Below the 1000+ Questions with detail solution on Gate Aptitude, which were asked in previous year in all Branch of Engineering.
Question 11.
Given below are three statements and four conclusions drawn on the statements.- Statement 1: Some engineers are writers.Statement 2: No writer is an actor.
- Statement 3: All actors are engineers.Conclusion I: Some writers are engineers.Conclusion II: All engineers are actors.Conclusion II: All engineers are actors.Conclusion III: No actor is a writer.Conclusion IV: Some actors are writers.
Which one of the following options can be logically inferred?
Previously Asked in : Gate CH 2022 || Gate IN 2022 || Gate PI 2022 ||
Only conclusion I and conclusion III are correct
Only conclusion I is correct
Only conclusion II and conclusion III are correct
Either conclusion III or conclusion IV is correct
Answer (Detailed Solution Below)
Option Only conclusion I and conclusion III are correct is correct
Detailed Explanation :
Correct option is: Only conclusion I and conclusion III are correct
Question 12.
Both the numerator and denominator of \frac {3} {4} are increased by a positive integer, x , and those of \frac {15} {17} are decreased by same integer. This operation results in the same value for both the fractions.
What is the value of x ?
Previously Asked in : Gate CE-afternoon season 2022 ||
3
4
1
2
Answer (Detailed Solution Below)
Option 3 is correct
Detailed Solution :
From given statement, we can say
\Rightarrow \left(\dfrac {3+x} {4+x} \right) =\left ( \dfrac {15 - x} {17-x} \right)
Put x = 1, 2,3,4 \\ \textrm{Only} \; x = 3 is satisfying
Correct option is: 3
Question 13.
In a partnership business the monthly investment by three friends for the first six months is in the ratio 3 : 4 : 5 . After six months, they had to increase their monthly investments by 10\% , 15\% \, \textrm{and} \, 20\% respectively, of their initial monthly investment. the new investment ratio was kept constant for next six months.
What is the ratio of their shares in the total profit (in the same order) at the end of the year such that the share is proportional to their individual total investment over the year?
Previously Asked in : Gate CE-afternoon season 2022 ||
22 : 23 : 24
63 : 86 : 110
22 : 33 : 50
33 : 46 : 60
Answer (Detailed Solution Below)
Option 63 : 86 : 110 is correct
Detailed Solution :
Let capitals invested by three friends for 6months are
C_1\, = \,3x \, ; C_2\, = \,4x \, ; \, C_3 \, = \, 5x \\ P_1 : \, P_2 : \, P_3 \, = I_1 : I_2 : I_3
( notation : C- cost , P – profit and I-Investment )
\therefore P_1 : P_2 : P_3 = \\\ : \,\left (3x \times 6 \, 1.1 \times 3x \times 6 \right) \\\ : \, \left (4x \times 6 \, + \, 1.15 \times 4x \times 6\right) \\\ : \, \left (5x \times 6 \, + \, 1.2 \times 5x \times 6 \right)
= 6.3 \, : \, 8.6 \, : \, 11 \\\ = 63 : 86 : 110
Correct option is: 63 : 86 : 110
Question 14.
Both the numerator and denominator of \frac {3} {4} are increased by a positive integer, x , and those of \frac {15} {17} are decreased by same integer. This operation results in the same value for both the fractions.
What is the value of x ?
Previously Asked in : Gate CE-afternoon season 2022 ||
3
4
1
2
Answer (Detailed Solution Below)
Option 3 is correct
Detailed Solution :
From given statement, we can say
\Rightarrow \left(\dfrac {3+x} {4+x} \right) =\left ( \dfrac {15 - x} {17-x} \right)
Put x = 1, 2,3,4 \\ \textrm{Only} \; x = 3 is satisfying
Correct option is: 3
Question 15.
In a partnership business the monthly investment by three friends for the first six months is in the ratio 3 : 4 : 5 . After six months, they had to increase their monthly investments by 10\% , 15\% \, \textrm{and} \, 20\% respectively, of their initial monthly investment. the new investment ratio was kept constant for next six months.
What is the ratio of their shares in the total profit (in the same order) at the end of the year such that the share is proportional to their individual total investment over the year?
Previously Asked in : Gate CE-afternoon season 2022 ||
22 : 23 : 24
63 : 86 : 110
22 : 33 : 50
33 : 46 : 60
Answer (Detailed Solution Below)
Option 63 : 86 : 110 is correct
Detailed Solution :
Let capitals invested by three friends for 6months are
C_1\, = \,3x \, ; C_2\, = \,4x \, ; \, C_3 \, = \, 5x \\ P_1 : \, P_2 : \, P_3 \, = I_1 : I_2 : I_3
( notation : C- cost , P – profit and I-Investment )
\therefore P_1 : P_2 : P_3 = \\\ : \,\left (3x \times 6 \, 1.1 \times 3x \times 6 \right) \\\ : \, \left (4x \times 6 \, + \, 1.15 \times 4x \times 6\right) \\\ : \, \left (5x \times 6 \, + \, 1.2 \times 5x \times 6 \right)
= 6.3 \, : \, 8.6 \, : \, 11 \\\ = 63 : 86 : 110
Correct option is: 63 : 86 : 110
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Question 16.
Consider the following equations of straight lines :
Line L_1: \, 2x - 3y = 5
Line L_2 : \,3x + 2y = 8
Line L_3 : \, 4x-6y = 5
Line L_4 : \, 6x-9y = 6
which one of the following is the correct statement?
Previously Asked in : Gate CE-afternoon season 2022 ||
L4 is perpendicular to L2 and L4 is parallel to L3
L1 is parallel to L2 and L1 is perpendicular to L3
L2 is parallel to L4 and L2 is perpendicular to L1
L3 is perpendicular to L4 and L3 is parallel to L2
Answer (Detailed Solution Below)
Option L 4 is parallel to L 2 and L4 is parallel to L3 is correct
Detailed Solution :
Line L_1 : 2x-3y = 5\\ y = \dfrac {4x-5} {3}
\therefore \, \dfrac {dy} {dx} \, = \, \dfrac {2} {3}
Similarly for other lines
\textrm {Line} \, L_2 : 3x + 2y = 8 \\ \dfrac {dy} {dx} \, = \, \dfrac {-3} {2} \\ \textrm{Line} \, L_3 : 4x -6y = 5 \\ \dfrac {dy} {dx} \, = \, \dfrac{2} {3} \\ \textrm {Line} \, L_4 : 6x -9y = 6 \\ \dfrac {dy} {dx} \, = \, \dfrac{2} {3}
\therefore \quad \left (\dfrac{dy}{dx}\right)_{L_1} = \, \left (\dfrac{dy} {dx} \right)_{L_3} = \, \left (\dfrac {dy}{dx} \right)_{L_4} = \, \dfrac {2}{3}and \left(\frac{dy}{dx} \right)_{L_2} \times \left(\frac{dy}{dx}\right)_{L_1} = \left(\frac{dy}{dx} \right)_{L_2} \times \left( \frac{dy} {dx} \right)_{L_3} = \left (\frac{dy} {dx} \right)_{L_2} \times \left (\frac{dy}{dx} \right)_{L_4} = -1
\therefore L1, L3, L4 are parallel to each other and perpendicular to L2 .
Correct option is: L 4 is parallel to L 2 and L4 is parallel to L3
Question 17.
x : y : z = \frac {1}{2} : \frac {1}{3} : \frac {1}{4}
what is the value of \dfrac {x + z -y} {y} \, ?
Previously Asked in : Gate CE-afternoon season 2022 ||
1.25
0.75
2.25
3.25
Answer (Detailed Solution Below)
Option 1.25 is correct
Detailed Solution :
let x = \dfrac{A}{2} \, ; \, y = \dfrac{A}{3} \, ; \, z = \dfrac{A}{4}
\therefore \textrm{value of}\dfrac {x + z -y} {y} = \dfrac{\frac{A}{2} + \frac {A}{4} - \frac{A}{3}}{\frac{A}{3}}
\dfrac {5A}{12} \times \dfrac{3}{A} = \dfrac {5}{4}
which is equal to 1.25
Correct option is: 1.25
Question 18.
A survey of 450 students about their subjects of interest resulted in the following outcome.- 150 students are interested in Mathematics.200 students are interested in Physics.175 students are interested in Chemistry.50 students are interested in Mathematics and Physics.60 students are interested in Physics and Chemistry.40 students are interested in Mathematics and Chemistry.30 students are interested in Mathematics, Physics and Chemistry.Remaining students are interested in Humanities.
Based on the above information, the number of students in Humanities is
Previously Asked in : Gate CE-afternoon season 2022 ||
45
10
30
40
Answer (Detailed Solution Below)
Option 45 is correct
Detailed Solution :
from above equation
total (T) = \, n(M \cup P \cup c) + x
450 = [(150+200 + 175)- (50+60+40) + 30] + x
x = 45
Correct option is: 45
Question 19.
Given below are two statements and four conclusions drawn based on the statements.- Statement 1 : Some soaps are clean.
- Statement 2 : All clean objects are wet.
- Conclusion I : Some clean objects are soaps.
- Conclusion II : No clean object is a soap.
- Conclusion III : Some wet objects are soaps.
- Conclusion IV : All wet objects are soaps.
Which one of the following options can be logically inferred?
Previously Asked in : Gate CE-afternoon season 2022 ||
Only conclusion I and conclusion III is correct
Either conclusion I or conclusion II is correct
Either conclusion III or conclusion IV is correct
Only conclusion I is correct
Answer (Detailed Solution Below)
Option Only conclusion I and conclusion III are correct is correct
Detailed Solution :
From above diagram, we can say
Conclusion I followed in both possibilities.
Conclusion II not followed.
Conclusion III followed in both possibilities.
Conclusion IV not followed
Option Only conclusion I and conclusion III are correct is correct
Question 20.
An ant walks in a straight line on a plane leaving behind a trace of its movement. The initial position of the ant is at point P facing east.
The ant first turns 72^{\circ} anticlockwise at P, and then does the following two steps in sequence exactly FIVE times before halting. - moves forward for 10cm
- turns 144^{\circ} clockwise.
The pattern made by the trace left behind by the ant is
Previously Asked in : Gate CE-afternoon season 2022 ||
a
c
b
d
Answer (Detailed Solution Below)
Option b is correct
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