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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.

800 board questions•Model answers•Marking-scheme points•Every chapter•CBSE · ISC · State boards

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Class 11 Physics · +1Class 11 Chemistry · +1Class 11 Maths · +1Class 11 Biology · +1Class 12 Physics · +2Class 12 Chemistry · +2Class 12 Maths · +2Class 12 Biology · +2
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MathsClass 112 marksmedium

Permutations and Combinations

Find the value of r if 10Cr = 10C(r + 2).

Reveal model answer + marking points▾

We use the property that nCa = nCb implies either a = b or a + b = n. Since r is not equal to r + 2, we must have r + (r + 2) = 10, so 2r + 2 = 10, giving 2r = 8 and r = 4.

nCa = nCb => a = b or a + b = n

Marking-scheme points

  • ✓nCa = nCb => a = b or a + b = n
  • ✓Here r + (r + 2) = 10
  • ✓r = 4
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MathsClass 112 markseasy

Binomial Theorem

State the binomial theorem for (a + b)^n where n is a positive integer, and write the general term.

Reveal model answer + marking points▾

The binomial theorem states that (a + b)^n = nC0 a^n + nC1 a^(n-1) b + nC2 a^(n-2) b^2 + ... + nCn b^n = sum over r from 0 to n of nCr a^(n-r) b^r. The general term (the (r+1)th term) is T(r+1) = nCr a^(n-r) b^r.

T(r+1) = nCr a^(n-r) b^r

Marking-scheme points

  • ✓(a + b)^n = sum of nCr a^(n-r) b^r, r = 0 to n
  • ✓There are (n + 1) terms
  • ✓General term T(r+1) = nCr a^(n-r) b^r
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MathsClass 112 marksmedium

Binomial Theorem

Find the middle term in the expansion of (x + 2y)^6.

Reveal model answer + marking points▾

Here n = 6 is even, so there is one middle term, the (n/2 + 1) = 4th term. T4 = 6C3 x^3 (2y)^3 = 20 x^3 x 8 y^3 = 160 x^3 y^3.

middle term = (n/2 + 1)th term when n is even

Marking-scheme points

  • ✓n = 6 even -> single middle term = 4th term
  • ✓T4 = 6C3 x^3 (2y)^3
  • ✓= 20 x 8 x^3 y^3 = 160 x^3 y^3
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