List of top Mathematics Questions asked in CBSE Class XI

\(\text{Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers)}\)\((px+q)(\frac{r}{x}+s).\)

\(\text{Find the number of non-zero integral solutions of the equation }|1-i|^x=2^2.\)
If α and β are different complex numbers with |β|=1, then find \(| \frac{β-α}{1-\bar{α}β} |.\)
If \((x+iy) ^3=u+iv,\) then show that \(\frac{u}{x}+\frac{v}{y}=4(x^2-y^2).\)
Find the modulus of \(\frac{1+i}{1+i}-\frac{1-i}{1+i}.\)
\(Let\, z_1=2 – i,z_2 = –2+i.\, Find\, (i) Re(\frac{z_1z_2}{z_1}), (ii) \,Im(\frac{1}{z_1z_1})\)
\(If a + ib =\frac{(x+1)^2}{2x^2+1},\,prove\, that\, a^2 + b^2 =\frac{(x^2+1)^2}{(2x^2+1)}\)
\(If \,z_1=2-i,z_2=1+i, find \,|\frac{z_1+z_2+1}{z1-z2+1}|.\)
\(if\, x-iy=√\frac{a-ib}{c-id}\) prove that \((x^2y^2)^2=\frac{a^2+b^2}{c^2+d^2}.\)
For any two complex numbers z1 and z2, prove that Re (z1z2) = Re z1 Re z2-Im z1 Im z2.
Evaluate \([i^{18}+(\frac{1}{i})^{25}]^3.\)
A function f is defined by f(x) = 2x - 5. Write down the values of:
  1. f(0)
  2. f(7)
  3. f(-3)
Find the domain and range of the following real function:
  1. f(x) = |x|
  2. f(x)=\(\sqrt {9-x^2}\)
Which of the following relations are functions? Give reasons. If it is a function, determine its domain and range.
  1. {(2, 1), (5, 1), (8, 1), (11, 1), (14, 1), (17, 1)}
  2. {(2, 1), (4, 2), (6, 3), (8, 4), (10, 5), (12, 6), (14, 7)}
  3. {(1, 3), (1, 5), (2, 5)}
Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.
Evaluate the Given limit: \(\lim_{x\rightarrow 3}\) \(\frac{x^4-81}{2x^2-5x-3}\)
Solve: 12 x > 30, when
  1. x is a natural number 
  2. x is an integer
Find the equation of the set of points which are equidistant from the points (1, 2, 3) and (3, 2, –1).
Verify the following:
(i) (0, 7, –10), (1, 6, – 6) and (4, 9, – 6) are the vertices of an isosceles triangle.
(ii) (0, 7, 10), (–1, 6, 6) and (– 4, 9, 6) are the vertices of a right angled triangle.
(iii) (–1, 2, 1), (1, –2, 5), (4, –7, 8) and (2, –3, 4) are the vertices of a parallelogram.
If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that
(i) \((A ∪ B)' = A ' ∩ B'\) (ii) \((A ∩ B)' = A' ∪ B\)
Taking the set of natural numbers as the universal set, write down the complements of the following sets:
(i)  {x: x is an even natural number}
(ii)  {x: x is an odd natural number}
(iii)  {x: x is a positive multiple of 3}
(iv)  {x: x is a prime number}
(v)  {x: x is a natural number divisible by 3 and 5}
(vi)  {x: x is a perfect square}
(vii)  {x: x is perfect cube}
(viii)  {x: x + 5 = 8}
(ix)  {x: 2x + 5 = 9}
(x)  {x: \(x ≥ 7\)}
(xi)  {x: x \(\in\) N and \(2x + 1 > 10\)}
Let U ={1, 2, 3; 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find
(i) \(A'\)
(ii) \(B'\)
(iii) \((A ∪ C)'\)
(iv) \((A ∪ B)'\)
(v) \( (A')'\)
(vi) \((B-C)'\)
State whether each of the following statement is true or false. Justify your answer.
(i) {2, 3, 4, 5} and {3, 6} are disjoint sets.
(ii) {a, e, i, o, u} and {a, b, c, d} are disjoint sets.
(iii) {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.
(iv) {2, 6, 10} and {3, 7, 11} are disjoint sets.
If R is the set of real numbers and Q is the set of rational numbers, then what is R - Q?
If X = {a, b, c, d} and Y = {f, b, d, g}, find
(i) X - Y
(ii) Y - X
(iii) X \(\cap\) Y