Q. The quadratic equation x^2 - 4x + 4 = 0 can be expressed in which of the following forms? (2022)
A.
(x - 2)^2
B.
(x + 2)^2
C.
(x - 4)^2
D.
(x + 4)^2
Show solution
Solution
The equation can be factored as (x - 2)(x - 2) = 0, which is (x - 2)^2.
Correct Answer:
A
— (x - 2)^2
Learn More →
Q. The quadratic equation x^2 - 4x + 4 = 0 has how many distinct real roots?
Show solution
Solution
The discriminant is 0, indicating one distinct real root.
Correct Answer:
B
— 1
Learn More →
Q. The quadratic equation x^2 - 6x + 9 = 0 can be expressed as which of the following? (2021)
A.
(x - 3)^2 = 0
B.
(x + 3)^2 = 0
C.
(x - 2)(x - 4) = 0
D.
(x + 2)(x + 4) = 0
Show solution
Solution
The equation can be factored as (x - 3)(x - 3) = 0, or (x - 3)^2 = 0.
Correct Answer:
A
— (x - 3)^2 = 0
Learn More →
Q. The quadratic equation x^2 - 6x + 9 = 0 can be expressed in the form (x - a)^2 = 0. What is the value of a? (2021)
Show solution
Solution
The equation can be factored as (x - 3)^2 = 0, hence a = 3.
Correct Answer:
A
— 3
Learn More →
Q. The quadratic equation x^2 - 6x + 9 = 0 has how many distinct real roots?
A.
0
B.
1
C.
2
D.
Infinite
Show solution
Solution
The discriminant is 0, indicating that there is exactly one distinct real root.
Correct Answer:
B
— 1
Learn More →
Q. The quadratic equation x^2 - 6x + k = 0 has roots that are both positive. What is the condition on k?
A.
k > 0
B.
k < 0
C.
k > 9
D.
k < 9
Show solution
Solution
For both roots to be positive, k must be greater than the square of half the coefficient of x: k > (6/2)^2 = 9.
Correct Answer:
C
— k > 9
Learn More →
Q. The quadratic equation x^2 - 6x + k = 0 has roots that differ by 2. What is the value of k?
Show solution
Solution
Let the roots be r and r+2. Then, r + (r+2) = 6 and r(r+2) = k. Solving gives k = 10.
Correct Answer:
B
— 10
Learn More →
Q. The quadratic equation x² + 4x + 4 = 0 has how many distinct roots? (2021)
Show solution
Solution
The discriminant is 4² - 4*1*4 = 0, indicating one distinct root.
Correct Answer:
B
— 1
Learn More →
Q. The Quit India Movement of 1942 was significant because it: (1942)
A.
Marked the first mass uprising against British rule
B.
Was a call for immediate independence from British rule
C.
Led to the formation of the Indian National Army
D.
Resulted in the Cripps Mission
Show solution
Solution
The Quit India Movement of 1942 was significant as it was a mass protest demanding an end to British rule in India.
Correct Answer:
B
— Was a call for immediate independence from British rule
Learn More →
Q. The radius of a circle is increased by 50%. What is the percentage increase in the area of the circle? (2020)
A.
50%
B.
75%
C.
100%
D.
125%
Show solution
Solution
If r is the original radius, new radius = 1.5r. Area increases from πr² to π(1.5r)² = 2.25πr². Percentage increase = (2.25 - 1) × 100% = 125%.
Correct Answer:
C
— 100%
Learn More →
Q. The Rajya Sabha has a total of 245 members. If 12 members are nominated, what is the maximum number of elected members?
A.
233
B.
245
C.
233
D.
240
Show solution
Solution
Maximum elected members = 245 - 12 = 233
Correct Answer:
A
— 233
Learn More →
Q. The Rajya Sabha has a total of 250 members. If 12 members are nominated, what percentage of the total members are elected?
A.
80%
B.
85%
C.
90%
D.
88%
Show solution
Solution
Elected members = 250 - 12 = 238. Percentage = (238/250) * 100 = 95.2%.
Correct Answer:
C
— 90%
Learn More →
Q. The range of sin^(-1)(x) is:
A.
[-π/2, π/2]
B.
[0, π]
C.
[-1, 1]
D.
[0, 1]
Show solution
Solution
The range of sin^(-1)(x) is [-π/2, π/2].
Correct Answer:
A
— [-π/2, π/2]
Learn More →
Q. The range of the data set 1, 3, 5, 7, 9 is:
Show solution
Solution
Range = Maximum - Minimum = 9 - 1 = 8.
Correct Answer:
A
— 8
Learn More →
Q. The range of the data set {10, 15, 20, 25, 30} is?
Show solution
Solution
Range = Maximum value - Minimum value = 30 - 10 = 20.
Correct Answer:
A
— 15
Learn More →
Q. The range of the function f(x) = |x - 1| is:
A.
(-∞, 1)
B.
[0, ∞)
C.
(-1, 1)
D.
[1, ∞)
Show solution
Solution
The absolute value function has a minimum value of 0, hence the range is [0, ∞).
Correct Answer:
B
— [0, ∞)
Learn More →
Q. The range of the function y = sin^(-1)(x) is:
A.
(0, π)
B.
[-π/2, π/2]
C.
[-1, 1]
D.
[0, 1]
Show solution
Solution
The range of y = sin^(-1)(x) is [-π/2, π/2].
Correct Answer:
B
— [-π/2, π/2]
Learn More →
Q. The rate constant of a reaction is affected by which of the following? (2023)
A.
Nature of the reactants
B.
Temperature
C.
Catalysts
D.
All of the above
Show solution
Solution
The rate constant of a reaction is affected by the nature of the reactants, temperature, and the presence of catalysts.
Correct Answer:
D
— All of the above
Learn More →
Q. The rate law for a reaction is determined experimentally and is dependent on which of the following?
A.
Stoichiometry of the reaction
B.
Mechanism of the reaction
C.
Equilibrium constant
D.
Temperature only
Show solution
Solution
The rate law for a reaction is determined experimentally and is dependent on the mechanism of the reaction.
Correct Answer:
B
— Mechanism of the reaction
Learn More →
Q. The rate law for a reaction is determined experimentally. Which of the following is true?
A.
It can be derived from stoichiometry
B.
It is always first-order
C.
It depends on the mechanism
D.
It is independent of temperature
Show solution
Solution
The rate law for a reaction depends on the mechanism of the reaction.
Correct Answer:
C
— It depends on the mechanism
Learn More →
Q. The rate law for a reaction is given as rate = k[A][B]². What is the overall order of the reaction?
Show solution
Solution
The overall order of the reaction is the sum of the powers of the concentration terms, which is 1 + 2 = 3.
Correct Answer:
C
— 3
Learn More →
Q. The rate of a reaction doubles when the temperature is increased by 10°C. This is an example of which rule?
A.
Arrhenius equation
B.
Van 't Hoff rule
C.
Le Chatelier's principle
D.
Gibbs free energy
Show solution
Solution
This is an example of Van 't Hoff rule, which states that the rate of reaction doubles for every 10°C increase in temperature.
Correct Answer:
B
— Van 't Hoff rule
Learn More →
Q. The rate of a reaction is defined as the change in concentration of a reactant or product per unit time. What is the unit of rate?
A.
mol/L
B.
mol/L·s
C.
L/mol·s
D.
1/s
Show solution
Solution
The rate of reaction is expressed in terms of concentration change per unit time, hence the unit is mol/L·s.
Correct Answer:
B
— mol/L·s
Learn More →
Q. The rate of a reaction is defined as the change in concentration of a reactant or product per unit time. What is the general form of the rate equation? (2023)
A.
Rate = k[A]^n
B.
Rate = k[A][B]
C.
Rate = k[A]^2[B]
D.
Rate = k[A] + [B]
Show solution
Solution
The general form of the rate equation is Rate = k[A]^n, where n is the order of the reaction.
Correct Answer:
A
— Rate = k[A]^n
Learn More →
Q. The rate of a reaction is directly proportional to the concentration of one reactant raised to the power of 2. What is the order of the reaction? (2022)
A.
Zero order
B.
First order
C.
Second order
D.
Third order
Show solution
Solution
If the rate is proportional to the concentration of one reactant raised to the power of 2, the reaction is second order.
Correct Answer:
C
— Second order
Learn More →
Q. The rate of a reaction is directly proportional to the product of the concentrations of the reactants raised to their respective powers. This is known as what?
A.
Rate law
B.
Equilibrium constant
C.
Reaction quotient
D.
Catalytic law
Show solution
Solution
This relationship is known as the rate law of the reaction.
Correct Answer:
A
— Rate law
Learn More →
Q. The rate of a reaction is directly proportional to the product of the concentrations of the reactants raised to their respective powers. This statement defines:
A.
Rate law
B.
Equilibrium constant
C.
Reaction quotient
D.
Catalytic efficiency
Show solution
Solution
This statement defines the rate law of a reaction.
Correct Answer:
A
— Rate law
Learn More →
Q. The rate of a reaction is directly proportional to the product of the concentrations of the reactants raised to their respective powers. This statement defines which law?
A.
Law of conservation of mass
B.
Rate law
C.
Le Chatelier's principle
D.
Gibbs free energy
Show solution
Solution
This statement defines the rate law of a chemical reaction.
Correct Answer:
B
— Rate law
Learn More →
Q. The rate of a reaction is directly proportional to the product of the concentrations of the reactants raised to their respective powers. This statement defines which of the following? (2020)
A.
Rate law
B.
Equilibrium constant
C.
Le Chatelier's principle
D.
Reaction mechanism
Show solution
Solution
This statement defines the rate law of a reaction.
Correct Answer:
A
— Rate law
Learn More →
Q. The rate of a reaction is given by the equation rate = k[A]^2[B]. What is the overall order of the reaction? (2020)
Show solution
Solution
The overall order of the reaction is 2 (from [A]^2) + 1 (from [B]) = 3.
Correct Answer:
C
— 3
Learn More →
Showing 16441 to 16470 of 30202 (1007 Pages)
