List of top Mathematics Questions

Which term of the following sequences: 

(a) 2 ,\(2\sqrt{2}\) , 4 ,.... is 128 ?

 (b) \(\sqrt{3}\), 3, \(3\sqrt{3}\),... is 729 ? 

(c) \(\frac{1}{3},\frac{1}{9},\frac{1}{27}\) ,.... is \(\frac{1}{19683}\) ?

By using the concept of equation of a line, prove that the three points (3, 0), (– 2, – 2) and (8, 2) are collinear.
\(2cos \frac{π}{13}cos\frac{9π}{13}+cos \frac{3π}{13}+cos \frac{5π}{13}=0\)

Prove that (sin 3x+sin x) sinx+(cos 3x–cos x) cos x=0

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.
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.
Solve: 5x - 3 < 7, when 
  1. x is an integer.
  2. x is a real number.
The first term of a G.P. is 1. The sum of the third term and fifth term is 90. Find the common ratio of G.P.
Solve: 3x+8 > 2, when 
  1. x is an integer.
  2. x is a real number.
Evaluate the Given limit: \(\lim_{x\rightarrow 0}\) \(\frac{cos\,x}{\pi-x}\)
Evaluate the Given limit: \(\lim_{x\rightarrow 0}\) \(\frac{cos^2x-1}{cos\,x-1}\)
The sum of three numbers in G.P. is 56. If we subtract 1, 7, 21 from these numbers in that order, we obtain an arithmetic progression. Find the numbers.
Evaluate the Given limit: \(\lim_{x\rightarrow 0}\) \(\frac{ax+xcos\,x}{b\,sin\,x}\)
Evaluate the Given limit: \(\lim_{x\rightarrow 0} x\,sec\,x\)
Evaluate the Given limit: \(\lim_{x\rightarrow 0}\) sinax =\(\frac{bx}{ax}\)+ sinbx a,b,a+b ≠ 0
Evaluate the Given limit: \(\lim_{x\rightarrow 0}(cosec\,x-cot\,x)\)
A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.

If  \(\frac{ a + bx }{ a - bx }= \frac{b + cx }{ b - cx} =\frac{ c + dx }{ c - dx }(x ≠ 0),\) then show that a, b, c and d are in G.P.

Evaluate the Given limit: \(\lim_{x\rightarrow \frac{\pi}{2}}\frac{tan\,2x}{x}-\frac{\pi}{2}\)
Find \(\lim_{x\rightarrow 0}\) f(x) and \(\lim_{x\rightarrow 1}\) f(x) where { 2x+3, x≤0 3 (x+1), x>0
Find \(\lim_{x\rightarrow 1}\) f(x) where { x2 -1, x≤1 -x2-1, x>1

Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P2Rn = Sn.

Evaluate \(\lim_{x\rightarrow 0}\)f(x), where { |x|/x, x≠0 0, x=0
If a, b, c, d are in G.P, prove that \( (a^n+ b^n), (b^n+c^n), (c^n+d^n) \)dn) are in G.P.