If F is function such that F (0) = 2, F(1) = 3, F(x + 2)= 2F(x) - F(x + 1) for x > 0, then F(5) is equal to

• - 7

• - 3

• 17

• 13

Let S be a set containing n elements. Then, number of binary operations on S is

• nⁿ

• $2^{{\mathrm{n}}^2}$

• ${\mathrm{n}}^{{\mathrm{n}}^2}$

• n²

The numerically greatest term in the expansion of (3 - 5x)¹¹ when x = $\frac{1}{5}$, is

• $55 \times 3^9$

• $55 \times 3^6$

• $45 \times 3^9$

• $45 \times 3^6$

The number of solutions of the equation sin(e^x) = 5^x + 5^-x,  is

• 0

• 1

• 2

• infinitely many

If a^x = b^y = c^z = d^u and a, b, c, d are in GP, then x, y, z, u are in

• AP

• GP

• HP

• None of these

6.

If z satisfies the equation $\left|\mathrm{z}\right|$ - z = 1 + 2i, then z is equal to

• $\frac{3}{2} + 2\mathrm{i}$

• $\frac{3}{2} - 2\mathrm{i}$

• $2 - \frac{3}{2}\mathrm{i}$

• $2 + \frac{3}{2}\mathrm{i}$

If $\mathrm{z} = \frac{1 - \mathrm{i}\sqrt{3}}{1 + \mathrm{i}\sqrt{3}}$, then arg (z) is

• 60°

• 120°

• 240°

• 300°

If f (x) = $\sqrt{{\log }_{10}\left({\mathrm{x}}^2\right)}$. The set of all values of x for which f(x) is real, is

• [- 1, 1]

• $[1, \infty )$

• $(- \infty , - 1]$

• $(- \infty , - 1] \cup [1, \infty )$

For what values of m can the expression 2x² + mxy + 3y² - 5y - 2 be expressed as the product of two linear factors?

• 0

• $\pm 1$

• $\pm 7$

• 49

If $3\sin \left(\mathrm{\theta }\right) + 5\cos \left(\mathrm{\theta }\right)$, then the value of $5\sin \left(\mathrm{\theta }\right) - 3\cos \left(\mathrm{\theta }\right)$ is equal to

• 5

• 3

• 4

• None of these