GATE Practice Set 4

15 Q . Solved with answers
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Sections: General AptitudeCore SubjectEngineering Mathematics
Q1.
An ideal op-amp has infinite:
A. Output impedance
B. Input impedance
C. Bandwidth
D. Both B and C
Correct Answer: B
Ideal op-amp: infinite input impedance, zero output impedance, infinite gain.
Q2.
A heat engine rejects 300 J to sink while doing 200 J work. Heat supplied is:
A. 100 J
B. 300 J
C. 500 J
D. 600 J
Correct Answer: C
Q = W + Q = 200 + 300 = 500 J.
Q3. Core Subject
In a CPU, what is the main function of the cache memory?
A. To increase the size of the main memory
B. To decrease the time taken to access the main memory
C. To increase the speed of the CPU
D. To decrease the power consumption of the CPU
Correct Answer: B
The main function of the cache memory in a CPU is to store frequently used data and instructions, which reduces the time taken to access the main memory.
Q4.
The impedance of a capacitor of capacitance C at frequency is:
A. jC
B. 1/(jC)
C. C
D. 1/(C)
Correct Answer: B
Zc = 1/(jC) = -j/(C).
Q5. General Aptitude
A company has 15 employees, and each employee can speak two languages. What is the minimum number of languages that the company must have to satisfy this condition?
A. 7
B. 8
C. 15
D. 30
Correct Answer: B
Since each employee can speak two languages, we can consider each employee as an edge in a graph, and each language as a node. The minimum number of languages required is equal to the minimum number of nodes required to connect 15 edges, which is 8.
Q6. General Aptitude
If a train running at 72 km/h crosses a pole in 10 s, the length of train is:
A. 100 m
B. 150 m
C. 200 m
D. 250 m
Correct Answer: C
Speed = 72x(5/18) = 20 m/s. Length = 20x10 = 200 m.
Q7.
A steel rod of 10 mm diameter carries 31.4 kN load. Stress is:
A. 100 MPa
B. 200 MPa
C. 400 MPa
D. 314 MPa
Correct Answer: C
A = pi(0.01)^2/4 = 7.85x10 m^2. = 31400/7.85e-5 = 400 MPa.
Q8.
Beam deflection is maximum at:
A. Supports
B. Point of load
C. Depends on loading
D. Center always
Correct Answer: C
Deflection depends on loading type. For UDL: max at center. For point load: at load point.
Q9. General Aptitude
If x + y = 10 and xy = 21, then x^2 + y^2 is:
A. 100
B. 79
C. 58
D. 42
Correct Answer: C
x^2+y^2 = (x+y)^2 - 2xy = 100 - 42 = 58.
Q10.
The bending moment at a simply supported beam's center with point load P at center is:
A. PL/2
B. PL/4
C. PL/8
D. PL
Correct Answer: B
Mmax = PL/4 for simply supported beam with central point load.
Q11.
The total hardness of water is due to:
A. Na and K
B. Ca^2 and Mg^2
C. Cl and SO^2
D. Fe^2 and Mn^2
Correct Answer: B
Hardness: Ca^2 and Mg^2 ions (temporary: bicarbonates, permanent: sulfates/chlorides).
Q12. General Aptitude
The difference between the largest 4-digit number and the smallest 3-digit number is:
A. 8999
B. 9899
C. 9899
D. 9999
Correct Answer: C
9999 - 100 = 9899.
Q13.
In a min-heap, the smallest element is at:
A. Root
B. Leftmost leaf
C. Rightmost leaf
D. Last node
Correct Answer: A
Min-heap property: parent children, so root is always the minimum element.
Q14. General Aptitude
Simplify: 25 + 5 x 2 - 10
A. 50
B. 25
C. 25
D. 30
Correct Answer: C
Using BODMAS: 5x2=10, 25+10-10=25.
Q15. General Aptitude
The perimeter of a square is 40 cm. Its area is:
A. 80 cm^2
B. 160 cm^2
C. 100 cm^2
D. 200 cm^2
Correct Answer: C
Side = 40/4 = 10 cm. Area = 10^2 = 100 cm^2.