List of top Mathematics Questions

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.
Evaluate \(\lim_{x\rightarrow 0}\)f(x), where { |x|/x, x≠0 0, x=0

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.

Find \(\lim_{x\rightarrow 1}\) f(x) where { x2 -1, x≤1 -x2-1, x>1
Find \(\lim_{x\rightarrow 0}\) f(x) and \(\lim_{x\rightarrow 1}\) f(x) where { 2x+3, x≤0 3 (x+1), x>0
Solve the given inequality for real x: 4x+3 < 5x+7
Evaluate the Given limit: \(\lim_{x\rightarrow \frac{\pi}{2}}\frac{tan\,2x}{x}-\frac{\pi}{2}\)
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.
Evaluate the Given limit: \(\lim_{x\rightarrow 0}(cosec\,x-cot\,x)\)
Evaluate the Given limit: \(\lim_{x\rightarrow 0}\) sinax =\(\frac{bx}{ax}\)+ sinbx a,b,a+b ≠ 0
Evaluate the Given limit: \(\lim_{x\rightarrow 0} x\,sec\,x\)
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: \(\lim_{x\rightarrow 0}\) \(\frac{cos^2x-1}{cos\,x-1}\)
Evaluate the Given limit: \(\lim_{x\rightarrow 0}\) \(\frac{cos\,x}{\pi-x}\)
Solve: 3x+8 > 2, 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: 5x - 3 < 7, when 
  1. x is an integer.
  2. x is a real number.
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 ?