If the complex numbers z₁, z₂, z₃ and z₄ denote the vertices of a square taken in order. If z₁ = 3 + 4i and z₃ = 5 + 6i, then the other two vertices z₂ and z₄ are respectively

• 5 + 4i, 5 + 6i

• 5 + 4i, 3 + 6i

• 5 + 6i, 3 + 5i

• 3 + 6i, 5 + 3i

The 100th term of the sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, ... , is

• 12

• 13

• 14

• 15

Let S_n denotes the sum of first n terms of an AP.If S₄ = - 34, S₅ = - 60 and S₆ = - 93, then the common difference and the first term of the AP are respectively

• - 7, 2

• 7, - 4

• 7, - 2

• - 7, - 2

4.

An AP has the property that the sum of first ten terms is half the sum of next ten terms. If the second term is 13, then the common difference is

• 3

• 2

• 5

• 4

If $8!\left(\frac{1}{3!} + \frac{5}{4!}\right) = {}_9\mathrm{P}_{\mathrm{r}}$, then the value of r is

• 4

• 5

• 3

• 2

The domain of the function f(x) = $\frac{{\log }_2\left(\mathrm{x} +\hspace{0.17em}3\right)}{{\mathrm{x}}^2 + 3\mathrm{x} +\hspace{0.17em}2}$ is

• R - {- 1, - 2}

• R - {- 1, - 2, 0}

• (- 3, - 1) ∪ (- 1, $\infty$)

• (- 3, $\infty$) - {- 1, - 2}

If * is defined by a * b = a - b² and $\oplus$ is defined by a $\oplus$ b = a² + b, where a and b are integers, then (3 $\oplus$ 4) * 5 is equal to

• 164

• 38

• - 12

• - 28

If ${\cos }^{-1}\left(\frac{1 - {\mathrm{x}}^2}{1 + {\mathrm{x}}^2}\right) + {\cos }^{-1}\left(\frac{1 - {\mathrm{y}}^2}{1 + {\mathrm{y}}^2}\right) = \frac{\mathrm{\pi }}{2}$, where xy < 1, then

• x - y - xy = 1

• x - y + xy = 1

• x + y - xy = 1

• x + y + xy = 1

If $\tan \left[3{\tan }^{-1}\left(\frac{1}{5}\right), - \frac{\mathrm{\pi }}{4}\right]$ is equal to

• $- \frac{13}{46}$

• $- \frac{11}{46}$

• $- \frac{7}{46}$

• $- \frac{9}{46}$

If ${\tan }^{-1}\left(- \mathrm{x}\right) + {\cos }^{-1}\left(\frac{- 1}{2}\right) = \frac{\mathrm{\pi }}{2}$, then the value of x is

• $\sqrt{3}$

• $\frac{- 1}{\sqrt{3}}$

• $\frac{1}{\sqrt{3}}$

• $- \sqrt{3}$