Q. If the potential difference across a capacitor is increased, what happens to the charge stored in it? (2020)
A.
It decreases
B.
It remains the same
C.
It increases
D.
It becomes zero
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Solution
The charge (Q) stored in a capacitor is directly proportional to the potential difference (V) across it, given by Q = CV.
Correct Answer: C — It increases
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Q. If the potential difference between two points is 10 V and the work done to move a charge of 2 C between these points is: (2020)
A.
5 J
B.
10 J
C.
20 J
D.
40 J
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Solution
Work done (W) = Charge (Q) × Potential difference (V) = 2 C × 10 V = 20 J.
Correct Answer: C — 20 J
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Q. If the pressure of a gas is increased while keeping the temperature constant, what happens to its volume? (2020)
A.
It increases
B.
It decreases
C.
It remains the same
D.
It becomes zero
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Solution
According to Boyle's Law, P * V = constant at constant temperature, so if P increases, V must decrease.
Correct Answer: B — It decreases
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Q. If the price of a book is increased by 10% and then decreased by 10%, what is the net change in price?
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Solution
Let the original price be $100. After a 10% increase, the price becomes $110. After a 10% decrease, the price becomes $110 - $11 = $99. The net change is -1%, so the answer is 0%.
Correct Answer: A — 0%
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Q. If the principal amount is $2000 and the total amount after 3 years at a certain rate of simple interest is $2400, what is the rate of interest? (2000)
A.
5%
B.
6.67%
C.
10%
D.
12%
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Solution
The interest earned is $400. Using SI = PRT, we have 400 = 2000 * R * 3. Solving for R gives R = 6.67%.
Correct Answer: B — 6.67%
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Q. If the principal is $800 and the rate of interest is 4% per annum, what will be the total amount after 3 years at simple interest?
A.
$840
B.
$850
C.
$860
D.
$870
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Solution
Using the simple interest formula, Total Amount = Principal + SI = 800 + (800 * 4 * 3) / 100 = $840.
Correct Answer: A — $840
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Q. If the principal is $800 and the rate of interest is 6% per annum, what will be the total amount after 4 years at simple interest?
A.
$960
B.
$1040
C.
$800
D.
$840
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Solution
Total amount = Principal + SI = 800 + (800 * 6/100 * 4) = $1040.
Correct Answer: B — $1040
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Q. If the principal quantum number n = 4 and the azimuthal quantum number l = 2, what is the maximum number of electrons in this subshell?
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Solution
The maximum number of electrons in a subshell is given by 2(2l + 1). For l = 2, it is 2(2*2 + 1) = 10.
Correct Answer: C — 14
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Q. If the principal quantum number n = 4, what are the possible values of l?
A.
0, 1, 2, 3
B.
1, 2, 3, 4
C.
0, 1, 2, 3, 4
D.
0, 1, 2
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Solution
For n=4, l can take values 0, 1, 2, or 3.
Correct Answer: A — 0, 1, 2, 3
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Q. If the principal quantum number n = 4, what are the possible values of the azimuthal quantum number l?
A.
0, 1, 2, 3
B.
1, 2, 3, 4
C.
0, 1, 2, 3, 4
D.
0, 1, 2
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Solution
For n=4, l can take values from 0 to n-1, which are 0, 1, 2, and 3.
Correct Answer: A — 0, 1, 2, 3
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Q. If the probability of a student passing an exam is 0.75, what is the probability that the student fails?
A.
0.25
B.
0.5
C.
0.75
D.
0.1
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Solution
The probability of failing is 1 - P(passing) = 1 - 0.75 = 0.25.
Correct Answer: A — 0.25
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Q. If the probability of an event A is 0.3, what is the probability of the event not occurring?
A.
0.7
B.
0.3
C.
0.5
D.
0.2
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Solution
Probability of not A = 1 - P(A) = 1 - 0.3 = 0.7.
Correct Answer: A — 0.7
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Q. If the probability of an event A is 0.7, what is the probability of the event not occurring?
A.
0.3
B.
0.7
C.
0.5
D.
0.1
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Solution
Probability of not A = 1 - P(A) = 1 - 0.7 = 0.3.
Correct Answer: A — 0.3
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Q. If the probability of an event is 0.7, what is the probability of its complement?
A.
0.3
B.
0.7
C.
1
D.
0.5
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Solution
Probability of complement = 1 - P(event) = 1 - 0.7 = 0.3.
Correct Answer: A — 0.3
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Q. If the probability of an event is 0.7, what is the probability of the event not occurring?
A.
0.3
B.
0.7
C.
0.5
D.
0.1
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Solution
Probability of not occurring = 1 - P(event) = 1 - 0.7 = 0.3.
Correct Answer: A — 0.3
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Q. If the probability of an event occurring is 0.3, what is the probability of it not occurring? (2023)
A.
0.3
B.
0.7
C.
0.5
D.
0.1
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Solution
Probability of not occurring = 1 - P(event) = 1 - 0.3 = 0.7.
Correct Answer: B — 0.7
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Q. If the probability of event A is 0.2 and the probability of event B is 0.5, what is the probability of either A or B occurring if A and B are independent?
A.
0.7
B.
0.6
C.
0.5
D.
0.4
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Solution
The probability of either A or B occurring is P(A) + P(B) - P(A and B) = 0.2 + 0.5 - (0.2 * 0.5) = 0.7.
Correct Answer: A — 0.7
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Q. If the probability of event A is 0.4 and event B is 0.5, what is the probability of both events occurring if they are independent?
A.
0.2
B.
0.4
C.
0.5
D.
0.6
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Solution
P(A and B) = P(A) * P(B) = 0.4 * 0.5 = 0.2.
Correct Answer: A — 0.2
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Q. If the probability of event A is 0.4 and the probability of event B is 0.5, what is the probability of both A and B occurring if they are independent?
A.
0.2
B.
0.4
C.
0.5
D.
0.9
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Solution
For independent events, P(A and B) = P(A) * P(B) = 0.4 * 0.5 = 0.2.
Correct Answer: A — 0.2
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Q. If the probability of event C is 0.2 and the probability of event D is 0.3, what is the probability of either C or D occurring if they are mutually exclusive?
A.
0.5
B.
0.6
C.
0.3
D.
0.2
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Solution
For mutually exclusive events, P(C or D) = P(C) + P(D) = 0.2 + 0.3 = 0.5.
Correct Answer: B — 0.6
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Q. If the probability of rain tomorrow is 0.7, what is the probability that it will not rain?
A.
0.3
B.
0.5
C.
0.7
D.
0.9
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Solution
The probability that it will not rain is 1 - 0.7 = 0.3.
Correct Answer: A — 0.3
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Q. If the product of two consecutive integers is 72, which of the following pairs could represent these integers?
A.
8 and 9
B.
6 and 7
C.
5 and 6
D.
9 and 10
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Solution
6 and 7 are consecutive integers whose product is 42, not 72.
Correct Answer: B — 6 and 7
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Q. If the product of two numbers is a multiple of 15, which of the following must be true?
A.
At least one of the numbers is a multiple of 3.
B.
At least one of the numbers is a multiple of 5.
C.
Both numbers are even.
D.
Both numbers are odd.
Show solution
Solution
For the product to be a multiple of 15, at least one of the numbers must be a multiple of 5.
Correct Answer: B — At least one of the numbers is a multiple of 5.
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Q. If the quadratic equation ax^2 + bx + c = 0 has roots 3 and -2, what is the value of a?
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Solution
Using the fact that the product of the roots is c/a and the sum is -b/a, we can set a = 1, b = -1, c = -6.
Correct Answer: A — 1
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Q. If the quadratic equation ax^2 + bx + c = 0 has roots p and q, what is the value of p + q? (2020)
A.
-b/a
B.
b/a
C.
c/a
D.
-c/a
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Solution
By Vieta's formulas, the sum of the roots p + q = -b/a.
Correct Answer: A — -b/a
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Q. If the quadratic equation ax^2 + bx + c = 0 has roots p and q, which of the following is correct?
A.
p + q = -b/a and pq = c/a
B.
p + q = b/a and pq = -c/a
C.
p + q = c/a and pq = -b/a
D.
p + q = -c/a and pq = b/a
Show solution
Solution
According to Vieta's formulas, the sum of the roots p and q is -b/a and the product is c/a.
Correct Answer: A — p + q = -b/a and pq = c/a
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Q. If the quadratic equation x^2 + 2px + p^2 - 4 = 0 has real roots, what is the condition on p?
A.
p > 2
B.
p < 2
C.
p = 2
D.
p >= 2
Show solution
Solution
The discriminant must be non-negative: (2p)^2 - 4(1)(p^2 - 4) >= 0 => 4p^2 - 4p^2 + 16 >= 0, which is always true. Thus, p can be any real number.
Correct Answer: D — p >= 2
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Q. If the quadratic equation x^2 + 2px + p^2 - 4 = 0 has roots that are equal, what is the value of p?
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Solution
Setting the discriminant to zero: (2p)^2 - 4(1)(p^2 - 4) = 0 leads to p = ±2.
Correct Answer: C — -2
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Q. If the quadratic equation x^2 + 2x + 1 = 0 is solved, what are the roots? (2022)
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Solution
The equation can be factored as (x + 1)(x + 1) = 0, giving the root -1 with multiplicity 2.
Correct Answer: A — -1
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Q. If the quadratic equation x^2 + 2x + k = 0 has equal roots, what is the value of k?
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Solution
For equal roots, the discriminant must be zero: 2^2 - 4*1*k = 0, leading to k = 1.
Correct Answer: C — -1
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