Q. What is the area of a sector of a circle with radius 10 cm and angle 90 degrees? (2022)
-
A.
25π cm²
-
B.
50π cm²
-
C.
100π cm²
-
D.
75π cm²
Solution
Area of sector = (θ/360) × πr² = (90/360) × π × 10² = (1/4) × 100π = 25π cm².
Correct Answer:
A
— 25π cm²
Learn More →
Q. What is the area of a sector of a circle with radius 6 cm and a central angle of 90 degrees? (2023)
-
A.
9π cm²
-
B.
12π cm²
-
C.
18π cm²
-
D.
6π cm²
Solution
Area of sector = (θ/360) × πr² = (90/360) × π × 6² = (1/4) × 36π = 9π cm².
Correct Answer:
A
— 9π cm²
Learn More →
Q. What is the area of a sector of a circle with radius 6 cm and angle 90 degrees? (2021)
-
A.
9π cm²
-
B.
12π cm²
-
C.
18π cm²
-
D.
6π cm²
Solution
Area of sector = (θ/360) × πr² = (90/360) × π(6)² = (1/4) × 36π = 9π cm².
Correct Answer:
A
— 9π cm²
Learn More →
Q. What is the area of a square with a side length of 8 cm? (2023)
-
A.
64 cm²
-
B.
32 cm²
-
C.
16 cm²
-
D.
48 cm²
Solution
Area = side² = 8² = 64 cm²
Correct Answer:
A
— 64 cm²
Learn More →
Q. What is the area of a trapezium with bases 5 cm and 7 cm, and height 4 cm? (2023)
-
A.
24 cm²
-
B.
20 cm²
-
C.
30 cm²
-
D.
28 cm²
Solution
Area = 1/2 * (base1 + base2) * height = 1/2 * (5 + 7) * 4 = 24 cm²
Correct Answer:
A
— 24 cm²
Learn More →
Q. What is the area of a triangle with a base of 8 cm and a height of 5 cm? (2020)
-
A.
20 cm²
-
B.
30 cm²
-
C.
40 cm²
-
D.
10 cm²
Solution
The area of a triangle is given by A = 1/2 * base * height. Here, A = 1/2 * 8 * 5 = 20 cm².
Correct Answer:
A
— 20 cm²
Learn More →
Q. What is the area of an equilateral triangle with a side length of 6 cm? (2022)
-
A.
9√3 cm²
-
B.
12√3 cm²
-
C.
18√3 cm²
-
D.
24√3 cm²
Solution
Area = (√3/4) * side² = (√3/4) * 6² = (√3/4) * 36 = 9√3 cm².
Correct Answer:
A
— 9√3 cm²
Learn More →
Q. What is the area under the curve y = 1/x from x = 1 to x = 4?
-
A.
ln(4)
-
B.
ln(3)
-
C.
ln(2)
-
D.
ln(1)
Solution
The area under the curve is given by ∫(from 1 to 4) (1/x) dx = [ln(x)] from 1 to 4 = ln(4) - ln(1) = ln(4).
Correct Answer:
A
— ln(4)
Learn More →
Q. What is the area under the curve y = 2x^2 + 3 from x = 0 to x = 2?
Solution
The area under the curve is given by ∫(from 0 to 2) (2x^2 + 3) dx = [(2/3)x^3 + 3x] from 0 to 2 = (16/3 + 6) = 10.
Correct Answer:
B
— 12
Learn More →
Q. What is the axis of symmetry for the parabola given by the equation y = -3(x - 2)^2 + 5?
-
A.
x = 2
-
B.
y = 5
-
C.
y = -3
-
D.
x = -2
Solution
The axis of symmetry for a parabola in vertex form y = a(x - h)^2 + k is x = h. Here, h = 2.
Correct Answer:
A
— x = 2
Learn More →
Q. What is the axis of symmetry for the parabola given by the equation y^2 = 6x?
-
A.
x-axis
-
B.
y-axis
-
C.
y = x
-
D.
x = 0
Solution
The axis of symmetry for the parabola y^2 = 4px is the x-axis.
Correct Answer:
B
— y-axis
Learn More →
Q. What is the characteristic polynomial of the matrix E = [[2, 1], [1, 2]]? (2021)
-
A.
λ^2 - 3λ + 1
-
B.
λ^2 - 5λ + 4
-
C.
λ^2 - 4λ + 3
-
D.
λ^2 - 2λ + 1
Solution
The characteristic polynomial is det(E - λI) = det([[2-λ, 1], [1, 2-λ]]) = (2-λ)(2-λ) - 1 = λ^2 - 3λ + 1.
Correct Answer:
A
— λ^2 - 3λ + 1
Learn More →
Q. What is the characteristic polynomial of the matrix G = [[2, 1], [1, 2]]? (2020)
-
A.
λ^2 - 3λ + 1
-
B.
λ^2 - 5λ + 4
-
C.
λ^2 - 2λ + 1
-
D.
λ^2 - 4λ + 4
Solution
The characteristic polynomial is given by det(G - λI) = det([[2-λ, 1], [1, 2-λ]]) = (2-λ)(2-λ) - 1 = λ^2 - 3λ + 3.
Correct Answer:
A
— λ^2 - 3λ + 1
Learn More →
Q. What is the circumference of a circle with a diameter of 14 cm? (2023)
-
A.
22 cm
-
B.
28 cm
-
C.
44 cm
-
D.
56 cm
Solution
The circumference C of a circle is given by C = π * diameter. Here, C = π * 14 cm ≈ 3.14 * 14 ≈ 44 cm.
Correct Answer:
B
— 28 cm
Learn More →
Q. What is the circumference of a circle with a radius of 7 cm? (2019)
-
A.
14π cm
-
B.
21π cm
-
C.
7π cm
-
D.
28π cm
Solution
Circumference = 2 * π * radius = 2 * π * 7 = 14π cm
Correct Answer:
A
— 14π cm
Learn More →
Q. What is the coefficient of x^0 in the expansion of (x - 1)^5?
Solution
The coefficient of x^0 in (x - 1)^5 is given by 5C5 * (-1)^5 = -1.
Correct Answer:
C
— -5
Learn More →
Q. What is the coefficient of x^2 in the expansion of (2x + 5)^4?
-
A.
60
-
B.
80
-
C.
100
-
D.
120
Solution
Using the binomial theorem, the coefficient of x^2 in (2x + 5)^4 is given by 4C2 * (2)^2 * (5)^2 = 6 * 4 * 25 = 600.
Correct Answer:
A
— 60
Learn More →
Q. What is the coefficient of x^2 in the expansion of (2x - 5)^5? (2019)
-
A.
-300
-
B.
-600
-
C.
600
-
D.
300
Solution
The coefficient of x^2 in (2x - 5)^5 is given by 5C2 * (2)^2 * (-5)^3 = 10 * 4 * (-125) = -5000.
Correct Answer:
B
— -600
Learn More →
Q. What is the coefficient of x^2 in the expansion of (3x + 4)^5?
-
A.
60
-
B.
80
-
C.
100
-
D.
120
Solution
The coefficient of x^2 in (3x + 4)^5 is C(5, 2) * (3)^2 * (4)^3 = 10 * 9 * 64 = 5760.
Correct Answer:
B
— 80
Learn More →
Q. What is the coefficient of x^3 in the expansion of (3x + 2)^5? (2023)
-
A.
90
-
B.
180
-
C.
270
-
D.
360
Solution
The coefficient of x^3 in (3x + 2)^5 is given by 5C3 * (3)^3 * (2)^2 = 10 * 27 * 4 = 1080.
Correct Answer:
B
— 180
Learn More →
Q. What is the coefficient of x^3 in the expansion of (x + 5)^6?
-
A.
150
-
B.
300
-
C.
450
-
D.
600
Solution
The coefficient of x^3 in (x + 5)^6 is C(6, 3) * (5)^3 = 20 * 125 = 2500.
Correct Answer:
B
— 300
Learn More →
Q. What is the coefficient of x^4 in the expansion of (x + 3)^6?
-
A.
81
-
B.
162
-
C.
243
-
D.
324
Solution
The coefficient of x^4 in (x + 3)^6 is C(6, 4) * 3^2 = 15 * 9 = 135.
Correct Answer:
C
— 243
Learn More →
Q. What is the conjugate of the complex number z = 7 - 4i? (2021)
-
A.
7 + 4i
-
B.
7 - 4i
-
C.
-7 + 4i
-
D.
-7 - 4i
Solution
The conjugate of z is given by z* = 7 + 4i.
Correct Answer:
A
— 7 + 4i
Learn More →
Q. What is the continuity of the function f(x) = sqrt(x) at x = 0? (2022)
-
A.
Continuous
-
B.
Not continuous
-
C.
Only left continuous
-
D.
Only right continuous
Solution
The function f(x) = sqrt(x) is continuous at x = 0 as it is defined and the limit exists.
Correct Answer:
A
— Continuous
Learn More →
Q. What is the critical point of f(x) = x^2 - 4x + 4? (2022)
Solution
Set f'(x) = 2x - 4 = 0; solving gives x = 2.
Correct Answer:
B
— 2
Learn More →
Q. What is the critical point of the function f(x) = x^2 - 4x + 4? (2022)
Solution
Find f'(x) = 2x - 4. Set f'(x) = 0, giving 2x - 4 = 0, hence x = 2.
Correct Answer:
B
— 2
Learn More →
Q. What is the critical point of the function f(x) = x^4 - 4x^3 + 6? (2023)
Solution
First derivative f'(x) = 4x^3 - 12x^2. Setting f'(x) = 0 gives x = 0, 1, 3.
Correct Answer:
B
— 1
Learn More →
Q. What is the cross product of vectors A = i + 2j + 3k and B = 4i + 5j + 6k?
-
A.
-3i + 6j - 3k
-
B.
-3i + 6j + 3k
-
C.
3i - 6j + 3k
-
D.
3i + 6j - 3k
Solution
A × B = |i j k| |1 2 3| |4 5 6| = -3i + 6j - 3k.
Correct Answer:
A
— -3i + 6j - 3k
Learn More →
Q. What is the cross product of vectors A = i + 2j and B = 3i + 4j? (2021)
Solution
A × B = |i j k| |1 2 0| |3 4 0| = (0 - 0)i - (0 - 0)j + (4 - 6)k = -2k.
Correct Answer:
A
— -2k
Learn More →
Q. What is the cross product of vectors E = i + 2j and F = 3i + 4j?
Solution
E × F = |i j k| |1 2 0| |3 4 0| = (0 - 0)i - (0 - 0)j + (1*4 - 2*3)k = -2k.
Correct Answer:
A
— -2k
Learn More →
Showing 1201 to 1230 of 1593 (54 Pages)
