List of top Mathematics Questions

A geometric series has common ratio \(\frac{1}{3}\). If the sum of first four terms is 200, then the first term is
If \(z |z| = 24 + 7i\), where \(z\) is a complex number, then the value of \(|z|\) is equal to
The sum of the second and third terms of a G.P. is 8 and the fourth term is 4. The common ratio \(r \neq 1\) is
Let \(z = \frac{a - \frac{i}{2}}{i - 2}\), where \(a\) is a real number and \(i = \sqrt{-1}\). If \(\text{Im}(z) = 0\), then the value of \(a\) is equal to
In a complex plane, if two vertices of an equilateral triangle are at \(-3(1+i)\) and \(3(1-i)\), then the area of the triangle (in sq.units) is equal to
Let \(f : [-\frac{\pi}{2}, \frac{\pi}{2}] \rightarrow (-\infty, \infty)\) be given by \(f(x) = \tan(x)\sin(x)\). Then \(f(x)\) is
Let A and B denote the sets of students in a school who play cricket and football respectively. If \(n(A) = 45, n(B) = 35\) and \(n(A \cap B) = 13\), then \(n((A \cap B)' \cap (A \cup B))\) =
Find the total area of the region bounded between the curve \( y = x^3 \), the x-axis, and the vertical lines \( x = -1 \) and \( x = 1 \).
The focus of the parabola \( y^2 = 16x \) is
The integral of \(f(x)=1+x^2+x^4\) with respect to \(x^2\) is
A bag contains 6 blue and 6 green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue ball and one green ball is:
Consider the following statements:
Statement I : If $A$ is a non-singular matrix, then $A^{-1}$ exists.
Statement II : If $A$ and $B$ are symmetric matrices of same order, then $(AB - BA)$ is a skew symmetric matrix.
Choose the correct option.
The graph of \(y = f(x)\) is given. The number of zeroes of \(f(x)\) is :
Find the area of the region bounded by the curve \(y^2 = 4x\) and the line \(x = 3\).
If the sum of the first four terms of an A.P. is \(6\) and the sum of its first six terms is \(4\), then the sum of its first twelve terms is
Find the value of \( \left| \begin{matrix} 0 & c & b \\ c & 0 & a \\ b & a & 0 \end{matrix} \right|^2 \)
In Linear Programming Problem (LPP), the objective function $Z = ax + by$ has the same maximum value at two corner points. The number of points at which $Z_{max}$ occurs is

\[ \int \frac{3e^x + 5e^{-x}}{1 - 4e^{-x}} \, dx = 3f(x) + \frac{5}{4}g(x) + \frac{53}{4}\log h(x) + c \] Given the above conditions, find: \[ f(1) + g(1) + h(1) \] 

\[ \int_{0}^{8} x^{\frac{5}{3}} \left(4 - x^{\frac{2}{3}}\right)^{\frac{3}{2}} \, dx = \ ? \] 

\[ \lim_{x \rightarrow \frac{2}{3}} \frac{\sin\left(\pi \cos^2(3x-2)\right)} {9x^2-12x+4} = \ ? \] 

If \(A\) and \(B\) are the domain and range of the real valued function, \[ f(x)=\dfrac{|x|}{\sqrt{1-|x|}} \] then \(A \cup B =\ ?\) 

Differential equation for family \(y=ae^{2x}+bx^2\) is
If \(y=f(x)\) satisfies \[ \tan x \frac{dy}{dx}+(1+\tan^2 x)y=\tan x(1+\tan^2 x)^2 \] and passes through \(\left(\frac{\pi}{4},\frac{3}{4}\right)\), find \(f\left(\frac{\pi}{3}\right)\)
\(\int_0^2 |2x^2-9x+9|dx=\)
Area enclosed by \(x^2-2x+y+1=0\) and \(3x+y-3=0\)