Engineering Entrance
Q. What is the value of (2 + 3i) / (1 + i)? (2015)
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A.
1 + 2i
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B.
2 - i
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C.
3 + 2i
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D.
1 - 2i
Solution
Multiply numerator and denominator by the conjugate of the denominator: (2 + 3i)(1 - i) / (1 + i)(1 - i) = (2 - 2i + 3i + 3) / (1 + 1) = (5 + i) / 2 = 2.5 + 0.5i.
Correct Answer: B — 2 - i
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Q. What is the value of (2 + 3i)(2 - 3i)? (2019)
Solution
Using the difference of squares: (a + b)(a - b) = a² - b². Here, (2)² - (3i)² = 4 - (-9) = 4 + 9 = 13.
Correct Answer: A — 13
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Q. What is the value of (2 - 3)^5?
-
A.
-1
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B.
-32
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C.
-243
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D.
-125
Solution
Using the binomial theorem, (2 - 3)^5 = (-1)^5 = -1.
Correct Answer: D — -125
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Q. What is the value of (3 + 4i) / (1 + i)? (2021)
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A.
2 + i
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B.
1 + 2i
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C.
3 - 4i
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D.
1 - i
Solution
Multiplying numerator and denominator by the conjugate of the denominator: (3 + 4i)(1 - i) / (1 + i)(1 - i) = (3 - 3i + 4i + 4) / 2 = (7 + i) / 2 = 2 + i.
Correct Answer: A — 2 + i
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Q. What is the value of (3 + 5) × (2 + 4)? (2020)
Solution
(3 + 5) = 8 and (2 + 4) = 6, so 8 × 6 = 48.
Correct Answer: B — 56
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Q. What is the value of (3 + 5) × (2 - 1)? (2020)
Solution
(3 + 5) = 8 and (2 - 1) = 1, so 8 × 1 = 8.
Correct Answer: A — 8
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Q. What is the value of (3 + 5) × (6 - 2)? (2020)
Solution
(3 + 5) = 8 and (6 - 2) = 4, so 8 × 4 = 32.
Correct Answer: B — 24
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Q. What is the value of (3 + 5) × 2? (2023)
Solution
(3 + 5) × 2 = 8 × 2 = 16.
Correct Answer: B — 14
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Q. What is the value of (3^3) - (2^3)? (2016)
Solution
3^3 = 27 and 2^3 = 8, so 27 - 8 = 19.
Correct Answer: A — 19
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Q. What is the value of (x + 1)^5 when x = 2?
-
A.
32
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B.
64
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C.
128
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D.
256
Solution
Using the binomial theorem, (x + 1)^5 = C(5,0)(2)^5 + C(5,1)(2)^4 + C(5,2)(2)^3 + C(5,3)(2)^2 + C(5,4)(2)^1 + C(5,5)(2)^0 = 32 + 80 + 80 + 40 + 10 + 1 = 243.
Correct Answer: C — 128
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Q. What is the value of 100 - 37? (2014)
Q. What is the value of 100 ÷ 4 + 6? (2023) 2023
Solution
100 ÷ 4 = 25, so 25 + 6 = 31.
Correct Answer: C — 28
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Q. What is the value of 12 × 12? (2020)
-
A.
144
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B.
124
-
C.
156
-
D.
132
Solution
12 × 12 = 144.
Correct Answer: A — 144
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Q. What is the value of 12 × 8? (2020)
Q. What is the value of 12 ÷ (2 + 4)? (2018)
Solution
12 ÷ (2 + 4) = 12 ÷ 6 = 2.
Correct Answer: B — 3
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Q. What is the value of 12% of 250? (2020)
Solution
12% of 250 = (12/100) * 250 = 30.
Correct Answer: A — 30
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Q. What is the value of 15% of 200? (2014)
Solution
15% of 200 = (15/100) * 200 = 30.
Correct Answer: A — 30
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Q. What is the value of 5 × (6 + 4)? (2016)
Solution
6 + 4 = 10, then 5 × 10 = 50.
Correct Answer: A — 50
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Q. What is the value of 5! (5 factorial)? (2016) 2016
-
A.
120
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B.
60
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C.
100
-
D.
150
Solution
5! = 5 × 4 × 3 × 2 × 1 = 120.
Correct Answer: A — 120
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Q. What is the value of 5! (5 factorial)? (2023) 2023
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A.
120
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B.
100
-
C.
150
-
D.
110
Solution
5! = 5 × 4 × 3 × 2 × 1 = 120.
Correct Answer: A — 120
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Q. What is the value of 7^2 + 3^2? (2023) 2023
Solution
7^2 = 49 and 3^2 = 9, so 49 + 9 = 58.
Correct Answer: A — 58
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Q. What is the value of 8 × (2 + 3)? (2023) 2023
Solution
2 + 3 = 5, so 8 × 5 = 40.
Correct Answer: A — 40
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Q. What is the value of 9 - 3 × 2? (2015)
Solution
Using BODMAS, 3 × 2 = 6, so 9 - 6 = 3.
Correct Answer: B — 6
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Q. What is the value of 9 × 9? (2014)
Q. What is the value of 9^2 - 4^2? (2016)
Solution
9^2 = 81 and 4^2 = 16, so 81 - 16 = 65.
Correct Answer: A — 65
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Q. What is the value of cot(45°)?
Solution
cot(45°) = 1/tan(45°) = 1/1 = 1
Correct Answer: B — 1
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Q. What is the value of cot(90°)? (2018)
-
A.
0
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B.
1
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C.
undefined
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D.
∞
Solution
cot(90°) = 1/tan(90°) = 1/0 = undefined.
Correct Answer: C — undefined
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Q. What is the value of k for which the equation x² - 6x + k = 0 has roots 2 and 4? (2022)
Solution
The product of the roots is k = 2 * 4 = 8.
Correct Answer: B — 12
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Q. What is the value of k if the equation x² + kx + 16 = 0 has no real roots? (2022)
Solution
For no real roots, the discriminant must be less than zero: k² - 4*1*16 < 0, thus k < -8 or k > 8.
Correct Answer: A — -8
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Q. What is the value of k if the equation x² - 4x + k = 0 has no real roots? (2021)
Solution
For no real roots, the discriminant must be less than zero: (-4)² - 4*1*k < 0, hence k > 4.
Correct Answer: B — 6
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