Q. What is the value of (3/4) + (1/2)?
-
A.
1
-
B.
5/4
-
C.
3/2
-
D.
7/4
Solution
Convert 1/2 to 2/4, then (3/4) + (2/4) = 5/4.
Correct Answer: B — 5/4
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Q. What is the value of (−1) × (−1) × (−1)? (2021)
Solution
Multiplying three negative ones gives −1.
Correct Answer: C — −1
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Q. What is the value of (−1)^3?
Q. What is the value of (−1)² + (−2)²? (2019)
Solution
(−1)² = 1 and (−2)² = 4, so 1 + 4 = 5.
Correct Answer: C — 5
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Q. What is the value of (−2)²? (2022)
Q. What is the value of (−5)²? (2021)
-
A.
25
-
B.
−25
-
C.
10
-
D.
−10
Q. What is the value of (−7) + (−3)? (2019)
Solution
−7 + (−3) = −10.
Correct Answer: A — −10
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Q. What is the value of 3 + 4 × 2?
Solution
According to BODMAS, 4 × 2 = 8, so 3 + 8 = 11.
Correct Answer: B — 11
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Q. What is the value of 3.5 + 2.8? (2021)
-
A.
5.3
-
B.
6.3
-
C.
7.3
-
D.
8.3
Solution
3.5 + 2.8 = 6.3.
Correct Answer: B — 6.3
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Q. What is the value of 3√(27)? (2023)
Solution
3√(27) = 3 × 3 = 9.
Correct Answer: A — 9
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Q. What is the value of k for which the equation x^2 + kx + 16 = 0 has no real roots? (2021)
Solution
The discriminant must be less than zero. Thus, k^2 - 4*1*16 < 0 leads to k^2 < 64, giving k < 8 and k > -8.
Correct Answer: A — -8
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Q. What is the value of k if the equation x^2 + kx + 4 = 0 has equal roots? (2022)
Solution
For equal roots, the discriminant must be zero. Thus, k^2 - 4*1*4 = 0, which gives k^2 = 16, so k = ±4.
Correct Answer: A — 4
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Q. What is the value of k if the equation x^2 - kx + 9 = 0 has roots that are both positive?
Solution
For both roots to be positive, k must be greater than 6 (sum of roots) and k^2 - 36 > 0 (discriminant). Thus, k > 6 and k < 12.
Correct Answer: C — 10
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Q. What is the value of k if the quadratic equation x^2 + kx + 16 = 0 has roots that are real and distinct? (2019)
Solution
For real and distinct roots, the discriminant must be positive: k^2 - 4(1)(16) > 0. Thus, k^2 > 64, leading to k < -8 or k > 8.
Correct Answer: B — -4
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Q. What is the value of k if the quadratic equation x^2 + kx + 16 = 0 has roots that are both negative? (2019)
Solution
For both roots to be negative, k must be negative and |k| > 8. Thus, k = -8.
Correct Answer: A — -8
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Q. What is the value of k if the quadratic equation x^2 + kx + 9 = 0 has roots that are both positive? (2023)
Solution
For both roots to be positive, k must be negative and k^2 > 36. Thus, k < -6.
Correct Answer: A — -6
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Q. What is the value of k if the quadratic equation x^2 + kx + 9 = 0 has roots that are both negative? (2023)
Solution
For both roots to be negative, k must be positive and k^2 > 4(1)(9). Thus, k > 6.
Correct Answer: A — -6
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Q. What is the value of k if the roots of the equation x^2 + kx + 4 = 0 are -2 and -2?
Solution
The sum of the roots is -2 + -2 = -4, so k = 4.
Correct Answer: C — 6
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Q. What is the value of k if the roots of the equation x^2 + kx + 9 = 0 are imaginary?
-
A.
k < 0
-
B.
k > 0
-
C.
k = 0
-
D.
k ≤ 0
Solution
The discriminant must be less than zero: k^2 - 4*1*9 < 0 leads to k^2 < 36, hence k < 0 or k > 0.
Correct Answer: A — k < 0
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Q. What is the value of k if the roots of the equation x^2 - 5x + k = 0 are equal? (2020)
Solution
For the roots to be equal, the discriminant must be zero. Thus, (-5)^2 - 4(1)(k) = 0. Solving gives k = 6.25.
Correct Answer: A — 6.25
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Q. What is the value of k if the roots of the equation x^2 - kx + 16 = 0 are real and distinct?
Solution
For the roots to be real and distinct, the discriminant must be positive: k^2 - 64 > 0, leading to k > 8 or k < -8.
Correct Answer: C — 12
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Q. What is the value of k if the roots of the equation x^2 - kx + 8 = 0 are 2 and 4? (2023)
Solution
The sum of the roots is 2 + 4 = 6, so k = 6.
Correct Answer: A — 6
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Q. What is the value of k if the roots of the equation x^2 - kx + 9 = 0 are 3 and 3?
Solution
The sum of the roots is 3 + 3 = 6, so k = 6.
Correct Answer: A — 6
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Q. What is the value of log_10(0.01)?
Solution
log_10(0.01) = log_10(10^-2) = -2.
Correct Answer: B — -2
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Q. What is the value of log_2(1/8)? (2023)
Solution
log_2(1/8) = log_2(2^-3) = -3.
Correct Answer: A — -3
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Q. What is the value of log_5(1)?
-
A.
0
-
B.
1
-
C.
5
-
D.
undefined
Solution
log_5(1) = 0 because 5^0 = 1.
Correct Answer: A — 0
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Q. What is the value of the 5th term in the expansion of (x + 2)^7?
-
A.
672
-
B.
672x^4
-
C.
672x^3
-
D.
672x^2
Solution
The 5th term is C(7,4) * (2)^4 * x^3 = 35 * 16 * x^3 = 560x^3.
Correct Answer: C — 672x^3
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Q. What is the value of the coefficient of x^4 in the expansion of (x + 5)^6?
-
A.
150
-
B.
300
-
C.
600
-
D.
750
Solution
The coefficient of x^4 in (x + 5)^6 is given by 6C4 * 5^2 = 15 * 25 = 375.
Correct Answer: B — 300
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Q. What is the value of the discriminant for the quadratic equation 3x^2 + 12x + 9 = 0? (2019)
Solution
The discriminant D = b^2 - 4ac = 12^2 - 4*3*9 = 0, indicating equal roots.
Correct Answer: A — 0
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Q. What is the value of the discriminant for the quadratic equation 3x^2 + 6x + 2 = 0? (2023)
Solution
The discriminant is b^2 - 4ac = 6^2 - 4(3)(2) = 36 - 24 = 12.
Correct Answer: B — 4
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