List of top Mathematics Questions

If $-\frac{2{3}<x<\frac{2}{3}$, then the value of the $5^{th}$ term in the expansion of $\frac{1}{\sqrt{2-3x}}$ when $x = \frac{1}{2}$ is}

The sum of all integers between 1 and 100 (both inclusive) which are divisible by 5 or 13 is

If the sum of two roots of the equation \( x^4 + 2x^3 - 7x^2 - 8x + 12 = 0 \) is zero, then the sum of the squares of the other two roots is

\( (1+\sqrt{3}i)^6 - (\sqrt{3}+i)^6 = \)

If \( \alpha, \beta \) are the roots of the equation \( x^2 + bx + c = 0 \) satisfying the conditions \( \alpha+\beta=5 \) and \( \alpha^3+\beta^3=60 \), then \( 3c+2 = \)

For any two non-zero complex numbers \(z_1\) and \(z_2\), if \(|z_1 + z_2|^2 = |z_1|^2 + |z_2|^2\), then

If \(1, \omega, \omega^2\) are the cube roots of unity, then \( \left(1\left(2+\frac{1}{\omega}\right)\left(2+\frac{1}{\omega^2}\right) + 2\left(3+\frac{1}{\omega}\right)\left(3+\frac{1}{\omega^2}\right) + 3\left(4+\frac{1}{\omega}\right)\left(4+\frac{1}{\omega^2}\right) + \dots + 10 \text{ terms\right) = \)}

The range of the real valued function \( f(x) = \cos^{-1 \left( \dfrac{3}{\sqrt{9x^2 - 12x + 22}} \right) \) is}

If \( t_n = \dfrac{1}{n(n+2)} \), \( n \in \mathbb{N} \), then which one of the following is true?
Assertion (A): \[ t_1 + t_2 + \cdots + t_{2003} = \dfrac{2003}{3005} \]
Reason (R): \[ t_n = \dfrac{1}{n(n+2)} = \dfrac{1}{2} \left( \dfrac{1}{n} - \dfrac{1}{n+2} \right) \]