List of top Mathematics Questions asked in CBSE Class XI

Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that

1. A x (B ∩C) = (A x B) ∩(A x C)
2. A x C is a subset of B x D

Prove that \(tan\,4x=\frac{4\,tanx(1-tan^2x)}{1-6\,tan^2x+tan^4x}\).

Find n if ^n-1P₃: ⁿP₃ = 1: 9.

Prove that cos² 2x-cos² 6x = sin 4x sin 8x

If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20},
C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}; find
(i) A - B
(ii) A - C
(iii) A - D
(iv) B - A
(v) C - A
(vi) D - A
(vii) B - C
(viii) B - D
(ix) C - B
(x) D - B
(xi) C - D
(xii) D - C

The Cartesian product A x A has 9 elements among which are found (-1, 0) and (0, 1). Find the set A and the remaining elements of A x A.

If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:
(i) A = {a, b, c}
(ii) B = {d, e, f, g}
(iii) C = {a, c, e, g}
(iv) D = {f, g, h, a}

Write the following as intervals:
(i) {\(x: x ∈ R, -4 < x ≤ 6\)}
(ii) {\(x: x ∈ R, -12 < x < -10\)}
(iii) {\(x: x ∈ R, 0 ≤ x < 7\)}
(iv) {\(x: x ∈ R, 3 ≤ x ≤ 4\)}

Reduce the following equations into intercept form and find their intercepts on the axes.
(i)  \(3x+2y-12=0\)
(ii)  \(4x-3y=6\)
(iii)  \(3y+2=0. \)

If A = {-1, 1}, find A x A x A.

List all the elements of the following sets: 
(i) A = {x: x is an odd natural number} 
(ii) B = {x: x is an \(\frac{-1}{2} < x <\frac{ 9}{2}\)  integer,} 
(iii) C = {x: x is an \(x^2 ≤ 4 \) integer, 
(iv) D = {x: x is a letter in the word “LOYAL“} 
(v) E = {x: x is a month of a year not having 31 days} 
(vi) F = {x: x is a consonant in the English alphabet which proceeds k}.

How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?

In the following, state whether A = B or not:
(i) A = {a, b, c, d}; B = {d, c, b, a}
(ii) A = {4, 8, 12, 16}; B = {8, 4, 16, 18}
(iii) A = {2, 4, 6, 8, 10}; B = {x: x is positive even integer and x ≤ 10} (iv) A = {x: x is a multiple of 10}; B = {10, 15, 20, 25, 30 ...}

Find \((x + 1)^6 - (x - 1)^6\). Hence or otherwise evaluate \((\sqrt2 + 1)^6 + (\sqrt2 - 1)^6.\)

Find the sum to indicated number of terms in each of the geometric progressions in 1, – a, \(a^2\), –\(a^3\), ... n terms (if a ≠ – 1).

Find the multiplicative inverse of the complex number \(√5+3i\)\(\)

Find the derivative of x² – 2 at x = 10

Find \((a + b)^4 - (a - b)^4\). Hence, evaluate \((\sqrt3 + \sqrt2)^4 - (\sqrt3 - \sqrt2)^4\).

In the triangle ABC with vertices A (2, 3), B (4, –1) and C (1, 2), find the equation and length of altitude from the vertex A.

In Class XI of a school 40% of the student's study Mathematics and 30% study Biology. 10% of the class study both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology.

Find the distance between parallel lines
(i) \(15x + 8y – 34 = 0\) and \(15x + 8y + 31 = 0\)
(ii) \(l (x + y) + p = 0\) and \(l (x + y) – r = 0.\)

Prove that cos 4x =1-8 sin² x cos² x

The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio (3+2√2) : (3-2√2).