List of top Questions asked in CBSE Class XI

The sum of some terms of G.P. is 315 whose first term and the common ratio are 5 and 2, respectively. Find the last term and the number of terms.
Let f be the subset of Z x Z defined by f = {(ab, a+b): a, b ∈ Z}. Is f a function from Z to Z? Justify your answer.
Let A = {9, 10, 11, 12, 13} and let f: A \(→\) N be defined by f(n) = the highest prime factor of n. Find the range of f.
Evaluate the Given limit: \(\lim_{x\rightarrow \pi}\) \(\frac{sin(\pi-x)}{\pi(\pi-x)}\)
If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.
If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are A±√(A+G)(A-G).

The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2nd hour, 4th hour and nth hour ?

What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?
Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Are the following true?
  1. f is a relation from A to B.
  2. f is a function from A to B.
Justify your answer in each case.
Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola \(16x^ 2 - 9y^2 = 576\)
Let f = {(1, 1), (2, 3), (0, -1), (-1, -3)} be a function from Z to Z defined by \(f(x) = ax+ b\), for some integers a, b. Determine a, b.
Let R be a relation from N to N defined by R = {(a, b): a, b ∈ N and a = b2}. Are the following true?
  1. (a, a) ∈ R, for all a ∈ N
  2. (a, b) ∈ R, implies (b, a) ∈ R
  3. (a, b) ∈ R, (b, c) ∈ R implies (a, c) ∈ R.
Justify your answer in each case.
Insert two numbers between 3 and 81 so that the resulting sequence is G.P.
If a, b, c and d are in G.P. show that (a 2 + b 2 + c 2 ) (b 2 + c 2 + d 2 ) = (ab + bc + cd)2.
Evaluate the Given limit: \(\lim_{x\rightarrow 0}\) \(\frac{sin\,ax}{sin\,bx}\) ,a,b ≠0
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|.