Board Boosters
The questions your board exam loves to ask
800 most-asked Class 11 & 12 (+1 / +2) questions across Physics, Chemistry, Maths and Biology — each with a model answer and the exact marking-scheme points examiners reward. Revise smart, walk in calm.
MathsClass 112 markseasy
Sets
If A = {1, 2, 3}, write the power set of A and state n(P(A)).
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The power set is the set of all subsets of A. P(A) = { {}, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3} }. The number of elements n(P(A)) = 2^n = 2^3 = 8.
n(P(A)) = 2^n
Marking-scheme points
- ✓Power set = set of all subsets (including empty set and A itself)
- ✓List all 8 subsets
- ✓n(P(A)) = 2^3 = 8
The concept
The power set is the set of ALL subsets of a set, including the empty set and the set itself.
Why it matters
Power sets underpin logic, probability and computer science (every combination of options).
💡 Memory trick
n elements -> 2^n subsets. For {1,2,3}: 2^3 = 8 subsets.
MathsClass 112 markseasy
Sets
In a class of 35 students, 24 like cricket and 16 like football. If each student likes at least one of the two games, how many like both?
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Let n(C) = 24, n(F) = 16, n(C union F) = 35 (each likes at least one). By the formula n(C union F) = n(C) + n(F) - n(C intersection F), we get 35 = 24 + 16 - n(C intersection F), so n(C intersection F) = 40 - 35 = 5. Hence 5 students like both games.
n(A union B) = n(A) + n(B) - n(A intersection B)
Marking-scheme points
- ✓n(C union F) = n(C) + n(F) - n(C intersection F)
- ✓35 = 24 + 16 - x
- ✓x = 5 students like both
MathsClass 113 marksmedium
Sets
In a survey of 600 students, 150 drink tea, 225 drink coffee and 100 drink both tea and coffee. Find how many students drink neither tea nor coffee.
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n(T) = 150, n(C) = 225, n(T intersection C) = 100. Students drinking at least one = n(T union C) = n(T) + n(C) - n(T intersection C) = 150 + 225 - 100 = 275. Students drinking neither = total - n(T union C) = 600 - 275 = 325.
neither = n(U) - n(A union B)
Marking-scheme points
- ✓n(T union C) = 150 + 225 - 100 = 275
- ✓Neither = total - n(T union C)
- ✓600 - 275 = 325 students
MathsClass 112 markseasy
Sets
Define union, intersection and difference of two sets with an example each.
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Sets
Verify De Morgan's law (A union B)' = A' intersection B' for U = {1,2,3,4,5,6,7,8,9,10}, A = {2,3,4,5}, B = {4,5,6,7,8}.
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Sets
Write the set {x : x is a real number, -3 <= x < 5} in interval notation, and write (2, 9] in set-builder form.
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Relations and Functions
If A = {1, 2} and B = {3, 4}, find A x B and n(A x B).
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Relations and Functions
If the ordered pairs (x + 1, y - 2) = (3, 1), find the values of x and y.
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Relations and Functions
For the relation R = {(1, 2), (2, 4), (3, 6)}, write its domain and range. Define domain and range.
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Relations and Functions
Find the domain and range of the function f(x) = sqrt(9 - x^2).
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Relations and Functions
Define a one-one (injective) function and an onto (surjective) function.
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Relations and Functions
If f(x) = x^2 + 1, find f(2), f(-1), and all values of x for which f(x) = 10.
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Trigonometric Functions
Convert 5pi/6 radians into degrees and 240 degrees into radians.
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Trigonometric Functions
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
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Trigonometric Functions
Find the value of sin 75 degrees.
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Trigonometric Functions
Prove that cos(A + B) cos(A - B) = cos^2 A - sin^2 B.
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Trigonometric Functions
If cos x = -3/5 and x lies in the second quadrant, find sin x and tan x.
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Trigonometric Functions
Prove that 1 + tan^2 x = sec^2 x.
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Trigonometric Functions
Find the general solution of the equation sin x = 1/2.
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Trigonometric Functions
Find the general solution of the equation tan x = sqrt(3).
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