Q. If the circumference of a circle is 31.4 cm, what is the radius?
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
Using the formula C = 2πr, we find r = C/(2π) = 31.4/(2*3.14) = 5 cm.
Correct Answer: A — 5 cm
Learn More →
Q. If the circumference of a circle is 31.4 cm, what is the radius? (2020) 2020
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
Show solution
Solution
Circumference = 2πr. Therefore, r = Circumference / (2π) = 31.4 cm / (2 * 3.14) = 5 cm.
Correct Answer: A — 5 cm
Learn More →
Q. If the circumference of a circle is measured as 31.4 cm with an error of 0.2 cm, what is the percentage error?
A.
0.64%
B.
0.5%
C.
1%
D.
0.2%
Show solution
Solution
Percentage error = (Absolute error / Measured value) * 100 = (0.2 / 31.4) * 100 ≈ 0.64%.
Correct Answer: A — 0.64%
Learn More →
Q. If the circumference of a circle is measured as 31.4 cm with an error of 0.2 cm, what is the radius?
A.
5 cm
B.
4.5 cm
C.
5.0 cm
D.
6 cm
Show solution
Solution
Circumference = 2πr. Measured circumference = 31.4 cm. Thus, r = 31.4 / (2π) ≈ 5.0 cm.
Correct Answer: C — 5.0 cm
Learn More →
Q. If the circumradius of triangle ABC is 10 cm and the area is 48 cm², what is the length of the side opposite to angle A?
A.
12 cm
B.
14 cm
C.
16 cm
D.
18 cm
Show solution
Solution
Using the formula R = (abc)/(4 * Area), we can find the side opposite to angle A. Let a = side opposite to A. Then, a = (4 * Area * R) / (bc) = (4 * 48 * 10) / (b * c).
Correct Answer: B — 14 cm
Learn More →
Q. If the circumradius R of triangle ABC is 5 cm, what is the maximum area of the triangle?
A.
12.5 cm²
B.
15 cm²
C.
20 cm²
D.
25 cm²
Show solution
Solution
The maximum area of a triangle with circumradius R is given by the formula Area = (abc)/(4R). For maximum area, the triangle should be equilateral, thus Area = (3√3/4) * (R^2) = (3√3/4) * (5^2) = 25√3/4 cm².
Correct Answer: C — 20 cm²
Learn More →
Q. If the coefficient of x^k in the expansion of (x + 1)^n is given by C(n,k), what does C(n,k) represent?
A.
The number of ways to choose k items from n.
B.
The total number of terms in the expansion.
C.
The sum of the coefficients.
D.
The product of the coefficients.
Show solution
Solution
C(n,k) represents the number of ways to choose k items from n, which corresponds to the coefficient of x^k.
Correct Answer: A — The number of ways to choose k items from n.
Learn More →
Q. If the concentration of a reactant is increased in a system at equilibrium, what will happen according to Le Chatelier's principle?
A.
The equilibrium will shift to the right.
B.
The equilibrium will shift to the left.
C.
The equilibrium will not change.
D.
The reaction will stop.
Show solution
Solution
According to Le Chatelier's principle, if a change is made to a system at equilibrium, the system will adjust to counteract that change. Increasing the concentration of a reactant will shift the equilibrium to the right, favoring the formation of products.
Correct Answer: A — The equilibrium will shift to the right.
Learn More →
Q. If the concentration of a reactant is tripled in a second-order reaction, how does the rate change? (2023)
A.
Increases by 3 times
B.
Increases by 6 times
C.
Increases by 9 times
D.
Increases by 12 times
Show solution
Solution
For a second-order reaction, if concentration is tripled, the rate increases by 3² = 9 times.
Correct Answer: C — Increases by 9 times
Learn More →
Q. If the concentration of Cu²⁺ in a cell is increased, what happens to the cell potential?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Becomes zero
Show solution
Solution
Increasing the concentration of Cu²⁺ increases the cell potential according to the Nernst equation.
Correct Answer: A — Increases
Learn More →
Q. If the concentration of reactants is increased in a system at equilibrium, what will happen to the position of equilibrium?
A.
Shift to the right
B.
Shift to the left
C.
No change
D.
Depends on temperature
Show solution
Solution
According to Le Chatelier's principle, increasing the concentration of reactants will shift the equilibrium position to the right, favoring the formation of products.
Correct Answer: A — Shift to the right
Learn More →
Q. If the coordinates of a point are (x, y) and it lies on the line 2x + 3y = 12, what is the value of y when x = 2?
Show solution
Solution
Substituting x = 2: 2(2) + 3y = 12 => 4 + 3y = 12 => 3y = 8 => y = 8/3 ≈ 2.67, closest is 3.
Correct Answer: B — 3
Learn More →
Q. If the coordinates of a point are (x, y) and it lies on the line 3x + 4y = 12, what is y when x = 0?
Show solution
Solution
Substituting x = 0: 3(0) + 4y = 12 => 4y = 12 => y = 3.
Correct Answer: B — 4
Learn More →
Q. If the coordinates of a point P are (1, -1, 2), what is the x-coordinate of the point Q if it is reflected across the yz-plane? (2023)
Show solution
Solution
Reflection across the yz-plane changes the sign of the x-coordinate. So, Q = (-1, -1, 2).
Correct Answer: B — -1
Learn More →
Q. If the coordinates of point A are (1, 2) and point B are (4, 6), what is the length of AB? (2023)
Show solution
Solution
Length AB = √[(4-1)² + (6-2)²] = √[9 + 16] = √25 = 5.
Correct Answer: A — 5
Learn More →
Q. If the coordinates of point C are (5, 5) and point D are (5, 10), what is the distance CD? (2021)
Show solution
Solution
Distance CD = |10 - 5| = 5.
Correct Answer: A — 5
Learn More →
Q. If the coordinates of point C are (5, 5) and point D are (5, 10), what is the length of CD? (2021)
Show solution
Solution
Length CD = |10 - 5| = 5.
Correct Answer: A — 5
Learn More →
Q. If the coordinates of point C are (5, 5) and the slope of line AC is 1, what is the equation of line AC? (2021)
A.
y = x
B.
y = 5
C.
y = x + 5
D.
y = x - 5
Show solution
Solution
Using point-slope form: y - 5 = 1(x - 5) => y = x
Correct Answer: A — y = x
Learn More →
Q. If the coordinates of point C are (5, 5) and the slope of the line is 1, what is the equation of the line? (2021) 2021
A.
y = x
B.
y = 5
C.
y = 2x - 5
D.
y = x + 5
Show solution
Solution
Using point-slope form: y - 5 = 1(x - 5) => y = x.
Correct Answer: A — y = x
Learn More →
Q. If the coordinates of points A and B are (1, 2) and (3, 4) respectively, what is the distance AB?
Show solution
Solution
Distance AB = √((3-1)² + (4-2)²) = √(4) = 2.
Correct Answer: A — 2√2
Learn More →
Q. If the coordinates of points A and B are (1, 2) and (4, 6) respectively, what is the distance AB?
Show solution
Solution
Distance AB = √((4-1)² + (6-2)²) = √(9 + 16) = √25 = 5.
Correct Answer: A — 5
Learn More →
Q. If the coordinates of the vertices of a triangle are (1, 1), (4, 5), and (7, 2), what is the perimeter of the triangle?
Show solution
Solution
Calculate distances AB, BC, CA and sum them: AB = 5, BC = 5, CA = 7. Perimeter = 5 + 5 + 7 = 17.
Correct Answer: B — 14
Learn More →
Q. If the coordinates of the vertices of a triangle are (1, 2), (3, 4), and (5, 2), what is the perimeter of the triangle?
Show solution
Solution
Perimeter = AB + BC + CA = √[(3-1)² + (4-2)²] + √[(5-3)² + (2-4)²] + √[(1-5)² + (2-2)²] = 2.83 + 2.83 + 4 = 10.
Correct Answer: B — 10
Learn More →
Q. If the coordinates of the vertices of a triangle are (1, 2), (4, 6), and (7, 2), what is the perimeter of the triangle?
Show solution
Solution
Perimeter = AB + BC + CA = √[(4-1)² + (6-2)²] + √[(7-4)² + (2-6)²] + √[(1-7)² + (2-2)²] = 3 + √(9 + 16) + 6 = 3 + 5 + 6 = 14.
Correct Answer: B — 14
Learn More →
Q. If the coordinates of the vertices of a triangle are A(1, 1), B(4, 5), and C(7, 2), what is the area of the triangle?
Show solution
Solution
Area = 1/2 | x1(y2-y3) + x2(y3-y1) + x3(y1-y2) | = 1/2 | 1(5-2) + 4(2-1) + 7(1-5) | = 1/2 | 3 + 4 - 28 | = 1/2 * 21 = 10.5.
Correct Answer: B — 12
Learn More →
Q. If the cost function is C(x) = 3x^2 + 12x + 5, find the minimum cost. (2020)
Show solution
Solution
The minimum cost occurs at x = -b/(2a) = -12/(2*3) = -2. C(-2) = 3(-2)^2 + 12(-2) + 5 = 8.
Correct Answer: B — 8
Learn More →
Q. If the cost function is C(x) = 3x^2 + 12x + 5, find the minimum cost. (2020) 2020
Show solution
Solution
The minimum cost occurs at x = -b/(2a) = -12/(2*3) = -2. C(-2) = 3(-2)^2 + 12(-2) + 5 = 8.
Correct Answer: B — 8
Learn More →
Q. If the cost function is C(x) = 5x^2 + 20x + 100, find the minimum cost. (2020)
A.
100
B.
120
C.
140
D.
160
Show solution
Solution
The minimum cost occurs at x = -b/(2a) = -20/(2*5) = -2. C(-2) = 5(-2)^2 + 20(-2) + 100 = 120.
Correct Answer: B — 120
Learn More →
Q. If the critical angle for a certain material is 30°, what is the refractive index of that material?
A.
1.00
B.
1.15
C.
1.73
D.
2.00
Show solution
Solution
The refractive index n can be calculated using n = 1/sin(θc). For θc = 30°, n = 1/sin(30°) = 1/0.5 = 2.00.
Correct Answer: C — 1.73
Learn More →
Q. If the critical angle for a certain material is 45°, what is the refractive index of that material?
A.
1.41
B.
1.00
C.
1.73
D.
0.71
Show solution
Solution
Using the formula n = 1/sin(θc), where θc = 45°, we find n = 1/sin(45°) = 1/0.7071 ≈ 1.41.
Correct Answer: A — 1.41
Learn More →
Showing 5611 to 5640 of 19340 (645 Pages)
