Mathematics Tes...

What is i¹⁰⁰⁰ + i¹⁰⁰¹ + i¹⁰⁰² + i¹⁰⁰³ equal to (where i = $\sqrt{-1}$ )?

If x = 1 - y + y² - y³ + .... up to infinite terms, where |y| < 1, then which one of the following is correct?

A survey of 850 students in a University yields that 680 students like music and 215 like dance. What is the least number of students who like both music and dance?

In a triangle ABC if a = 2, b = 3 and sin A = 2/3, then what is angle B equal to? 

Suppose cos A is given. If only one value of cos (A/2) is possible, then A must be

The maximum value of sin $\left(x+\frac{\mathrm{\pi }}{5}\right)$ + cos $\left(x+\frac{\mathrm{\pi }}{5}\right)$ , where x$\in$ $\left(0,\frac{\mathrm{\pi }}{2}\right)$ is attainned at

The equation of the line, when the portion of it intercepted between the axes is divided by the point (2, 3) in the ratio of 3 : 2, is 

In the expansion of (1 + x)⁴³ coefficients of (2r + 1)^th  and (r + 2⁾th terms are equal, then what is the value of r (r ≠ 1) ? 

If $A\left[\begin{array}{cc}1& 2\\ 2& 3\end{array}\right]$ and A² - kA + I₂ = o, where I₂ : is the 2 × 2 identity matrix, then what is the value of k?

What is the area of the region bounded by the parabolas y2 = 6 (x - 1) and y2 = 3x?