What is the value of x in the equation 2^x + 2^x = 10?
A. 1
B. 2
C. 3
D. 4
Correct Answer: B Given equation is 2^x + 2^x = 10, which can be simplified as 2 * 2^x = 10, then 2^x = 5. Since 2^2 = 4 and 2^3 = 8, the value of x that satisfies the equation is between 2 and 3, but closest to the given options is 2.
Q2.
Which language is accepted by Pushdown Automata?
A. Regular
B. Context-Free
C. Context-Sensitive
D. Recursively Enumerable
Correct Answer: B PDA accepts exactly the class of Context-Free Languages (CFL).
Q3.
The height of a complete binary tree with n nodes is:
A. n
B. n/2
C. logn
D. sqrtn
Correct Answer: C Height of a complete binary tree with n nodes is logn.
Q4. 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.
Q5.
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.
Q6.
How many AND gates are needed for 8-to-1 multiplexer?
A. 4
B. 6
C. 8
D. 16
Correct Answer: C 8-to-1 MUX needs 8 AND gates (one per input) + 1 OR gate.
Q7. Core Subject
In a computer network, what is the purpose of the router?
A. To connect multiple devices within a network
B. To connect multiple networks together
C. To provide network security
D. To provide network storage
Correct Answer: B The purpose of the router in a computer network is to connect multiple networks together and route traffic between them.
Q8.
A 4-bit R-2R DAC uses resistors of values:
A. Only R
B. Only 2R
C. R and 2R
D. R, 2R, 4R
Correct Answer: C R-2R ladder DAC uses only R and 2R resistors for binary-weighted conversion.
Q9.
Which of the following is NOT a valid Boolean algebra property?
A. A . 0 = 0
B. A + 1 = 1
C. A . A = A
D. A + A = 0
Correct Answer: D A + A = A (idempotent law), not 0. A + A = 1 and A . A = 0.
Q10. General Aptitude
If the radius of a circle is doubled, the area becomes:
A. Double
B. Four times
C. Eight times
D. Same
Correct Answer: B A r^2. If r -> 2r, A -> 4A.
Q11. General Aptitude
The number of diagonals in a pentagon is:
A. 3
B. 4
C. 5
D. 6
Correct Answer: C n(n-3)/2 = 5(2)/2 = 5 diagonals.
Q12. General Aptitude
A car travels 60 km in 1.5 hours. Its average speed is:
A. 30 km/h
B. 40 km/h
C. 50 km/h
D. 90 km/h
Correct Answer: B Speed = 60/1.5 = 40 km/h.
Q13. Engineering Mathematics
What is the value of the integral of x^2 dx from 0 to 2?
A. 2/3
B. 8/3
C. 4/3
D. 16/3
Correct Answer: B The integral of x^2 dx from 0 to 2 is (1/3)x^3 from 0 to 2, which is (1/3)(2^3) - (1/3)(0^3) = (1/3)(8) = 8/3.
Q14.
Concrete is strong in:
A. Tension
B. Compression
C. Shear
D. Torsion
Correct Answer: B Concrete has high compressive strength but low tensile strength (reinforced with steel).
Q15.
The Chezy's coefficient C in Manning's formula relates to:
A. Channel roughness
B. Channel depth
C. Both roughness and hydraulic radius
D. Discharge
Correct Answer: C Manning: V = (1/n)R^(2/3)S^(1/2). Chezy: C = (1/n)R^(1/6).