origin. The graph passes through the origin, which suggests that . Step 2: Analyze behavior for positive . For , the function rises to a positive peak and then decays towards zero. This matches the form , where the exponential decay dominates for large . Step 3: Analyze behavior for negative . For , the graph goes below the axis (negative values) and approaches as . This matches , because for , , giving , which is negative but approaches 0 as . Step 4: Eliminate other options. - (A) is always non-negative (since ), but the graph shows negative values for . Wrong. - (C) is always non-negative as well. Wrong. - (D) is not symmetric with respect to , and doesnβt match the decay behavior. Wrong. Hence, the correct function is (B). Final Answer: