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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 113 marksmedium
Permutations and Combinations
From 7 men and 5 women, in how many ways can a committee of 5 members be formed consisting of exactly 3 men and 2 women?
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Choose 3 men from 7 in 7C3 ways and 2 women from 5 in 5C2 ways. 7C3 = (7 x 6 x 5)/(3 x 2 x 1) = 35 and 5C2 = (5 x 4)/(2 x 1) = 10. By the multiplication principle, total ways = 35 x 10 = 350.
total = 7C3 x 5C2
Marking-scheme points
- ✓Choose men: 7C3 = 35
- ✓Choose women: 5C2 = 10
- ✓Total = 35 x 10 = 350
MathsClass 113 marksmedium
Binomial Theorem
Expand (2x - 3)^4 using the binomial theorem.
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(2x - 3)^4 = 4C0 (2x)^4 + 4C1 (2x)^3(-3) + 4C2 (2x)^2(-3)^2 + 4C3 (2x)(-3)^3 + 4C4 (-3)^4 = 16x^4 + 4(8x^3)(-3) + 6(4x^2)(9) + 4(2x)(-27) + 81 = 16x^4 - 96x^3 + 216x^2 - 216x + 81.
(a + b)^4 expansion
Marking-scheme points
- ✓Use T(r+1) = 4Cr (2x)^(4-r)(-3)^r
- ✓Compute each of the 5 terms
- ✓= 16x^4 - 96x^3 + 216x^2 - 216x + 81
MathsClass 113 marksmedium
Binomial Theorem
Find the coefficient of x^5 in the expansion of (x + 3)^8.
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The general term is T(r+1) = 8Cr x^(8-r) 3^r. For the term in x^5, we need 8 - r = 5, so r = 3. The coefficient = 8C3 x 3^3 = 56 x 27 = 1512.
T(r+1) = nCr a^(n-r) b^r
Marking-scheme points
- ✓General term = 8Cr x^(8-r) 3^r
- ✓For x^5: 8 - r = 5 -> r = 3
- ✓Coefficient = 8C3 x 3^3 = 56 x 27 = 1512
MathsClass 113 markshard
Binomial Theorem
Find the term independent of x in the expansion of (x^2 - 1/x)^6.
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Binomial Theorem
Using the binomial theorem, evaluate (sqrt2 + 1)^4 + (sqrt2 - 1)^4.
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Binomial Theorem
Find the coefficient of x^6 y^3 in the expansion of (x + 2y)^9.
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Sequences and Series
Find the sum of the first 20 terms of the arithmetic progression 3, 7, 11, 15, ...
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Sequences and Series
The sum of three numbers in AP is 24 and their product is 440. Find the numbers.
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Sequences and Series
Find the sum of the first 6 terms of the geometric progression 5, 15, 45, ...
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Sequences and Series
Find the sum to infinity of the geometric progression 1 + 1/3 + 1/9 + 1/27 + ...
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Sequences and Series
Find the sum of the squares of the first 10 natural numbers, that is 1^2 + 2^2 + ... + 10^2.
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Straight Lines
Find the equation of the line passing through the points (1, 2) and (3, 6).
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Straight Lines
Find the acute angle between the lines x + sqrt(3) y = 1 and sqrt(3) x + y = 1.
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Straight Lines
Find the distance of the point (3, -5) from the line 3x - 4y - 26 = 0.
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Straight Lines
Find the equation of the line which makes intercepts -3 and 2 on the x-axis and y-axis respectively.
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Straight Lines
Find the equation of the perpendicular bisector of the line segment joining the points (1, 1) and (3, 5).
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Conic Sections
For the parabola y^2 = 12x, find the coordinates of the focus, the equation of the directrix, the axis and the length of the latus rectum.
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Conic Sections
For the ellipse x^2/25 + y^2/9 = 1, find the vertices, foci, eccentricity and length of the latus rectum.
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Conic Sections
For the hyperbola x^2/16 - y^2/9 = 1, find the vertices, foci and eccentricity.
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Conic Sections
Find the equation of the ellipse with vertices (+/-5, 0) and foci (+/-4, 0).
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