In how many number of ways can 10 students be divided into three teams, one containing four students and the other three?

• 400

• 700

• 1050

• 2100

If R be a relation defined as aRb iff $\left|\mathrm{a} - \mathrm{b}\right|$ > 0, then the relation is

• reflexive

• symmetric

• transitive

• symmetric and transitive

A manufacturer of cotter pins knows that 5% of his product is defective. He sells pins in boxes of 100 and guarantees that not more than one pin will be defective in a box. In order to find the probability that a box will fail to meet the guaranteed quality, the probability distribution one has to employ is

• binomial

• poisson

• normal

• exponential

Mean and standard deviation from the following observations of marks of 5 students of a tutorial group (marks out of 25)

8,12,13,15,22 are

• 14, 4.604

• 15, 4.604

• 14, 5.604

• None of these

Probability of getting positive integral roots of the equation x - n = 0 for the integer n, $1 \le \mathrm{n} \le 40$ is

• $\frac{1}{5}$

• $\frac{1}{10}$

• $\frac{3}{20}$

• $\frac{1}{20}$

The number of real roots of the equation ${\mathrm{x}}^4 + \sqrt{{\mathrm{x}}^4 + 20} = 22$ is

• 4

• 2

• 0

• 1

Let $\mathrm{\alpha }, \mathrm{\beta }$ be the roots of the equation x² - ax + b = 0 and ${\mathrm{A}}_{\mathrm{n}} = {\mathrm{\alpha }}^{\mathrm{n}} + {\mathrm{\beta }}^{\mathrm{n}}$. Then, A_{n + 1} - aA_n + bA_{n - 1} is equal to

• - a

• b

• 0

• a - b

18.

If the sides of a right angle triangle form an AP, the 'sin' of the acute angles are

• $\left(\frac{3}{5}, \frac{4}{5}\right)$

• $\left(\sqrt{3}, \frac{1}{\sqrt{3}}\right)$

• $\left(\sqrt{\frac{\sqrt{5} - 1}{2}}, \sqrt{\frac{\sqrt{5} - 1}{2}}\right)$

• $\left(\sqrt{\frac{\sqrt{3} - 1}{2}}, \sqrt{\frac{\sqrt{3} - 1}{2}}\right)$

The simplified expression of sin(tan^-1(x)) for any real number x is given by

In a triangle ABC, the sides b and c are the roots of the equation x² - 61x + 820 = 0 and A = ${\tan }^{-1}\left(\frac{4}{3}\right)$, then a² is equal to

• 1098

• 1096

• 1097

• 1095