List of top Mathematics Questions asked in CBSE Class XI

Let f, g:R\(\to\)R be defined, respectively by f(x) = x+1, g(x) = 2x-3. Find f+g, f-g and \(\frac fg\).
Show that the ratio of the sum of first n terms of a G.P. to the sum of terms from (n + 1)th to (2n) th term is \(\frac{1 }{ r^n}.\)
Draw appropriate Venn diagram for each of the following: 
(i) (A ∪ B)' 
(ii) A' ∩ B'
(iii) (A ∩ B)'
(iv) A' ∪ B'
Let \(f={(x,\frac {x^2}{1+x^2}):x∈R}\)  be a function from R into R. Determine the range of f.
Evaluate the Given limit: \(\lim_{x\rightarrow 0}\)\(\frac{sin\,ax}{bx}\)
Evaluate the Given limit: \(\lim_{x\rightarrow -2}\) \(\frac{\frac{1}{x}+\frac{1}{2}}{x+2}\)
Find sets A, B and C such that \(A ∩ B, B ∩ C\) and \(A ∩ C\) are non-empty sets and \(A ∩ B ∩ C = \phi.\)

If the first and the nth term of a G.P. are a and b, respectively, and if P is the product of n terms, prove that P2 = (ab) n .

Evaluate the Given limit: \(\lim_{x\rightarrow 1}\) \(\frac{ax^2+bx+c}{cx^2+bx+a}\) , a + b + c ≠0
Find the domain and the range of the real function f defined by f(x) = |x-1|.
Let A and B be sets. If \(A ∩ X = B ∩ X = \phi\) and \(A ∪ X = B ∪ X\) for some set X, show that A = B.  (Hints \(A = A ∩ (A ∪ X), B = B ∩ (B ∪ X)\) and use distributive law)
Evaluate the Given limit: \(\lim_{z\rightarrow 1}\) \(\frac{z^{\frac{1}{3}}-1}{z^{\frac{1}{6}}-1}\)
Find the domain and the range of the real function f defined by \(f(x)=\sqrt {(x-1)}\)
Show that \(A ∩ B = A ∩ C\) need not imply B = C.
If the pth, qth and rth terms of a G.P. are a, b and c, respectively. Prove that \(a^{q-r} b^{r-p} c^{p-q}=1.\)
Evaluate the Given limit: \(\lim_{x\rightarrow 0}\) \(\frac{ax+b}{cx}\) + 1
Using properties of sets show that (i) \(A ∪ (A ∩ B) = A \) (ii) \(A ∩ (A ∪ B) = A.\)
Show that for any sets A and B, \(A = (A ∩ B) ∪ (A – B)\) and \(A ∪ (B – A) = (A ∪ B)\)

Show that the products of the corresponding terms of the sequences a, ar, ar2,…arn – 1 and A, AR, AR2, … ARn – 1 form a G.P, and find the common ratio.

Show that if \(A ⊂ B\), then \(C – B ⊂ C – A.\)
Find the domain of the function \(f(x)=\frac {x^2+2x+1}{x^2-8x+12}\)
Show that the following four conditions are equivalent: \((i) A ⊂ B (ii) A – B = \phi (iii) A ∪ B = B (iv) A ∩ B = A\)
If \(f(x) = x^2 \), find \(\frac {f(1.1)-f(1)}{(1.1-1)}\)
The relation f is defined by

\(f(x) =   \begin{cases}     x^2,       & \quad  0≤x≤3\\     3x,  & \quad  3≤x≤10 \end{cases}\)
The relation g is defined by
\(g(x) =   \begin{cases}     x^2,       & \quad  0≤x≤2\\     3x,  & \quad  2≤x≤10 \end{cases}\)
Show that f is a function and g is not a function.

The function 't' which maps temperature in degree Celsius into temperature in degree Fahrenheit is defined by:  \(t(C)=\frac {9C}{5}+32\)
Find:
  1. t(0) 
  2. t(28) 
  3. t(-10) 
  4. The value of C, when t(C) = 212